diff --git a/.gitignore b/.gitignore
index dd4626d19..214a404be 100644
--- a/.gitignore
+++ b/.gitignore
@@ -3,6 +3,7 @@ job.json
 out.txt
 .DS_Store
 tests/data/jobs/
+main.html
 
 # Byte-compiled / optimized / DLL files
 __pycache__/
diff --git a/pdm.lock b/pdm.lock
index 31ade7608..e7b2812ba 100644
--- a/pdm.lock
+++ b/pdm.lock
@@ -2,11 +2,11 @@
 # It is not intended for manual editing.
 
 [metadata]
-groups = ["default", "dev", "doc", "testing"]
+groups = ["default", "dev", "doc"]
 cross_platform = true
 static_urls = false
 lock_version = "4.3"
-content_hash = "sha256:63a2dd30c4441e4ea6b82b05c2eb01db05d5ea0387146726cfb6380e6f2c8cef"
+content_hash = "sha256:72518b3823d94e807ca39069b2c51bc3606d008f841f4d67567909dec6dbc103"
 
 [[package]]
 name = "amazon-braket-default-simulator"
@@ -75,16 +75,17 @@ files = [
 
 [[package]]
 name = "anyio"
-version = "3.6.2"
-requires_python = ">=3.6.2"
+version = "4.0.0"
+requires_python = ">=3.8"
 summary = "High level compatibility layer for multiple asynchronous event loop implementations"
 dependencies = [
+    "exceptiongroup>=1.0.2; python_version < \"3.11\"",
     "idna>=2.8",
     "sniffio>=1.1",
 ]
 files = [
-    {file = "anyio-3.6.2-py3-none-any.whl", hash = "sha256:fbbe32bd270d2a2ef3ed1c5d45041250284e31fc0a4df4a5a6071842051a51e3"},
-    {file = "anyio-3.6.2.tar.gz", hash = "sha256:25ea0d673ae30af41a0c442f81cf3b38c7e79fdc7b60335a4c14e05eb0947421"},
+    {file = "anyio-4.0.0-py3-none-any.whl", hash = "sha256:cfdb2b588b9fc25ede96d8db56ed50848b0b649dca3dd1df0b11f683bb9e0b5f"},
+    {file = "anyio-4.0.0.tar.gz", hash = "sha256:f7ed51751b2c2add651e5747c891b47e26d2a21be5d32d9311dfe9692f3e5d7a"},
 ]
 
 [[package]]
@@ -98,15 +99,15 @@ files = [
 
 [[package]]
 name = "argon2-cffi"
-version = "21.3.0"
-requires_python = ">=3.6"
-summary = "The secure Argon2 password hashing algorithm."
+version = "23.1.0"
+requires_python = ">=3.7"
+summary = "Argon2 for Python"
 dependencies = [
     "argon2-cffi-bindings",
 ]
 files = [
-    {file = "argon2-cffi-21.3.0.tar.gz", hash = "sha256:d384164d944190a7dd7ef22c6aa3ff197da12962bd04b17f64d4e93d934dba5b"},
-    {file = "argon2_cffi-21.3.0-py3-none-any.whl", hash = "sha256:8c976986f2c5c0e5000919e6de187906cfd81fb1c72bf9d88c01177e77da7f80"},
+    {file = "argon2_cffi-23.1.0-py3-none-any.whl", hash = "sha256:c670642b78ba29641818ab2e68bd4e6a78ba53b7eff7b4c3815ae16abf91c7ea"},
+    {file = "argon2_cffi-23.1.0.tar.gz", hash = "sha256:879c3e79a2729ce768ebb7d36d4609e3a78a4ca2ec3a9f12286ca057e3d0db08"},
 ]
 
 [[package]]
@@ -156,24 +157,37 @@ files = [
 
 [[package]]
 name = "asttokens"
-version = "2.2.1"
+version = "2.3.0"
 summary = "Annotate AST trees with source code positions"
 dependencies = [
-    "six",
+    "six>=1.12.0",
 ]
 files = [
-    {file = "asttokens-2.2.1-py2.py3-none-any.whl", hash = "sha256:6b0ac9e93fb0335014d382b8fa9b3afa7df546984258005da0b9e7095b3deb1c"},
-    {file = "asttokens-2.2.1.tar.gz", hash = "sha256:4622110b2a6f30b77e1473affaa97e711bc2f07d3f10848420ff1898edbe94f3"},
+    {file = "asttokens-2.3.0-py2.py3-none-any.whl", hash = "sha256:bef1a51bc256d349e9f94e7e40e44b705ed1162f55294220dd561d24583d9877"},
+    {file = "asttokens-2.3.0.tar.gz", hash = "sha256:2552a88626aaa7f0f299f871479fc755bd4e7c11e89078965e928fb7bb9a6afe"},
+]
+
+[[package]]
+name = "async-lru"
+version = "2.0.4"
+requires_python = ">=3.8"
+summary = "Simple LRU cache for asyncio"
+dependencies = [
+    "typing-extensions>=4.0.0; python_version < \"3.11\"",
+]
+files = [
+    {file = "async-lru-2.0.4.tar.gz", hash = "sha256:b8a59a5df60805ff63220b2a0c5b5393da5521b113cd5465a44eb037d81a5627"},
+    {file = "async_lru-2.0.4-py3-none-any.whl", hash = "sha256:ff02944ce3c288c5be660c42dbcca0742b32c3b279d6dceda655190240b99224"},
 ]
 
 [[package]]
 name = "attrs"
-version = "21.4.0"
-requires_python = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+version = "23.1.0"
+requires_python = ">=3.7"
 summary = "Classes Without Boilerplate"
 files = [
-    {file = "attrs-21.4.0-py2.py3-none-any.whl", hash = "sha256:2d27e3784d7a565d36ab851fe94887c5eccd6a463168875832a1be79c82828b4"},
-    {file = "attrs-21.4.0.tar.gz", hash = "sha256:626ba8234211db98e869df76230a137c4c40a12d72445c45d5f5b716f076e2fd"},
+    {file = "attrs-23.1.0-py3-none-any.whl", hash = "sha256:1f28b4522cdc2fb4256ac1a020c78acf9cba2c6b461ccd2c126f3aa8e8335d04"},
+    {file = "attrs-23.1.0.tar.gz", hash = "sha256:6279836d581513a26f1bf235f9acd333bc9115683f14f7e8fae46c98fc50e015"},
 ]
 
 [[package]]
@@ -283,22 +297,22 @@ files = [
 
 [[package]]
 name = "boto3"
-version = "1.26.122"
+version = "1.28.40"
 requires_python = ">= 3.7"
 summary = "The AWS SDK for Python"
 dependencies = [
-    "botocore<1.30.0,>=1.29.122",
+    "botocore<1.32.0,>=1.31.40",
     "jmespath<2.0.0,>=0.7.1",
     "s3transfer<0.7.0,>=0.6.0",
 ]
 files = [
-    {file = "boto3-1.26.122-py3-none-any.whl", hash = "sha256:4d575c180312bec6108852bae12e6396b9d1bb404154d652c57ee849c62fbb83"},
-    {file = "boto3-1.26.122.tar.gz", hash = "sha256:38ca632be379963f2a2749b5f63a81fe1679913b954914f470ad282c77674bbc"},
+    {file = "boto3-1.28.40-py3-none-any.whl", hash = "sha256:bd7c760afb195eaeaab907dc6b2c21fa64ddbba3fed4a869e80d820ddbd6cc70"},
+    {file = "boto3-1.28.40.tar.gz", hash = "sha256:6ff9a5b815e106656596064d51c9b6ba97a307807baa5f89634384b7d3f7ecc6"},
 ]
 
 [[package]]
 name = "botocore"
-version = "1.29.122"
+version = "1.31.40"
 requires_python = ">= 3.7"
 summary = "Low-level, data-driven core of boto 3."
 dependencies = [
@@ -307,18 +321,18 @@ dependencies = [
     "urllib3<1.27,>=1.25.4",
 ]
 files = [
-    {file = "botocore-1.29.122-py3-none-any.whl", hash = "sha256:c3b41078d235761b9c5dc22f534a76952622ef96787b96bbd10242ec4d73f2a5"},
-    {file = "botocore-1.29.122.tar.gz", hash = "sha256:9e4984a9e9777c6b949aa1e98323fa35480d9f99d447af7e179ae611f7ed5af9"},
+    {file = "botocore-1.31.40-py3-none-any.whl", hash = "sha256:df766969f0d9ef9eda1a9c9946e0e173c10199f37a9e4c92861f11ddb5c9e702"},
+    {file = "botocore-1.31.40.tar.gz", hash = "sha256:ce22a82ef8674f49691477d09558992cc87e7331f65c6a5b0da897ab192240ca"},
 ]
 
 [[package]]
 name = "certifi"
-version = "2022.12.7"
+version = "2023.7.22"
 requires_python = ">=3.6"
 summary = "Python package for providing Mozilla's CA Bundle."
 files = [
-    {file = "certifi-2022.12.7-py3-none-any.whl", hash = "sha256:4ad3232f5e926d6718ec31cfc1fcadfde020920e278684144551c91769c7bc18"},
-    {file = "certifi-2022.12.7.tar.gz", hash = "sha256:35824b4c3a97115964b408844d64aa14db1cc518f6562e8d7261699d1350a9e3"},
+    {file = "certifi-2023.7.22-py3-none-any.whl", hash = "sha256:92d6037539857d8206b8f6ae472e8b77db8058fec5937a1ef3f54304089edbb9"},
+    {file = "certifi-2023.7.22.tar.gz", hash = "sha256:539cc1d13202e33ca466e88b2807e29f4c13049d6d87031a3c110744495cb082"},
 ]
 
 [[package]]
@@ -355,65 +369,65 @@ files = [
 
 [[package]]
 name = "cfgv"
-version = "3.3.1"
-requires_python = ">=3.6.1"
+version = "3.4.0"
+requires_python = ">=3.8"
 summary = "Validate configuration and produce human readable error messages."
 files = [
-    {file = "cfgv-3.3.1-py2.py3-none-any.whl", hash = "sha256:c6a0883f3917a037485059700b9e75da2464e6c27051014ad85ba6aaa5884426"},
-    {file = "cfgv-3.3.1.tar.gz", hash = "sha256:f5a830efb9ce7a445376bb66ec94c638a9787422f96264c98edc6bdeed8ab736"},
+    {file = "cfgv-3.4.0-py2.py3-none-any.whl", hash = "sha256:b7265b1f29fd3316bfcd2b330d63d024f2bfd8bcb8b0272f8e19a504856c48f9"},
+    {file = "cfgv-3.4.0.tar.gz", hash = "sha256:e52591d4c5f5dead8e0f673fb16db7949d2cfb3f7da4582893288f0ded8fe560"},
 ]
 
 [[package]]
 name = "charset-normalizer"
-version = "3.1.0"
+version = "3.2.0"
 requires_python = ">=3.7.0"
 summary = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 files = [
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 dependencies = [
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 requires_python = ">=3.6"
 summary = "Jupyter Python Comm implementation, for usage in ipykernel, xeus-python etc."
 dependencies = [
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 [[package]]
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 [[package]]
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 [[package]]
@@ -737,15 +764,15 @@ files = [
 
 [[package]]
 name = "importlib-metadata"
-version = "6.6.0"
-requires_python = ">=3.7"
+version = "6.8.0"
+requires_python = ">=3.8"
 summary = "Read metadata from Python packages"
 dependencies = [
     "zipp>=0.5",
 ]
 files = [
-    {file = "importlib_metadata-6.6.0-py3-none-any.whl", hash = "sha256:43dd286a2cd8995d5eaef7fee2066340423b818ed3fd70adf0bad5f1fac53fed"},
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+    {file = "importlib_metadata-6.8.0-py3-none-any.whl", hash = "sha256:3ebb78df84a805d7698245025b975d9d67053cd94c79245ba4b3eb694abe68bb"},
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 [[package]]
@@ -819,19 +846,19 @@ files = [
 
 [[package]]
 name = "ipywidgets"
-version = "8.0.6"
+version = "8.1.0"
 requires_python = ">=3.7"
 summary = "Jupyter interactive widgets"
 dependencies = [
-    "ipykernel>=4.5.1",
+    "comm>=0.1.3",
     "ipython>=6.1.0",
     "jupyterlab-widgets~=3.0.7",
     "traitlets>=4.3.1",
     "widgetsnbextension~=4.0.7",
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 files = [
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+    {file = "ipywidgets-8.1.0-py3-none-any.whl", hash = "sha256:6c8396cc7b8c95dfb4e9ab0054f48c002f045e7e5d7ae523f559d64e525a98ab"},
+    {file = "ipywidgets-8.1.0.tar.gz", hash = "sha256:ce97dd90525b3066fd00094690964e7eac14cf9b7745d35565b5eeac20cce687"},
 ]
 
 [[package]]
@@ -849,28 +876,28 @@ files = [
 
 [[package]]
 name = "jaraco-classes"
-version = "3.2.3"
-requires_python = ">=3.7"
+version = "3.3.0"
+requires_python = ">=3.8"
 summary = "Utility functions for Python class constructs"
 dependencies = [
     "more-itertools",
 ]
 files = [
-    {file = "jaraco.classes-3.2.3-py3-none-any.whl", hash = "sha256:2353de3288bc6b82120752201c6b1c1a14b058267fa424ed5ce5984e3b922158"},
-    {file = "jaraco.classes-3.2.3.tar.gz", hash = "sha256:89559fa5c1d3c34eff6f631ad80bb21f378dbcbb35dd161fd2c6b93f5be2f98a"},
+    {file = "jaraco.classes-3.3.0-py3-none-any.whl", hash = "sha256:10afa92b6743f25c0cf5f37c6bb6e18e2c5bb84a16527ccfc0040ea377e7aaeb"},
+    {file = "jaraco.classes-3.3.0.tar.gz", hash = "sha256:c063dd08e89217cee02c8d5e5ec560f2c8ce6cdc2fcdc2e68f7b2e5547ed3621"},
 ]
 
 [[package]]
 name = "jedi"
-version = "0.18.2"
+version = "0.19.0"
 requires_python = ">=3.6"
 summary = "An autocompletion tool for Python that can be used for text editors."
 dependencies = [
-    "parso<0.9.0,>=0.8.0",
+    "parso<0.9.0,>=0.8.3",
 ]
 files = [
-    {file = "jedi-0.18.2-py2.py3-none-any.whl", hash = "sha256:203c1fd9d969ab8f2119ec0a3342e0b49910045abe6af0a3ae83a5764d54639e"},
-    {file = "jedi-0.18.2.tar.gz", hash = "sha256:bae794c30d07f6d910d32a7048af09b5a39ed740918da923c6b780790ebac612"},
+    {file = "jedi-0.19.0-py2.py3-none-any.whl", hash = "sha256:cb8ce23fbccff0025e9386b5cf85e892f94c9b822378f8da49970471335ac64e"},
+    {file = "jedi-0.19.0.tar.gz", hash = "sha256:bcf9894f1753969cbac8022a8c2eaee06bfa3724e4192470aaffe7eb6272b0c4"},
 ]
 
 [[package]]
@@ -914,50 +941,74 @@ files = [
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 ]
 
+[[package]]
+name = "json5"
+version = "0.9.14"
+summary = "A Python implementation of the JSON5 data format."
+files = [
+    {file = "json5-0.9.14-py2.py3-none-any.whl", hash = "sha256:740c7f1b9e584a468dbb2939d8d458db3427f2c93ae2139d05f47e453eae964f"},
+    {file = "json5-0.9.14.tar.gz", hash = "sha256:9ed66c3a6ca3510a976a9ef9b8c0787de24802724ab1860bc0153c7fdd589b02"},
+]
+
 [[package]]
 name = "jsonpointer"
-version = "2.3"
-requires_python = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+version = "2.4"
+requires_python = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*, !=3.6.*"
 summary = "Identify specific nodes in a JSON document (RFC 6901) "
 files = [
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+    {file = "jsonpointer-2.4-py2.py3-none-any.whl", hash = "sha256:15d51bba20eea3165644553647711d150376234112651b4f1811022aecad7d7a"},
+    {file = "jsonpointer-2.4.tar.gz", hash = "sha256:585cee82b70211fa9e6043b7bb89db6e1aa49524340dde8ad6b63206ea689d88"},
 ]
 
 [[package]]
 name = "jsonschema"
-version = "4.17.3"
-requires_python = ">=3.7"
+version = "4.19.0"
+requires_python = ">=3.8"
 summary = "An implementation of JSON Schema validation for Python"
 dependencies = [
-    "attrs>=17.4.0",
-    "pyrsistent!=0.17.0,!=0.17.1,!=0.17.2,>=0.14.0",
+    "attrs>=22.2.0",
+    "jsonschema-specifications>=2023.03.6",
+    "referencing>=0.28.4",
+    "rpds-py>=0.7.1",
+]
+files = [
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+    {file = "jsonschema-4.19.0.tar.gz", hash = "sha256:6e1e7569ac13be8139b2dd2c21a55d350066ee3f80df06c608b398cdc6f30e8f"},
+]
+
+[[package]]
+name = "jsonschema-specifications"
+version = "2023.7.1"
+requires_python = ">=3.8"
+summary = "The JSON Schema meta-schemas and vocabularies, exposed as a Registry"
+dependencies = [
+    "referencing>=0.28.0",
 ]
 files = [
-    {file = "jsonschema-4.17.3-py3-none-any.whl", hash = "sha256:a870ad254da1a8ca84b6a2905cac29d265f805acc57af304784962a2aa6508f6"},
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+    {file = "jsonschema_specifications-2023.7.1-py3-none-any.whl", hash = "sha256:05adf340b659828a004220a9613be00fa3f223f2b82002e273dee62fd50524b1"},
+    {file = "jsonschema_specifications-2023.7.1.tar.gz", hash = "sha256:c91a50404e88a1f6ba40636778e2ee08f6e24c5613fe4c53ac24578a5a7f72bb"},
 ]
 
 [[package]]
 name = "jsonschema"
-version = "4.17.3"
+version = "4.19.0"
 extras = ["format-nongpl"]
-requires_python = ">=3.7"
+requires_python = ">=3.8"
 summary = "An implementation of JSON Schema validation for Python"
 dependencies = [
     "fqdn",
     "idna",
     "isoduration",
     "jsonpointer>1.13",
-    "jsonschema==4.17.3",
+    "jsonschema==4.19.0",
     "rfc3339-validator",
     "rfc3986-validator>0.1.0",
     "uri-template",
     "webcolors>=1.11",
 ]
 files = [
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+    {file = "jsonschema-4.19.0-py3-none-any.whl", hash = "sha256:043dc26a3845ff09d20e4420d6012a9c91c9aa8999fa184e7efcfeccb41e32cb"},
+    {file = "jsonschema-4.19.0.tar.gz", hash = "sha256:6e1e7569ac13be8139b2dd2c21a55d350066ee3f80df06c608b398cdc6f30e8f"},
 ]
 
 [[package]]
@@ -1005,7 +1056,7 @@ files = [
 
 [[package]]
 name = "jupyter-client"
-version = "8.2.0"
+version = "8.3.1"
 requires_python = ">=3.8"
 summary = "Jupyter protocol implementation and client libraries"
 dependencies = [
@@ -1016,8 +1067,8 @@ dependencies = [
     "traitlets>=5.3",
 ]
 files = [
-    {file = "jupyter_client-8.2.0-py3-none-any.whl", hash = "sha256:b18219aa695d39e2ad570533e0d71fb7881d35a873051054a84ee2a17c4b7389"},
-    {file = "jupyter_client-8.2.0.tar.gz", hash = "sha256:9fe233834edd0e6c0aa5f05ca2ab4bdea1842bfd2d8a932878212fc5301ddaf0"},
+    {file = "jupyter_client-8.3.1-py3-none-any.whl", hash = "sha256:5eb9f55eb0650e81de6b7e34308d8b92d04fe4ec41cd8193a913979e33d8e1a5"},
+    {file = "jupyter_client-8.3.1.tar.gz", hash = "sha256:60294b2d5b869356c893f57b1a877ea6510d60d45cf4b38057f1672d85699ac9"},
 ]
 
 [[package]]
@@ -1042,7 +1093,7 @@ files = [
 
 [[package]]
 name = "jupyter-core"
-version = "5.3.0"
+version = "5.3.1"
 requires_python = ">=3.8"
 summary = "Jupyter core package. A base package on which Jupyter projects rely."
 dependencies = [
@@ -1051,31 +1102,45 @@ dependencies = [
     "traitlets>=5.3",
 ]
 files = [
-    {file = "jupyter_core-5.3.0-py3-none-any.whl", hash = "sha256:d4201af84559bc8c70cead287e1ab94aeef3c512848dde077b7684b54d67730d"},
-    {file = "jupyter_core-5.3.0.tar.gz", hash = "sha256:6db75be0c83edbf1b7c9f91ec266a9a24ef945da630f3120e1a0046dc13713fc"},
+    {file = "jupyter_core-5.3.1-py3-none-any.whl", hash = "sha256:ae9036db959a71ec1cac33081eeb040a79e681f08ab68b0883e9a676c7a90dce"},
+    {file = "jupyter_core-5.3.1.tar.gz", hash = "sha256:5ba5c7938a7f97a6b0481463f7ff0dbac7c15ba48cf46fa4035ca6e838aa1aba"},
 ]
 
 [[package]]
 name = "jupyter-events"
-version = "0.6.3"
-requires_python = ">=3.7"
+version = "0.7.0"
+requires_python = ">=3.8"
 summary = "Jupyter Event System library"
 dependencies = [
-    "jsonschema[format-nongpl]>=3.2.0",
+    "jsonschema[format-nongpl]>=4.18.0",
     "python-json-logger>=2.0.4",
     "pyyaml>=5.3",
+    "referencing",
     "rfc3339-validator",
     "rfc3986-validator>=0.1.1",
     "traitlets>=5.3",
 ]
 files = [
-    {file = "jupyter_events-0.6.3-py3-none-any.whl", hash = "sha256:57a2749f87ba387cd1bfd9b22a0875b889237dbf2edc2121ebb22bde47036c17"},
-    {file = "jupyter_events-0.6.3.tar.gz", hash = "sha256:9a6e9995f75d1b7146b436ea24d696ce3a35bfa8bfe45e0c33c334c79464d0b3"},
+    {file = "jupyter_events-0.7.0-py3-none-any.whl", hash = "sha256:4753da434c13a37c3f3c89b500afa0c0a6241633441421f6adafe2fb2e2b924e"},
+    {file = "jupyter_events-0.7.0.tar.gz", hash = "sha256:7be27f54b8388c03eefea123a4f79247c5b9381c49fb1cd48615ee191eb12615"},
+]
+
+[[package]]
+name = "jupyter-lsp"
+version = "2.2.0"
+requires_python = ">=3.8"
+summary = "Multi-Language Server WebSocket proxy for Jupyter Notebook/Lab server"
+dependencies = [
+    "jupyter-server>=1.1.2",
+]
+files = [
+    {file = "jupyter-lsp-2.2.0.tar.gz", hash = "sha256:8ebbcb533adb41e5d635eb8fe82956b0aafbf0fd443b6c4bfa906edeeb8635a1"},
+    {file = "jupyter_lsp-2.2.0-py3-none-any.whl", hash = "sha256:9e06b8b4f7dd50300b70dd1a78c0c3b0c3d8fa68e0f2d8a5d1fbab62072aca3f"},
 ]
 
 [[package]]
 name = "jupyter-server"
-version = "2.5.0"
+version = "2.7.3"
 requires_python = ">=3.8"
 summary = "The backend—i.e. core services, APIs, and REST endpoints—to Jupyter web applications."
 dependencies = [
@@ -1084,23 +1149,24 @@ dependencies = [
     "jinja2",
     "jupyter-client>=7.4.4",
     "jupyter-core!=5.0.*,>=4.12",
-    "jupyter-events>=0.4.0",
+    "jupyter-events>=0.6.0",
     "jupyter-server-terminals",
     "nbconvert>=6.4.4",
     "nbformat>=5.3.0",
+    "overrides",
     "packaging",
     "prometheus-client",
     "pywinpty; os_name == \"nt\"",
     "pyzmq>=24",
-    "send2trash",
+    "send2trash>=1.8.2",
     "terminado>=0.8.3",
     "tornado>=6.2.0",
     "traitlets>=5.6.0",
     "websocket-client",
 ]
 files = [
-    {file = "jupyter_server-2.5.0-py3-none-any.whl", hash = "sha256:e6bc1e9e96d7c55b9ce9699ff6cb9a910581fe7349e27c40389acb67632e24c0"},
-    {file = "jupyter_server-2.5.0.tar.gz", hash = "sha256:9fde612791f716fd34d610cd939704a9639643744751ba66e7ee8fdc9cead07e"},
+    {file = "jupyter_server-2.7.3-py3-none-any.whl", hash = "sha256:8e4b90380b59d7a1e31086c4692231f2a2ea4cb269f5516e60aba72ce8317fc9"},
+    {file = "jupyter_server-2.7.3.tar.gz", hash = "sha256:d4916c8581c4ebbc534cebdaa8eca2478d9f3bfdd88eae29fcab0120eac57649"},
 ]
 
 [[package]]
@@ -1117,6 +1183,30 @@ files = [
     {file = "jupyter_server_terminals-0.4.4.tar.gz", hash = "sha256:57ab779797c25a7ba68e97bcfb5d7740f2b5e8a83b5e8102b10438041a7eac5d"},
 ]
 
+[[package]]
+name = "jupyterlab"
+version = "4.0.5"
+requires_python = ">=3.8"
+summary = "JupyterLab computational environment"
+dependencies = [
+    "async-lru>=1.0.0",
+    "ipykernel",
+    "jinja2>=3.0.3",
+    "jupyter-core",
+    "jupyter-lsp>=2.0.0",
+    "jupyter-server<3,>=2.4.0",
+    "jupyterlab-server<3,>=2.19.0",
+    "notebook-shim>=0.2",
+    "packaging",
+    "tomli; python_version < \"3.11\"",
+    "tornado>=6.2.0",
+    "traitlets",
+]
+files = [
+    {file = "jupyterlab-4.0.5-py3-none-any.whl", hash = "sha256:13b3a326e7b95d72746fe20dbe80ee1e71165d6905e01ceaf1320eb809cb1b47"},
+    {file = "jupyterlab-4.0.5.tar.gz", hash = "sha256:de49deb75f9b9aec478ed04754cbefe9c5d22fd796a5783cdc65e212983d3611"},
+]
+
 [[package]]
 name = "jupyterlab-pygments"
 version = "0.2.2"
@@ -1127,14 +1217,33 @@ files = [
     {file = "jupyterlab_pygments-0.2.2.tar.gz", hash = "sha256:7405d7fde60819d905a9fa8ce89e4cd830e318cdad22a0030f7a901da705585d"},
 ]
 
+[[package]]
+name = "jupyterlab-server"
+version = "2.24.0"
+requires_python = ">=3.7"
+summary = "A set of server components for JupyterLab and JupyterLab like applications."
+dependencies = [
+    "babel>=2.10",
+    "jinja2>=3.0.3",
+    "json5>=0.9.0",
+    "jsonschema>=4.17.3",
+    "jupyter-server<3,>=1.21",
+    "packaging>=21.3",
+    "requests>=2.28",
+]
+files = [
+    {file = "jupyterlab_server-2.24.0-py3-none-any.whl", hash = "sha256:5f077e142bb8dc9b843d960f940c513581bceca3793a0d80f9c67d9522c4e876"},
+    {file = "jupyterlab_server-2.24.0.tar.gz", hash = "sha256:4e6f99e0a5579bbbc32e449c4dbb039561d4f1a7827d5733273ed56738f21f07"},
+]
+
 [[package]]
 name = "jupyterlab-widgets"
-version = "3.0.7"
+version = "3.0.8"
 requires_python = ">=3.7"
 summary = "Jupyter interactive widgets for JupyterLab"
 files = [
-    {file = "jupyterlab_widgets-3.0.7-py3-none-any.whl", hash = "sha256:c73f8370338ec19f1bec47254752d6505b03601cbd5a67e6a0b184532f73a459"},
-    {file = "jupyterlab_widgets-3.0.7.tar.gz", hash = "sha256:c3a50ed5bf528a0c7a869096503af54702f86dda1db469aee1c92dc0c01b43ca"},
+    {file = "jupyterlab_widgets-3.0.8-py3-none-any.whl", hash = "sha256:4715912d6ceab839c9db35953c764b3214ebbc9161c809f6e0510168845dfdf5"},
+    {file = "jupyterlab_widgets-3.0.8.tar.gz", hash = "sha256:d428ab97b8d87cc7c54cbf37644d6e0f0e662f23876e05fa460a73ec3257252a"},
 ]
 
 [[package]]
@@ -1156,8 +1265,8 @@ files = [
 
 [[package]]
 name = "keyring"
-version = "23.13.1"
-requires_python = ">=3.7"
+version = "24.2.0"
+requires_python = ">=3.8"
 summary = "Store and access your passwords safely."
 dependencies = [
     "SecretStorage>=3.2; sys_platform == \"linux\"",
@@ -1167,56 +1276,77 @@ dependencies = [
     "pywin32-ctypes>=0.2.0; sys_platform == \"win32\"",
 ]
 files = [
-    {file = "keyring-23.13.1-py3-none-any.whl", hash = "sha256:771ed2a91909389ed6148631de678f82ddc73737d85a927f382a8a1b157898cd"},
-    {file = "keyring-23.13.1.tar.gz", hash = "sha256:ba2e15a9b35e21908d0aaf4e0a47acc52d6ae33444df0da2b49d41a46ef6d678"},
+    {file = "keyring-24.2.0-py3-none-any.whl", hash = "sha256:4901caaf597bfd3bbd78c9a0c7c4c29fcd8310dab2cffefe749e916b6527acd6"},
+    {file = "keyring-24.2.0.tar.gz", hash = "sha256:ca0746a19ec421219f4d713f848fa297a661a8a8c1504867e55bfb5e09091509"},
 ]
 
 [[package]]
 name = "kiwisolver"
-version = "1.4.4"
+version = "1.4.5"
 requires_python = ">=3.7"
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 [[package]]
@@ -1330,15 +1460,15 @@ files = [
 
 [[package]]
 name = "mdit-py-plugins"
-version = "0.3.5"
-requires_python = ">=3.7"
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+requires_python = ">=3.8"
 summary = "Collection of plugins for markdown-it-py"
 dependencies = [
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+    "markdown-it-py<4.0.0,>=1.0.0",
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 files = [
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 [[package]]
@@ -1378,11 +1508,12 @@ files = [
 
 [[package]]
 name = "mistune"
-version = "2.0.5"
-summary = "A sane Markdown parser with useful plugins and renderers"
+version = "3.0.1"
+requires_python = ">=3.7"
+summary = "A sane and fast Markdown parser with useful plugins and renderers"
 files = [
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 [[package]]
@@ -1412,16 +1543,16 @@ files = [
 
 [[package]]
 name = "mkdocs-autorefs"
-version = "0.4.1"
-requires_python = ">=3.7"
+version = "0.5.0"
+requires_python = ">=3.8"
 summary = "Automatically link across pages in MkDocs."
 dependencies = [
     "Markdown>=3.3",
     "mkdocs>=1.1",
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 files = [
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 [[package]]
@@ -1537,16 +1668,16 @@ files = [
 
 [[package]]
 name = "mkdocstrings-python"
-version = "0.9.0"
-requires_python = ">=3.7"
+version = "1.6.1"
+requires_python = ">=3.8"
 summary = "A Python handler for mkdocstrings."
 dependencies = [
-    "griffe>=0.24",
+    "griffe>=0.35",
     "mkdocstrings>=0.20",
 ]
 files = [
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 [[package]]
@@ -1566,12 +1697,12 @@ files = [
 
 [[package]]
 name = "more-itertools"
-version = "9.1.0"
-requires_python = ">=3.7"
+version = "10.1.0"
+requires_python = ">=3.8"
 summary = "More routines for operating on iterables, beyond itertools"
 files = [
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 [[package]]
@@ -1662,82 +1793,53 @@ files = [
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-requires_python = ">=3.7"
-summary = "Jupyter Notebook as a Jupyter Server extension."
-dependencies = [
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-    "argon2-cffi",
-    "ipykernel",
-    "ipython-genutils",
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-    "nbconvert>=5",
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-    "prometheus-client",
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-]
-
 [[package]]
 name = "nbclient"
-version = "0.7.4"
-requires_python = ">=3.7.0"
+version = "0.8.0"
+requires_python = ">=3.8.0"
 summary = "A client library for executing notebooks. Formerly nbconvert's ExecutePreprocessor."
 dependencies = [
     "jupyter-client>=6.1.12",
     "jupyter-core!=5.0.*,>=4.12",
     "nbformat>=5.1",
-    "traitlets>=5.3",
+    "traitlets>=5.4",
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 files = [
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 ]
 
 [[package]]
 name = "nbconvert"
-version = "7.3.1"
-requires_python = ">=3.7"
+version = "7.8.0"
+requires_python = ">=3.8"
 summary = "Converting Jupyter Notebooks"
 dependencies = [
     "beautifulsoup4",
-    "bleach",
+    "bleach!=5.0.0",
     "defusedxml",
     "jinja2>=3.0",
     "jupyter-core>=4.7",
     "jupyterlab-pygments",
     "markupsafe>=2.0",
-    "mistune<3,>=2.0.3",
+    "mistune<4,>=2.0.3",
     "nbclient>=0.5.0",
-    "nbformat>=5.1",
+    "nbformat>=5.7",
     "packaging",
     "pandocfilters>=1.4.1",
     "pygments>=2.4.1",
     "tinycss2",
-    "traitlets>=5.0",
+    "traitlets>=5.1",
 ]
 files = [
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 ]
 
 [[package]]
 name = "nbformat"
-version = "5.8.0"
-requires_python = ">=3.7"
+version = "5.9.2"
+requires_python = ">=3.8"
 summary = "The Jupyter Notebook format"
 dependencies = [
     "fastjsonschema",
@@ -1746,18 +1848,18 @@ dependencies = [
     "traitlets>=5.1",
 ]
 files = [
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 ]
 
 [[package]]
 name = "nest-asyncio"
-version = "1.5.6"
+version = "1.5.7"
 requires_python = ">=3.5"
 summary = "Patch asyncio to allow nested event loops"
 files = [
-    {file = "nest_asyncio-1.5.6-py3-none-any.whl", hash = "sha256:b9a953fb40dceaa587d109609098db21900182b16440652454a146cffb06e8b8"},
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 ]
 
 [[package]]
@@ -1772,43 +1874,32 @@ files = [
 
 [[package]]
 name = "nodeenv"
-version = "1.7.0"
+version = "1.8.0"
 requires_python = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,!=3.6.*"
 summary = "Node.js virtual environment builder"
 dependencies = [
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 files = [
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 ]
 
 [[package]]
 name = "notebook"
-version = "6.5.4"
-requires_python = ">=3.7"
-summary = "A web-based notebook environment for interactive computing"
+version = "7.0.3"
+requires_python = ">=3.8"
+summary = "Jupyter Notebook - A web-based notebook environment for interactive computing"
 dependencies = [
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-    "argon2-cffi",
-    "ipykernel",
-    "ipython-genutils",
-    "jinja2",
-    "jupyter-client>=5.3.4",
-    "jupyter-core>=4.6.1",
-    "nbclassic>=0.4.7",
-    "nbconvert>=5",
-    "nbformat",
-    "nest-asyncio>=1.5",
-    "prometheus-client",
-    "pyzmq>=17",
-    "terminado>=0.8.3",
-    "tornado>=6.1",
-    "traitlets>=4.2.1",
+    "jupyter-server<3,>=2.4.0",
+    "jupyterlab-server<3,>=2.22.1",
+    "jupyterlab<5,>=4.0.2",
+    "notebook-shim<0.3,>=0.2",
+    "tornado>=6.2.0",
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 files = [
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+    {file = "notebook-7.0.3-py3-none-any.whl", hash = "sha256:786ab2e3287c068667adce3029b540dd18fc5d23f49181b4b4ee4f6b48a7ca81"},
+    {file = "notebook-7.0.3.tar.gz", hash = "sha256:07f3c5062fd0e6e69864437a0347abc485d991aae87a92c47d659699f571b729"},
 ]
 
 [[package]]
@@ -1915,6 +2006,16 @@ files = [
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 ]
 
+[[package]]
+name = "overrides"
+version = "7.4.0"
+requires_python = ">=3.6"
+summary = "A decorator to automatically detect mismatch when overriding a method."
+files = [
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+    {file = "overrides-7.4.0.tar.gz", hash = "sha256:9502a3cca51f4fac40b5feca985b6703a5c1f6ad815588a7ca9e285b9dca6757"},
+]
+
 [[package]]
 name = "packaging"
 version = "23.1"
@@ -1983,12 +2084,12 @@ files = [
 
 [[package]]
 name = "pathspec"
-version = "0.11.1"
+version = "0.11.2"
 requires_python = ">=3.7"
 summary = "Utility library for gitignore style pattern matching of file paths."
 files = [
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-    {file = "pathspec-0.11.1.tar.gz", hash = "sha256:2798de800fa92780e33acca925945e9a19a133b715067cf165b8866c15a31687"},
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 ]
 
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 [[package]]
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 requires_python = ">=3.7"
 summary = "A small Python package for determining appropriate platform-specific dirs, e.g. a \"user data dir\"."
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 [[package]]
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 [[package]]
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 [[package]]
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 summary = "Library for building powerful interactive command lines in Python"
 dependencies = [
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 [[package]]
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+    {file = "soupsieve-2.5.tar.gz", hash = "sha256:5663d5a7b3bfaeee0bc4372e7fc48f9cff4940b3eec54a6451cc5299f1097690"},
 ]
 
 [[package]]
@@ -2870,21 +3072,21 @@ files = [
 
 [[package]]
 name = "tornado"
-version = "6.3.1"
+version = "6.3.3"
 requires_python = ">= 3.8"
 summary = "Tornado is a Python web framework and asynchronous networking library, originally developed at FriendFeed."
 files = [
-    {file = "tornado-6.3.1-cp38-abi3-macosx_10_9_universal2.whl", hash = "sha256:db181eb3df8738613ff0a26f49e1b394aade05034b01200a63e9662f347d4415"},
-    {file = "tornado-6.3.1-cp38-abi3-macosx_10_9_x86_64.whl", hash = "sha256:b4e7b956f9b5e6f9feb643ea04f07e7c6b49301e03e0023eedb01fa8cf52f579"},
-    {file = "tornado-6.3.1-cp38-abi3-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:9661aa8bc0e9d83d757cd95b6f6d1ece8ca9fd1ccdd34db2de381e25bf818233"},
-    {file = "tornado-6.3.1-cp38-abi3-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:81c17e0cc396908a5e25dc8e9c5e4936e6dfd544c9290be48bd054c79bcad51e"},
-    {file = "tornado-6.3.1-cp38-abi3-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:a27a1cfa9997923f80bdd962b3aab048ac486ad8cfb2f237964f8ab7f7eb824b"},
-    {file = "tornado-6.3.1-cp38-abi3-musllinux_1_1_aarch64.whl", hash = "sha256:d7117f3c7ba5d05813b17a1f04efc8e108a1b811ccfddd9134cc68553c414864"},
-    {file = "tornado-6.3.1-cp38-abi3-musllinux_1_1_i686.whl", hash = "sha256:ffdce65a281fd708da5a9def3bfb8f364766847fa7ed806821a69094c9629e8a"},
-    {file = "tornado-6.3.1-cp38-abi3-musllinux_1_1_x86_64.whl", hash = "sha256:90f569a35a8ec19bde53aa596952071f445da678ec8596af763b9b9ce07605e6"},
-    {file = "tornado-6.3.1-cp38-abi3-win32.whl", hash = "sha256:3455133b9ff262fd0a75630af0a8ee13564f25fb4fd3d9ce239b8a7d3d027bf8"},
-    {file = "tornado-6.3.1-cp38-abi3-win_amd64.whl", hash = "sha256:1285f0691143f7ab97150831455d4db17a267b59649f7bd9700282cba3d5e771"},
-    {file = "tornado-6.3.1.tar.gz", hash = "sha256:5e2f49ad371595957c50e42dd7e5c14d64a6843a3cf27352b69c706d1b5918af"},
+    {file = "tornado-6.3.3-cp38-abi3-macosx_10_9_universal2.whl", hash = "sha256:502fba735c84450974fec147340016ad928d29f1e91f49be168c0a4c18181e1d"},
+    {file = "tornado-6.3.3-cp38-abi3-macosx_10_9_x86_64.whl", hash = "sha256:805d507b1f588320c26f7f097108eb4023bbaa984d63176d1652e184ba24270a"},
+    {file = "tornado-6.3.3-cp38-abi3-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:1bd19ca6c16882e4d37368e0152f99c099bad93e0950ce55e71daed74045908f"},
+    {file = "tornado-6.3.3-cp38-abi3-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:7ac51f42808cca9b3613f51ffe2a965c8525cb1b00b7b2d56828b8045354f76a"},
+    {file = "tornado-6.3.3-cp38-abi3-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:71a8db65160a3c55d61839b7302a9a400074c9c753040455494e2af74e2501f2"},
+    {file = "tornado-6.3.3-cp38-abi3-musllinux_1_1_aarch64.whl", hash = "sha256:ceb917a50cd35882b57600709dd5421a418c29ddc852da8bcdab1f0db33406b0"},
+    {file = "tornado-6.3.3-cp38-abi3-musllinux_1_1_i686.whl", hash = "sha256:7d01abc57ea0dbb51ddfed477dfe22719d376119844e33c661d873bf9c0e4a16"},
+    {file = "tornado-6.3.3-cp38-abi3-musllinux_1_1_x86_64.whl", hash = "sha256:9dc4444c0defcd3929d5c1eb5706cbe1b116e762ff3e0deca8b715d14bf6ec17"},
+    {file = "tornado-6.3.3-cp38-abi3-win32.whl", hash = "sha256:65ceca9500383fbdf33a98c0087cb975b2ef3bfb874cb35b8de8740cf7f41bd3"},
+    {file = "tornado-6.3.3-cp38-abi3-win_amd64.whl", hash = "sha256:22d3c2fa10b5793da13c807e6fc38ff49a4f6e1e3868b0a6f4164768bb8e20f5"},
+    {file = "tornado-6.3.3.tar.gz", hash = "sha256:e7d8db41c0181c80d76c982aacc442c0783a2c54d6400fe028954201a2e032fe"},
 ]
 
 [[package]]
@@ -2933,12 +3135,12 @@ files = [
 
 [[package]]
 name = "typing-extensions"
-version = "4.6.3"
+version = "4.7.1"
 requires_python = ">=3.7"
 summary = "Backported and Experimental Type Hints for Python 3.7+"
 files = [
-    {file = "typing_extensions-4.6.3-py3-none-any.whl", hash = "sha256:88a4153d8505aabbb4e13aacb7c486c2b4a33ca3b3f807914a9b4c844c471c26"},
-    {file = "typing_extensions-4.6.3.tar.gz", hash = "sha256:d91d5919357fe7f681a9f2b5b4cb2a5f1ef0a1e9f59c4d8ff0d3491e05c0ffd5"},
+    {file = "typing_extensions-4.7.1-py3-none-any.whl", hash = "sha256:440d5dd3af93b060174bf433bccd69b0babc3b15b1a8dca43789fd7f61514b36"},
+    {file = "typing_extensions-4.7.1.tar.gz", hash = "sha256:b75ddc264f0ba5615db7ba217daeb99701ad295353c45f9e95963337ceeeffb2"},
 ]
 
 [[package]]
@@ -2953,22 +3155,22 @@ files = [
 
 [[package]]
 name = "uri-template"
-version = "1.2.0"
-requires_python = ">=3.6"
+version = "1.3.0"
+requires_python = ">=3.7"
 summary = "RFC 6570 URI Template Processor"
 files = [
-    {file = "uri_template-1.2.0-py3-none-any.whl", hash = "sha256:f1699c77b73b925cf4937eae31ab282a86dc885c333f2e942513f08f691fc7db"},
-    {file = "uri_template-1.2.0.tar.gz", hash = "sha256:934e4d09d108b70eb8a24410af8615294d09d279ce0e7cbcdaef1bd21f932b06"},
+    {file = "uri-template-1.3.0.tar.gz", hash = "sha256:0e00f8eb65e18c7de20d595a14336e9f337ead580c70934141624b6d1ffdacc7"},
+    {file = "uri_template-1.3.0-py3-none-any.whl", hash = "sha256:a44a133ea12d44a0c0f06d7d42a52d71282e77e2f937d8abd5655b8d56fc1363"},
 ]
 
 [[package]]
 name = "urllib3"
-version = "1.26.15"
+version = "1.26.16"
 requires_python = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*"
 summary = "HTTP library with thread-safe connection pooling, file post, and more."
 files = [
-    {file = "urllib3-1.26.15-py2.py3-none-any.whl", hash = "sha256:aa751d169e23c7479ce47a0cb0da579e3ede798f994f5816a74e4f4500dcea42"},
-    {file = "urllib3-1.26.15.tar.gz", hash = "sha256:8a388717b9476f934a21484e8c8e61875ab60644d29b9b39e11e4b9dc1c6b305"},
+    {file = "urllib3-1.26.16-py2.py3-none-any.whl", hash = "sha256:8d36afa7616d8ab714608411b4a3b13e58f463aee519024578e062e141dce20f"},
+    {file = "urllib3-1.26.16.tar.gz", hash = "sha256:8f135f6502756bde6b2a9b28989df5fbe87c9970cecaa69041edcce7f0589b14"},
 ]
 
 [[package]]
@@ -2998,17 +3200,17 @@ files = [
 
 [[package]]
 name = "virtualenv"
-version = "20.23.0"
+version = "20.24.4"
 requires_python = ">=3.7"
 summary = "Virtual Python Environment builder"
 dependencies = [
-    "distlib<1,>=0.3.6",
-    "filelock<4,>=3.11",
-    "platformdirs<4,>=3.2",
+    "distlib<1,>=0.3.7",
+    "filelock<4,>=3.12.2",
+    "platformdirs<4,>=3.9.1",
 ]
 files = [
-    {file = "virtualenv-20.23.0-py3-none-any.whl", hash = "sha256:6abec7670e5802a528357fdc75b26b9f57d5d92f29c5462ba0fbe45feacc685e"},
-    {file = "virtualenv-20.23.0.tar.gz", hash = "sha256:a85caa554ced0c0afbd0d638e7e2d7b5f92d23478d05d17a76daeac8f279f924"},
+    {file = "virtualenv-20.24.4-py3-none-any.whl", hash = "sha256:29c70bb9b88510f6414ac3e55c8b413a1f96239b6b789ca123437d5e892190cb"},
+    {file = "virtualenv-20.24.4.tar.gz", hash = "sha256:772b05bfda7ed3b8ecd16021ca9716273ad9f4467c801f27e83ac73430246dca"},
 ]
 
 [[package]]
@@ -3069,22 +3271,22 @@ files = [
 
 [[package]]
 name = "websocket-client"
-version = "1.5.1"
-requires_python = ">=3.7"
+version = "1.6.2"
+requires_python = ">=3.8"
 summary = "WebSocket client for Python with low level API options"
 files = [
-    {file = "websocket-client-1.5.1.tar.gz", hash = "sha256:3f09e6d8230892547132177f575a4e3e73cfdf06526e20cc02aa1c3b47184d40"},
-    {file = "websocket_client-1.5.1-py3-none-any.whl", hash = "sha256:cdf5877568b7e83aa7cf2244ab56a3213de587bbe0ce9d8b9600fc77b455d89e"},
+    {file = "websocket-client-1.6.2.tar.gz", hash = "sha256:53e95c826bf800c4c465f50093a8c4ff091c7327023b10bfaff40cf1ef170eaa"},
+    {file = "websocket_client-1.6.2-py3-none-any.whl", hash = "sha256:ce54f419dfae71f4bdba69ebe65bf7f0a93fe71bc009ad3a010aacc3eebad537"},
 ]
 
 [[package]]
 name = "widgetsnbextension"
-version = "4.0.7"
+version = "4.0.8"
 requires_python = ">=3.7"
 summary = "Jupyter interactive widgets for Jupyter Notebook"
 files = [
-    {file = "widgetsnbextension-4.0.7-py3-none-any.whl", hash = "sha256:be3228a73bbab189a16be2d4a3cd89ecbd4e31948bfdc64edac17dcdee3cd99c"},
-    {file = "widgetsnbextension-4.0.7.tar.gz", hash = "sha256:ea67c17a7cd4ae358f8f46c3b304c40698bc0423732e3f273321ee141232c8be"},
+    {file = "widgetsnbextension-4.0.8-py3-none-any.whl", hash = "sha256:2e37f0ce9da11651056280c7efe96f2db052fe8fc269508e3724f5cbd6c93018"},
+    {file = "widgetsnbextension-4.0.8.tar.gz", hash = "sha256:9ec291ba87c2dfad42c3d5b6f68713fa18be1acd7476569516b2431682315c17"},
 ]
 
 [[package]]
@@ -3119,12 +3321,12 @@ files = [
 
 [[package]]
 name = "xyzservices"
-version = "2023.2.0"
-requires_python = ">=3.7"
+version = "2023.7.0"
+requires_python = ">=3.8"
 summary = "Source of XYZ tiles providers"
 files = [
-    {file = "xyzservices-2023.2.0-py3-none-any.whl", hash = "sha256:8d29c4d7c33b0ad63f54744ec90f68c5a65d7c0d7e498b624b7c076c1d926998"},
-    {file = "xyzservices-2023.2.0.tar.gz", hash = "sha256:3342bba410d7941290eed0e58a2e5aadb0f7b97863ec4283b283c406ee723a28"},
+    {file = "xyzservices-2023.7.0-py3-none-any.whl", hash = "sha256:88e9cbf22b31a2f9c1b242e2b18690f5c705f0e539c9bfd37a10399e1037731b"},
+    {file = "xyzservices-2023.7.0.tar.gz", hash = "sha256:0ec928742227d6f5d4367ea7b457fcfed943429f4de2949b5b02a82cdf5569d6"},
 ]
 
 [[package]]
@@ -3172,10 +3374,10 @@ files = [
 
 [[package]]
 name = "zipp"
-version = "3.15.0"
-requires_python = ">=3.7"
+version = "3.16.2"
+requires_python = ">=3.8"
 summary = "Backport of pathlib-compatible object wrapper for zip files"
 files = [
-    {file = "zipp-3.15.0-py3-none-any.whl", hash = "sha256:48904fc76a60e542af151aded95726c1a5c34ed43ab4134b597665c86d7ad556"},
-    {file = "zipp-3.15.0.tar.gz", hash = "sha256:112929ad649da941c23de50f356a2b5570c954b65150642bccdd66bf194d224b"},
+    {file = "zipp-3.16.2-py3-none-any.whl", hash = "sha256:679e51dd4403591b2d6838a48de3d283f3d188412a9782faadf845f298736ba0"},
+    {file = "zipp-3.16.2.tar.gz", hash = "sha256:ebc15946aa78bd63458992fc81ec3b6f7b1e92d51c35e6de1c3804e73b799147"},
 ]
diff --git a/pyproject.toml b/pyproject.toml
index 7a1d4afd4..c80b49124 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -9,6 +9,7 @@ dependencies = [
     "juliacall>=0.9.12",
     "numpy>=1.24.2",
     "pydantic>=1.10.7",
+    "scipy>=1.9.3",
     "pandas>=2.0.1",
     "seaborn>=0.12.2",
     "bokeh>=3.1.1",
diff --git a/src/bloqade/builder/backend/bloqade.py b/src/bloqade/builder/backend/bloqade.py
index fd0d5742e..1bf8ec54a 100644
--- a/src/bloqade/builder/backend/bloqade.py
+++ b/src/bloqade/builder/backend/bloqade.py
@@ -18,8 +18,17 @@ def bloqade(self):
 
 
 class BloqadeDeviceRoute(Builder):
-    def python(self, solver: str):
-        raise NotImplementedError
+    def python(self):
+        """
+        - Specify bloqade python backend
+        - Possible Next:
+
+            -> `...python().run(shots, ...)`
+                :: Run the current program using bloqade python backend
+        """
+        from bloqade.ir.routine.bloqade import BloqadeServiceOptions
+
+        return BloqadeServiceOptions(self).python()
 
     def julia(self, solver: str, nthreads: int = 1):
         raise NotImplementedError
diff --git a/src/bloqade/emulate/codegen/emulator_ir.py b/src/bloqade/emulate/codegen/emulator_ir.py
index 5a51f1590..daafbc193 100644
--- a/src/bloqade/emulate/codegen/emulator_ir.py
+++ b/src/bloqade/emulate/codegen/emulator_ir.py
@@ -19,16 +19,17 @@
 from bloqade.emulate.ir.atom_type import ThreeLevelAtom, TwoLevelAtom
 from bloqade.emulate.ir.emulator import (
     DetuningOperatorData,
+    LevelCoupling,
     RabiOperatorData,
     RabiOperatorType,
     DetuningTerm,
+    CompiledWaveform,
     EmulatorProgram,
     Register,
-    LaserCoupling,
+    Fields,
     RabiTerm,
 )
 
-from dataclasses import dataclass
 from typing import Any, Dict, Optional, Union, List
 from numbers import Number, Real
 from decimal import Decimal
@@ -36,15 +37,6 @@
 ParamType = Union[Real, List[Real]]
 
 
-@dataclass(frozen=True)
-class CompiledWaveform:
-    assignments: Dict[str, Number]
-    source: waveform.Waveform
-
-    def __call__(self, t: float) -> float:
-        return self.source(t, **self.assignments)
-
-
 class WaveformCompiler(WaveformVisitor):
     # TODO: implement AST generator for waveforms.
     def __init__(self, assignments: Dict[str, Number] = {}):
@@ -61,9 +53,9 @@ def __init__(
         self.blockade_radius = Decimal(str(blockade_radius))
         self.assignments = assignments
         self.waveform_compiler = WaveformCompiler(assignments)
-        self.geometry = None
+        self.register = None
         self.duration = 0.0
-        self.drives = {}
+        self.pulses = {}
         self.level_couplings = set()
 
     def visit_analog_circuit(self, ast: ir.AnalogCircuit):
@@ -80,21 +72,25 @@ def visit_register(self, ast: AtomArrangement) -> Any:
                 positions.append(position)
 
         if sequence.hyperfine in self.level_couplings:
-            self.geometry = Register(
+            self.register = Register(
                 ThreeLevelAtom, positions, blockade_radius=self.blockade_radius
             )
         else:
-            self.geometry = Register(
+            self.register = Register(
                 TwoLevelAtom, positions, blockade_radius=self.blockade_radius
             )
 
     def visit_sequence(self, ast: sequence.SequenceExpr):
+        level_coupling_mapping = {
+            sequence.hyperfine: LevelCoupling.Hyperfine,
+            sequence.rydberg: LevelCoupling.Rydberg,
+        }
         match ast:
             case sequence.Sequence(pulses):
                 for level_coupling, sub_pulse in pulses.items():
                     self.level_couplings.add(level_coupling)
                     self.visit(sub_pulse)
-                    self.drives[level_coupling] = LaserCoupling(
+                    self.pulses[level_coupling_mapping[level_coupling]] = Fields(
                         detuning=self.detuning_terms,
                         rabi=self.rabi_terms,
                     )
@@ -324,7 +320,7 @@ def emit(self, circuit: ir.AnalogCircuit) -> EmulatorProgram:
 
         self.visit(circuit)
         return EmulatorProgram(
-            geometry=self.geometry,
+            register=self.register,
             duration=self.duration,
-            drives=self.drives,
+            pulses=self.pulses,
         )
diff --git a/src/bloqade/emulate/codegen/rydberg_hamiltonian.py b/src/bloqade/emulate/codegen/rydberg_hamiltonian.py
new file mode 100644
index 000000000..dbe47264f
--- /dev/null
+++ b/src/bloqade/emulate/codegen/rydberg_hamiltonian.py
@@ -0,0 +1,207 @@
+from bloqade.constants import RB_C6
+from bloqade.emulate.ir.emulator import (
+    DetuningOperatorData,
+    EmulatorProgram,
+    LevelCoupling,
+    Register,
+    Fields,
+    DetuningTerm,
+    RabiOperatorData,
+    RabiOperatorType,
+    RabiTerm,
+    Visitor,
+)
+from bloqade.emulate.ir.space import Space
+from bloqade.emulate.ir.atom_type import (
+    TwoLevelAtomType,
+    ThreeLevelAtomType,
+)
+from bloqade.emulate.ir.state_vector import (
+    RabiOperator,
+    DetuningOperator,
+    RydbergHamiltonian,
+)
+from bloqade.emulate.sparse_operator import IndexMapping
+from scipy.sparse import csr_matrix
+import numpy as np
+from numpy.typing import NDArray
+from typing import Dict, Optional, Tuple, Union
+from dataclasses import dataclass, field
+
+OperatorData = Union[DetuningOperatorData, RabiOperatorData]
+MatrixTypes = Union[csr_matrix, IndexMapping, NDArray]
+
+
+@dataclass
+class CompileCache:
+    """This class is used to cache the results of the code generation."""
+
+    operator_cache: Dict[Tuple[Register, OperatorData], MatrixTypes] = field(
+        default_factory=dict
+    )
+    space_cache: Dict[Register, Tuple[Space, NDArray]] = field(default_factory=dict)
+
+
+class RydbergHamiltonianCodeGen(Visitor):
+    def __init__(self, compile_cache: Optional[CompileCache] = None):
+        if compile_cache is None:
+            compile_cache = CompileCache()
+
+        self.rabi_ops = []
+        self.detuning_ops = []
+        self.level_coupling = None
+        self.level_couplings = set()
+        self.compile_cache = compile_cache
+
+    def visit_emulator_program(self, emulator_program: EmulatorProgram):
+        self.level_couplings = set(list(emulator_program.pulses.keys()))
+
+        self.visit(emulator_program.register)
+        for level_coupling, laser_coupling in emulator_program.pulses.items():
+            self.level_coupling = level_coupling
+            self.visit(laser_coupling)
+
+    def visit_register(self, register: Register):
+        self.register = register
+
+        if register in self.compile_cache.space_cache:
+            self.space, self.rydberg = self.compile_cache.space_cache[register]
+            return
+
+        self.space = Space.create(register)
+        sites = register.sites
+
+        # generate rydberg interaction elements
+        self.rydberg = np.zeros(self.space.size, dtype=np.float64)
+
+        for index_1, site_1 in enumerate(sites):
+            site_1 = np.asarray(list(map(float, site_1)))
+            is_rydberg_1 = self.space.is_rydberg_at(index_1)
+            for index_2, sites_2 in enumerate(sites[index_1 + 1 :], index_1 + 1):
+                sites_2 = np.asarray(list(map(float, sites_2)))
+                distance = np.linalg.norm(site_1 - sites_2)
+
+                rydberg_interaction = RB_C6 / (distance**6)
+
+                if rydberg_interaction <= np.finfo(np.float64).eps:
+                    continue
+
+                mask = np.logical_and(is_rydberg_1, self.space.is_rydberg_at(index_2))
+                self.rydberg[mask] += rydberg_interaction
+
+        self.compile_cache.space_cache[register] = (self.space, self.rydberg)
+
+    def visit_fields(self, fields: Fields):
+        terms = fields.detuning + fields.rabi
+        for term in terms:
+            self.visit(term)
+
+    def visit_detuning_operator_data(self, detuning_data: DetuningOperatorData):
+        if (self.register, detuning_data) in self.compile_cache.operator_cache:
+            return self.compile_cache.operator_cache[(self.space, detuning_data)]
+
+        diagonal = np.zeros(self.space.size, dtype=np.float64)
+        match (self.space.atom_type, self.level_coupling):
+            case (TwoLevelAtomType(), LevelCoupling.Rydberg):
+                state = TwoLevelAtomType.State.Rydberg
+            case (ThreeLevelAtomType(), LevelCoupling.Rydberg):
+                state = ThreeLevelAtomType.State.Rydberg
+            case (ThreeLevelAtomType(), LevelCoupling.Hyperfine):
+                state = ThreeLevelAtomType.State.Hyperfine
+
+        for atom_index, value in detuning_data.target_atoms.items():
+            diagonal[self.space.is_state_at(atom_index, state)] += float(value)
+
+        self.compile_cache.operator_cache[(self.register, detuning_data)] = diagonal
+        return diagonal
+
+    def visit_rabi_operator_data(self, rabi_operator_data: RabiOperatorData):
+        if (self.register, rabi_operator_data) in self.compile_cache.operator_cache:
+            return self.compile_cache.operator_cache[
+                (self.register, rabi_operator_data)
+            ]
+
+        # Get the from and to states for term
+        match (self.space.atom_type, self.level_coupling):
+            case (TwoLevelAtomType(), LevelCoupling.Rydberg):
+                to = TwoLevelAtomType.State.Ground
+                fro = TwoLevelAtomType.State.Rydberg
+            case (ThreeLevelAtomType(), LevelCoupling.Rydberg):
+                to = ThreeLevelAtomType.State.Hyperfine
+                fro = ThreeLevelAtomType.State.Rydberg
+            case (ThreeLevelAtomType(), LevelCoupling.Hyperfine):
+                to = ThreeLevelAtomType.State.Ground
+                fro = ThreeLevelAtomType.State.Hyperfine
+
+        # get matrix element generating function
+        if rabi_operator_data.operator_type is RabiOperatorType.RabiSymmetric:
+
+            def matrix_ele(atom_index):
+                return self.space.swap_state_at(atom_index, fro, to)
+
+        elif rabi_operator_data.operator_type is RabiOperatorType.RabiAsymmetric:
+
+            def matrix_ele(atom_index):
+                return self.space.transition_state_at(atom_index, fro, to)
+
+        # generate rabi operator
+        if len(rabi_operator_data.target_atoms) == 1:
+            ((atom_index, _),) = rabi_operator_data.target_atoms.items()
+            operator = IndexMapping(self.space.size, *matrix_ele(atom_index))
+        else:
+            indptr = np.zeros(self.space.size + 1, dtype=self.space.index_type)
+
+            for atom_index in rabi_operator_data.target_atoms:
+                row_indices, col_indices = matrix_ele(atom_index)
+                indptr[1:][row_indices] += 1
+            np.cumsum(indptr, out=indptr)
+
+            indices = np.zeros(indptr[-1], dtype=self.space.index_type)
+            data = np.zeros(indptr[-1], dtype=np.float64)
+
+            for atom_index, value in rabi_operator_data.target_atoms.items():
+                row_indices, col_indices = matrix_ele(atom_index)
+                indices[indptr[:-1][row_indices]] = col_indices
+                data[indptr[:-1][row_indices]] = value
+                indptr[:-1][row_indices] += 1
+
+            indptr[1:] = indptr[:-1]
+            indptr[0] = 0
+
+            operator = csr_matrix(
+                (data, indices, indptr),
+                shape=(self.space.size, self.space.size),
+            )
+
+        self.compile_cache.operator_cache[
+            (self.register, rabi_operator_data)
+        ] = operator
+        return operator
+
+    def visit_detuning_term(self, detuning_term: DetuningTerm):
+        self.detuning_ops.append(
+            DetuningOperator(
+                diagonal=self.visit(detuning_term.operator_data),
+                amplitude=detuning_term.amplitude,
+            )
+        )
+
+    def visit_rabi_term(self, rabi_term: RabiTerm):
+        self.rabi_ops.append(
+            RabiOperator(
+                op=self.visit(rabi_term.operator_data),
+                amplitude=rabi_term.amplitude,
+                phase=rabi_term.phase,
+            )
+        )
+
+    def emit(self, emulator_program: EmulatorProgram) -> RydbergHamiltonian:
+        self.visit(emulator_program)
+        hamiltonian = RydbergHamiltonian(
+            emulator_ir=emulator_program,
+            space=self.space,
+            rydberg=self.rydberg,
+            detuning_ops=self.detuning_ops,
+            rabi_ops=self.rabi_ops,
+        )
+        return hamiltonian
diff --git a/src/bloqade/emulate/ir/atom_type.py b/src/bloqade/emulate/ir/atom_type.py
index 88a72b34f..b875d442f 100644
--- a/src/bloqade/emulate/ir/atom_type.py
+++ b/src/bloqade/emulate/ir/atom_type.py
@@ -1,7 +1,7 @@
 from dataclasses import dataclass
-from enum import Enum
-import numpy as np
 from numpy.typing import NDArray
+import numpy as np
+from enum import Enum
 
 
 @dataclass(frozen=True)
diff --git a/src/bloqade/emulate/ir/emulator.py b/src/bloqade/emulate/ir/emulator.py
index 11e47e3a6..af8a0f4d8 100644
--- a/src/bloqade/emulate/ir/emulator.py
+++ b/src/bloqade/emulate/ir/emulator.py
@@ -1,9 +1,19 @@
 from dataclasses import dataclass
 from decimal import Decimal
-from typing import Any, Dict, List, Tuple, Optional, Callable
+from typing import Any, Dict, List, Tuple, Optional
 from enum import Enum
-from bloqade.ir.control.sequence import LevelCoupling
+from bloqade.ir.control.waveform import Waveform
 from bloqade.emulate.ir.atom_type import AtomType
+from numbers import Real
+
+
+@dataclass(frozen=True)
+class CompiledWaveform:
+    assignments: Dict[str, Real]
+    source: Waveform
+
+    def __call__(self, t: float) -> float:
+        return self.source(t, **self.assignments)
 
 
 class RabiOperatorType(Enum):
@@ -23,8 +33,8 @@ def __hash__(self):
 @dataclass(frozen=True)
 class RabiTerm:
     operator_data: RabiOperatorData
-    amplitude: Callable[[float], float]
-    phase: Optional[Callable[[float], float]] = None
+    amplitude: CompiledWaveform
+    phase: Optional[CompiledWaveform] = None
 
 
 @dataclass(frozen=True)
@@ -38,11 +48,11 @@ def __hash__(self) -> int:
 @dataclass(frozen=True)
 class DetuningTerm:
     operator_data: DetuningOperatorData
-    amplitude: Callable[[float], float]
+    amplitude: CompiledWaveform
 
 
 @dataclass(frozen=True)
-class LaserCoupling:
+class Fields:
     detuning: List[DetuningTerm]
     rabi: List[RabiTerm]
 
@@ -52,18 +62,18 @@ class Register:
     """This class represents the of the atoms in the system."""
 
     atom_type: AtomType
-    positions: List[Tuple[Decimal, Decimal]]
+    sites: List[Tuple[Decimal, Decimal]]
     blockade_radius: Decimal
 
     def __len__(self):
-        return len(self.positions)
+        return len(self.sites)
 
     def __eq__(self, other: Any):
         if isinstance(other, Register):
             return (
                 self.atom_type == other.atom_type
                 and self.blockade_radius == other.blockade_radius
-                and set(self.positions) == set(other.positions)
+                and set(self.sites) == set(other.sites)
             )
 
         return False
@@ -72,9 +82,7 @@ def __hash__(self) -> int:
         if self.blockade_radius == Decimal("0"):
             # if blockade radius is zero, then the positions are irrelevant
             # because the fock states generated by the geometry are the same
-            return (
-                hash(self.__class__) ^ hash(self.atom_type) ^ hash(len(self.positions))
-            )
+            return hash(self.__class__) ^ hash(self.atom_type) ^ hash(len(self.sites))
         else:
             # if blockade radius is non-zero, then the positions are relevant
             # because depending on the location of the atoms and the blockade
@@ -83,22 +91,30 @@ def __hash__(self) -> int:
                 hash(self.__class__)
                 ^ hash(self.atom_type)
                 ^ hash(self.blockade_radius)
-                ^ hash(frozenset(self.positions))
+                ^ hash(frozenset(self.sites))
             )
 
 
+class LevelCoupling(str, Enum):
+    Rydberg = "rydberg"
+    Hyperfine = "hyperfine"
+
+
 @dataclass(frozen=True)
 class EmulatorProgram:
-    geometry: Register
+    register: Register
     duration: float
-    drives: Dict[LevelCoupling, LaserCoupling]
+    pulses: Dict[LevelCoupling, Fields]
 
 
 class Visitor:
     def visit_emulator_program(self, ast: EmulatorProgram) -> Any:
         raise NotImplementedError
 
-    def visit_laser_coupling(self, ast: LaserCoupling) -> Any:
+    def visit_compiled_waveform(self, ast: CompiledWaveform) -> Any:
+        raise NotImplementedError
+
+    def visit_fields(self, ast: Fields) -> Any:
         raise NotImplementedError
 
     def visit_detuning_operator_data(self, ast: DetuningOperatorData) -> Any:
@@ -117,18 +133,21 @@ def visit_register(self, ast: Register) -> Any:
         raise NotImplementedError
 
     def visit(self, ast) -> Any:
-        match ast:
-            case EmulatorProgram():
-                return self.visit_emulator_program(ast)
-            case Register():
-                return self.visit_register(ast)
-            case LaserCoupling():
-                return self.visit_laser_coupling(ast)
-            case DetuningOperatorData():
-                return self.visit_detuning_operator_data(ast)
-            case RabiOperatorData():
-                return self.visit_rabi_operator_data(ast)
-            case DetuningTerm():
-                return self.visit_detuning_term(ast)
-            case RabiTerm():
-                return self.visit_rabi_term(ast)
+        if isinstance(ast, EmulatorProgram):
+            return self.visit_emulator_program(ast)
+        elif isinstance(ast, Register):
+            return self.visit_register(ast)
+        elif isinstance(ast, Fields):
+            return self.visit_fields(ast)
+        elif isinstance(ast, RabiTerm):
+            return self.visit_rabi_term(ast)
+        elif isinstance(ast, DetuningTerm):
+            return self.visit_detuning_term(ast)
+        elif isinstance(ast, RabiOperatorData):
+            return self.visit_rabi_operator_data(ast)
+        elif isinstance(ast, DetuningOperatorData):
+            return self.visit_detuning_operator_data(ast)
+        elif isinstance(ast, CompiledWaveform):
+            return self.visit_compiled_waveform(ast)
+        else:
+            raise NotImplementedError(f"Unknown AST node type {type(ast)}: {ast!r}")
diff --git a/src/bloqade/emulate/ir/space.py b/src/bloqade/emulate/ir/space.py
index fba4b6277..6ed0e72b6 100644
--- a/src/bloqade/emulate/ir/space.py
+++ b/src/bloqade/emulate/ir/space.py
@@ -17,15 +17,12 @@ class SpaceType(str, Enum):
 @dataclass(frozen=True)
 class Space:
     space_type: SpaceType
-    atom_type: AtomType
+    atom_type: "AtomType"
     geometry: "Register"
     configurations: NDArray
 
     @classmethod
-    def create(
-        cls,
-        register: "Register",
-    ):
+    def create(cls, register: "Register"):
         sites = register.sites
         n_atom = len(sites)
         atom_type = register.atom_type
@@ -47,7 +44,7 @@ def create(
         configurations = np.arange(Ns, dtype=np.min_scalar_type(Ns - 1))
 
         if all(len(sub_list) == 0 for sub_list in check_atoms):
-            return cls(SpaceType.FullSpace, atom_type, sites, configurations)
+            return Space(SpaceType.FullSpace, atom_type, sites, configurations)
 
         for index_1, indices in enumerate(check_atoms):
             # get which configurations are in rydberg state for the current index.
@@ -123,11 +120,15 @@ def transition_state_at(self, index: int, fro: int, to: int) -> NDArray:
             return (row_indices, col_config)
         else:
             col_indices = np.searchsorted(self.configurations, col_config)
+            row_indices = np.argwhere(row_indices).ravel()
+
             mask = col_indices < self.size
-            mask = np.logical_and(mask, col_config == self.configurations[col_indices])
+            col_indices = col_indices[mask]
+            row_indices = row_indices[mask]
 
+            mask = col_config == self.configurations[col_indices]
             col_indices = col_indices[mask]
-            row_indices = np.logical_and(row_indices, mask)
+            row_indices = row_indices[mask]
 
             return (row_indices, col_indices)
 
diff --git a/src/bloqade/emulate/ir/state_vector.py b/src/bloqade/emulate/ir/state_vector.py
index 4868c9af6..a3cc8c1a9 100644
--- a/src/bloqade/emulate/ir/state_vector.py
+++ b/src/bloqade/emulate/ir/state_vector.py
@@ -1,16 +1,13 @@
+from bloqade.emulate.ir.emulator import EmulatorProgram
 from bloqade.emulate.ir.space import Space
 from bloqade.emulate.sparse_operator import IndexMapping
 from scipy.sparse import csr_matrix
 from dataclasses import dataclass, field
 from numpy.typing import NDArray
-from typing import TYPE_CHECKING, List, Callable, Union, Optional
+from typing import List, Callable, Union, Optional
 import numpy as np
 from scipy.integrate import ode
 
-if TYPE_CHECKING:
-    from bloqade.emulate.ir.emulator import EmulatorProgram
-
-
 SparseOperator = Union[IndexMapping, csr_matrix]
 
 
@@ -46,7 +43,7 @@ def dot(self, register: NDArray, time: float):
 
 @dataclass(frozen=True)
 class RydbergHamiltonian:
-    emulator_ir: "EmulatorProgram"
+    emulator_ir: EmulatorProgram
     space: Space
     rydberg: NDArray
     detuning_ops: List[DetuningOperator] = field(default_factory=list)
@@ -161,6 +158,7 @@ def apply(
         atol: float = 1e-7,
         rtol: float = 1e-14,
         nsteps: int = 2_147_483_647,
+        times: List[float] = [],
     ):
         if state is None:
             state = self.hamiltonian.space.zero_state()
@@ -168,14 +166,23 @@ def apply(
         if solver_name not in AnalogGate.SUPPORTED_SOLVERS:
             raise ValueError(f"'{solver_name}' not supported.")
 
+        duration = self.hamiltonian.emulator_ir.duration
+
         state = np.asarray(state).astype(np.complex128, copy=False)
         solver = ode(self.hamiltonian._ode_real_kernel)
         solver.set_initial_value(state.view(np.float64))
         solver.set_integrator(solver_name, atol=atol, rtol=rtol, nsteps=nsteps)
-        solver.integrate(self.hamiltonian.emulator_ir.duration)
-        AnalogGate._error_check(solver_name, solver.get_return_code())
 
-        return solver.y.view(np.complex128)
+        if any(time >= duration or time < 0.0 for time in times):
+            raise ValueError("Times must be between 0 and duration.")
+
+        times = [*times, duration]
+
+        for time in times:
+            solver.integrate(time)
+            AnalogGate._error_check(solver_name, solver.get_return_code())
+            u = np.exp(-1j * time * self.hamiltonian.rydberg)
+            yield u * solver.y.view(np.complex128)
 
     def run(
         self,
@@ -189,7 +196,7 @@ def run(
         """Run the emulation with all atoms in the ground state,
         sampling the final state vector."""
         state = self.hamiltonian.space.zero_state()
-        result = self.apply(state, solver_name, atol, rtol, nsteps)
+        (result,) = self.apply(state, solver_name, atol, rtol, nsteps)
         result /= np.linalg.norm(result)
         return self.hamiltonian.space.sample_state_vector(
             result, shots, project_hyperfine=project_hyperfine
diff --git a/src/bloqade/emulate/sparse_operator.py b/src/bloqade/emulate/sparse_operator.py
index 2df93ad2f..8ff398a4d 100644
--- a/src/bloqade/emulate/sparse_operator.py
+++ b/src/bloqade/emulate/sparse_operator.py
@@ -21,6 +21,8 @@ def dot(self, other):
         result = np.zeros_like(other)
         result[self.row_indices] = other[self.col_indices]
 
+        return result
+
     def to_csr(self):
         indptr = np.zeros(self.n_row + 1, dtype=np.int64)
         indptr[1:][self.row_indices] = 1
diff --git a/src/bloqade/ir/analog_circuit.py b/src/bloqade/ir/analog_circuit.py
index 5d45df5ae..91aade54d 100644
--- a/src/bloqade/ir/analog_circuit.py
+++ b/src/bloqade/ir/analog_circuit.py
@@ -10,8 +10,7 @@
 # NOTE: this is just a dummy type bundle geometry and sequence
 #       information together and forward them to backends.
 class AnalogCircuit:
-
-    """Program is a dummy type that bundle register and sequence together."""
+    """AnalogCircuit is a dummy type that bundle register and sequence together."""
 
     def __init__(
         self,
@@ -85,63 +84,3 @@ def show(self, **assignments):
 
         """
         display_analog_circuit(self, assignments)
-
-
-# class BraketService:
-#     def __init__(self, batch: Batch):
-#         self.batch = batch
-
-#     @property
-#     def aquila(self) -> "BraketHardware":
-#         return BraketHardware(
-#             self.batch, "arn:aws:braket:us-east-1::device/qpu/quera/Aquila"
-#         )
-
-#     @property
-#     def local_emulator(self) -> "BraketLocalEmulator":
-#         return BraketLocalEmulator(self.batch)
-
-
-# class BraketHardware:
-#     def __init__(self, program: Program, device_arn: str):
-#         self.program = program
-#         self.device_arn = device_arn
-
-#     def _compile_batch(
-#         self, shots: int, args: Tuple[Real, ...], name: Optional[str] = None
-#     ) -> "RemoteBatch":
-#         from bloqade.compile.braket import BraketBatchCompiler
-#         from bloqade.submission.braket import BraketBackend
-
-#         backend = BraketBackend(
-#             device_arn=self.device_arn,
-#         )
-
-#         return BraketBatchCompiler(
-#             program=self.program,
-#             backend=backend,
-#         ).compile(shots, args, name=name)
-
-#     def submit(
-#         self, shots: int, args: Tuple[Real, ...], name: Optional[str] = None
-#     ) -> "RemoteBatch":
-#         batch = self._compile_batch(shots, args, name=name)
-#         batch._submit()
-
-#         return batch
-
-#     def run(
-#         self,
-#         shots: int,
-#         args: Tuple[Real, ...],
-#         name: Optional[str] = None,
-#         shuffle_submit_order: bool = False,
-#     ) -> "RemoteBatch":
-#         batch = self._compile_batch(shots, args, name=name)
-#         batch._submit(shuffle_submit_order=shuffle_submit_order)
-#         batch.pull()
-
-#         return batch
-
-#     def __call__(self, *args, shots: int = 1):
-#         return self.run(shots, args)
diff --git a/src/bloqade/ir/control/waveform.py b/src/bloqade/ir/control/waveform.py
index 235dd9c5c..df7a9bd6b 100644
--- a/src/bloqade/ir/control/waveform.py
+++ b/src/bloqade/ir/control/waveform.py
@@ -62,21 +62,12 @@ class Waveform:
     ```
     """
 
-    def __post_init__(self):
-        self._duration = None
+    # def __post_init__(self):
+    #     self._duration = None
 
     def __call__(self, clock_s: float, **kwargs) -> float:
         return float(self.eval_decimal(Decimal(str(clock_s)), **kwargs))
 
-    def __mul__(self, scalar: Scalar) -> "Waveform":
-        return self.scale(cast(scalar))
-
-    def __rmul__(self, scalar: Scalar) -> "Waveform":
-        return self.scale(cast(scalar))
-
-    def __add__(self, other: "Waveform"):
-        return self.add(other)
-
     def eval_decimal(self, clock_s: Decimal, **kwargs) -> Decimal:
         raise NotImplementedError
 
@@ -135,16 +126,47 @@ def __getitem__(self, s: slice) -> "Waveform":
     def record(self, variable_name: Union[str, Variable]):
         return Record(self, cast(variable_name))
 
+    def __add__(self, other: "Waveform") -> "Waveform":
+        if isinstance(other, Waveform):
+            return self.canonicalize(Add(self, other))
+
+        return NotImplemented
+
+    def __radd__(self, other: "Waveform") -> "Waveform":
+        if isinstance(other, Waveform):
+            return self.canonicalize(Add(self, other))
+
+        return NotImplemented
+
+    def __sub__(self, other: "Waveform") -> "Waveform":
+        if isinstance(other, Waveform):
+            return self + (-other)
+
+        return NotImplemented
+
+    def __rsubs__(self, other: "Waveform") -> "Waveform":
+        if isinstance(other, Waveform):
+            return other + (-self)
+
+        return NotImplemented
+
+    def __mul__(self, other: Any) -> "Waveform":
+        return self.scale(cast(other))
+
+    def __rmul__(self, other: Any) -> "Waveform":
+        return self.scale(cast(other))
+
+    def __truediv__(self, other: Any) -> "Waveform":
+        return self.scale(1 / cast(other))
+
     @property
     def duration(self) -> Scalar:
-        if self._duration:
+        if hasattr(self, "_duration"):
             return self._duration
 
         match self:
-            case Instruction(duration=duration):
-                self._duration = duration
             case AlignedWaveform(waveform=waveform, alignment=_, value=_):
-                self._duration = waveform.duration()
+                self._duration = waveform.duration
             case Slice(waveform=waveform, interval=interval):
                 match (interval.start, interval.stop):
                     case (None, None):
@@ -164,9 +186,13 @@ def duration(self) -> Scalar:
             case Sample(waveform=waveform, interpolation=_, dt=_):
                 self._duration = waveform.duration
             case Smooth(waveform=waveform, kernel=_, radius=_):
-                return waveform.duration
+                self._duration = waveform.duration
             case Record(waveform=waveform, var=_):
-                return waveform.duration
+                self._duration = waveform.duration
+            case Add(left=left, right=right):
+                self._duration = left.duration.max(right.duration)
+            case Scale(waveform=waveform, scalar=_):
+                self._duration = waveform.duration
             case _:
                 raise ValueError(f"Cannot compute duration of {self}")
         return self._duration
@@ -174,6 +200,14 @@ def duration(self) -> Scalar:
     @staticmethod
     def canonicalize(expr: "Waveform") -> "Waveform":
         match expr:
+            case Add(left=left, right=right):
+                if left == right:
+                    return left.scale(2)
+                if left.duration == cast(0):
+                    return right
+                if right.duration == cast(0):
+                    return left
+                return expr
             case Append([Append(lhs), Append(rhs)]):
                 return Append(list(map(Waveform.canonicalize, lhs + rhs)))
             case Append([Append(waveforms), waveform]):
diff --git a/src/bloqade/ir/routine/bloqade.py b/src/bloqade/ir/routine/bloqade.py
new file mode 100644
index 000000000..5d771ba07
--- /dev/null
+++ b/src/bloqade/ir/routine/bloqade.py
@@ -0,0 +1,151 @@
+from collections import OrderedDict
+from .base import RoutineBase
+from bloqade.task.batch import LocalBatch
+from typing import Tuple
+from numbers import Real
+from dataclasses import dataclass
+
+
+@dataclass(frozen=True)
+class BloqadeServiceOptions(RoutineBase):
+    def python(self):
+        return BloqadePythonRoutine(source=self.source)
+
+
+@dataclass(frozen=True)
+class BloqadePythonRoutine(RoutineBase):
+    def compile(
+        self,
+        shots: int,
+        args: Tuple[Real, ...] = (),
+        name: str | None = None,
+        blockade_radius: float = 0.0,
+        cache_matrices: bool = False,
+    ) -> LocalBatch:
+        from bloqade.codegen.common.assignment_scan import AssignmentScan
+        from bloqade.codegen.common.assign_variables import AssignAnalogCircuit
+        from bloqade.emulate.codegen.emulator_ir import EmulatorProgramCodeGen
+        from bloqade.emulate.codegen.rydberg_hamiltonian import CompileCache
+        from bloqade.task.bloqade import BloqadeTask
+
+        circuit, params = self.source.parse_source()
+
+        circuit = AssignAnalogCircuit(params.static_params).visit(circuit)
+
+        if cache_matrices:
+            matrix_cache = CompileCache()
+        else:
+            matrix_cache = None
+
+        tasks = OrderedDict()
+        for task_number, batch_param in enumerate(params.batch_assignments(*args)):
+            record_params = AssignmentScan(batch_param).emit(circuit)
+            final_circuit = AssignAnalogCircuit(record_params).visit(circuit)
+            emulator_ir = EmulatorProgramCodeGen(blockade_radius=blockade_radius).emit(
+                final_circuit
+            )
+            tasks[task_number] = BloqadeTask(
+                shots, emulator_ir, batch_param, matrix_cache
+            )
+
+        return LocalBatch(self.source, tasks, name)
+
+    def run(
+        self,
+        shots: int,
+        args: Tuple[Real, ...] = (),
+        name: str | None = None,
+        blockade_radius: float = 0.0,
+        cache_matrices: bool = False,
+        multiprocessing: bool = False,
+        num_workers: int | None = None,
+        solver_name: str = "dop853",
+        atol: float = 1e-14,
+        rtol: float = 1e-7,
+        nsteps: int = 2_147_483_647,
+    ) -> LocalBatch:
+        """Run the current program using bloqade python backend
+
+        Args:
+            shots (int): number of shots after running state vector simulation
+            args (Tuple[Real, ...], optional): The arguments defined in `flatten`.
+            Defaults to ().
+            name (str | None, optional): Name to give this run. Defaults to None.
+            blockade_radius (float, optional): Use the Blockade subspace given a
+            particular radius. Defaults to 0.0.
+            cache_matrices (bool, optional): Reuse previously evaluated matrcies when
+            possible. Defaults to False.
+            multiprocessing (bool, optional): Use multiple processes to process the
+            batches. Defaults to False.
+            num_workers (int | None, optional): Number of processes to run with
+            multiprocessing. Defaults to None.
+            solver_name (str, optional): Which SciPy Solver to use. Defaults to
+            "dop853".
+            atol (float, optional): Absolute tolerance for ODE solver. Defaults to
+            1e-14.
+            rtol (float, optional): Relative tolerance for adaptive step in ODE solver.
+            Defaults to 1e-7.
+            nsteps (int, optional): Maximum number of steps allowed per integration
+            step. Defaults to 2_147_483_647, the maximum value.
+
+        Raises:
+            ValueError: Cannot use multiprocessing and cache_matrices at the same time.
+
+        Returns:
+            LocalBatch: Batch of local tasks that have been executed.
+        """
+        if multiprocessing and cache_matrices:
+            raise ValueError(
+                "Cannot use multiprocessing and cache_matrices at the same time."
+            )
+
+        compile_options = dict(
+            shots=shots,
+            args=args,
+            name=name,
+            blockade_radius=blockade_radius,
+            cache_matrices=cache_matrices,
+        )
+
+        solver_options = dict(
+            multiprocessing=multiprocessing,
+            num_workers=num_workers,
+            solver_name=solver_name,
+            atol=atol,
+            rtol=rtol,
+            nsteps=nsteps,
+        )
+
+        batch = self.compile(**compile_options)
+        batch._run(**solver_options)
+
+        return batch
+
+    def __call__(
+        self,
+        *args: Real,
+        shots: int = 1,
+        name: str | None = None,
+        blockade_radius: float = 0.0,
+        multiprocessing: bool = False,
+        num_workers: int | None = None,
+        cache_matrices: bool = False,
+        solver_name: str = "dop853",
+        atol: float = 1e-7,
+        rtol: float = 1e-14,
+        nsteps: int = 2_147_483_647,
+    ):
+        options = dict(
+            shots=shots,
+            args=args,
+            name=name,
+            blockade_radius=blockade_radius,
+            multiprocessing=multiprocessing,
+            num_workers=num_workers,
+            cache_matrices=cache_matrices,
+            solver_name=solver_name,
+            atol=atol,
+            rtol=rtol,
+            nsteps=nsteps,
+        )
+        return self.run(**options)
diff --git a/src/bloqade/task/bloqade.py b/src/bloqade/task/bloqade.py
index e69de29bb..fb3ef7886 100644
--- a/src/bloqade/task/bloqade.py
+++ b/src/bloqade/task/bloqade.py
@@ -0,0 +1,70 @@
+from bloqade.task.base import Geometry, LocalTask
+from bloqade.emulate.ir.emulator import EmulatorProgram
+from bloqade.emulate.codegen.rydberg_hamiltonian import (
+    RydbergHamiltonianCodeGen,
+    CompileCache,
+)
+from bloqade.emulate.ir.state_vector import AnalogGate
+
+from bloqade.submission.ir.task_results import (
+    QuEraTaskResults,
+    QuEraShotResult,
+    QuEraTaskStatusCode,
+    QuEraShotStatusCode,
+)
+from typing import Dict
+from bloqade.builder.base import ParamType
+from dataclasses import dataclass
+from typing import Optional
+
+
+@dataclass
+class BloqadeTask(LocalTask):
+    shots: int
+    emulator_ir: EmulatorProgram
+    metadata: Dict[str, ParamType]
+    compile_cache: Optional[CompileCache] = None
+    task_result_ir: Optional[QuEraTaskResults] = None
+
+    def _geometry(self) -> Geometry:
+        sites = [tuple(map(float, site)) for site in self.emulator_ir.register.sites]
+
+        return Geometry(sites=sites, filling=[1 for _ in sites], parallel_decoder=None)
+
+    def result(self) -> QuEraTaskResults:
+        return self.task_result_ir
+
+    def run(
+        self,
+        solver_name: str = "dop853",
+        atol: float = 1e-14,
+        rtol: float = 1e-7,
+        nsteps: int = 2_147_483_647,
+    ) -> "BloqadeTask":
+        hamiltonian = RydbergHamiltonianCodeGen(self.compile_cache).emit(
+            self.emulator_ir
+        )
+        options = dict(
+            solver_name=solver_name,
+            atol=atol,
+            rtol=rtol,
+            nsteps=nsteps,
+        )
+        shots_array = AnalogGate(hamiltonian).run(
+            self.shots, project_hyperfine=True, **options
+        )
+
+        shot_outputs = []
+        for shot in shots_array[:]:
+            shot_result = QuEraShotResult(
+                shot_status=QuEraShotStatusCode.Completed,
+                pre_sequence=[1 for _ in shot],
+                post_sequence=list(shot),
+            )
+            shot_outputs.append(shot_result)
+
+        self.task_result_ir = QuEraTaskResults(
+            task_status=QuEraTaskStatusCode.Completed, shot_outputs=shot_outputs
+        )
+
+        return self
diff --git a/tests/test_emulator_codegen.py b/tests/test_emulator_codegen.py
index a9fd624d2..3b9d6ade7 100644
--- a/tests/test_emulator_codegen.py
+++ b/tests/test_emulator_codegen.py
@@ -4,12 +4,16 @@
     Register,
     RabiOperatorData,
     RabiTerm,
-    LaserCoupling,
+    Fields,
     DetuningTerm,
     DetuningOperatorData,
     RabiOperatorType,
 )
-from bloqade.emulate.codegen.emulator_ir import EmulatorProgramCodeGen, CompiledWaveform
+from bloqade.emulate.codegen.emulator_ir import (
+    EmulatorProgramCodeGen,
+    CompiledWaveform,
+    LevelCoupling,
+)
 from bloqade import start
 from bloqade.ir.control.sequence import rydberg
 from bloqade.ir.control.pulse import detuning, rabi
@@ -40,16 +44,19 @@ def test_codegen_detuning():
         compiled_waveform,
     )
 
-    rydberg_drive = LaserCoupling(detuning=[detuning_term], rabi=[])
+    rydberg_drive = Fields(detuning=[detuning_term], rabi=[])
 
-    drives = {rydberg: rydberg_drive}
+    drives = {LevelCoupling.Rydberg: rydberg_drive}
 
     expected_emulator_ir = EmulatorProgram(
-        geometry=geometry, duration=1.0, drives=drives
+        register=geometry, duration=1.0, pulses=drives
     )
 
     emulator_ir = EmulatorProgramCodeGen().emit(program)
 
+    print(emulator_ir)
+    print(expected_emulator_ir)
+
     assert emulator_ir == expected_emulator_ir
 
 
@@ -90,16 +97,19 @@ def test_codegen_detuning_and_rabi():
         None,
     )
 
-    rydberg_drive = LaserCoupling(detuning=[detuning_term], rabi=[rabi_term])
+    rydberg_drive = Fields(detuning=[detuning_term], rabi=[rabi_term])
 
-    drives = {rydberg: rydberg_drive}
+    drives = {LevelCoupling.Rydberg: rydberg_drive}
 
     expected_emulator_ir = EmulatorProgram(
-        geometry=geometry, duration=1.0, drives=drives
+        register=geometry, duration=1.0, pulses=drives
     )
 
     emulator_ir = EmulatorProgramCodeGen().emit(program)
 
+    print(emulator_ir)
+    print(expected_emulator_ir)
+
     assert emulator_ir == expected_emulator_ir
 
 
diff --git a/tests/test_python_emulator.py b/tests/test_python_emulator.py
new file mode 100644
index 000000000..22caf25ff
--- /dev/null
+++ b/tests/test_python_emulator.py
@@ -0,0 +1,42 @@
+from bloqade import start, var
+import numpy as np
+
+
+def test_integration_1():
+    (
+        start.add_position((0, 0))
+        .add_position((0, 1.0))
+        .scale("r")
+        .rydberg.detuning.uniform.piecewise_linear(
+            [0.1, "ramp_time", 0.1], [-100, -100, 100, 100]
+        )
+        .amplitude.uniform.piecewise_linear([0.1, "ramp_time", 0.1], [0, 10, 10, 0])
+        .assign(ramp_time=3.0)
+        .batch_assign(r=np.linspace(4, 10, 31).tolist())
+        .bloqade.python()
+        .run(10000, cache_matrices=True, blockade_radius=6.0)
+        .report()
+        .bitstrings()
+    )
+
+
+def test_integration_2():
+    ramp_time = var("ramp_time")
+    (
+        start.add_position((0, 0))
+        .add_position((0, 1.0))
+        .scale("r")
+        .rydberg.detuning.uniform.piecewise_linear(
+            [0.1, "ramp_time", 0.1], [-100, -100, 100, 100]
+        )
+        .amplitude.uniform.piecewise_linear([0.1, ramp_time, 0.1], [0, 10, 10, 0])
+        .phase.uniform.piecewise_constant(
+            [0.1, ramp_time / 2, ramp_time / 2, 0.1], [0, 0, np.pi, np.pi]
+        )
+        .assign(ramp_time=3.0)
+        .batch_assign(r=np.linspace(4, 10, 31).tolist())
+        .bloqade.python()
+        .run(10000, cache_matrices=True, blockade_radius=6.0)
+        .report()
+        .bitstrings()
+    )
diff --git a/tests/test_space.py b/tests/test_space.py
new file mode 100644
index 000000000..bcb5cdaf0
--- /dev/null
+++ b/tests/test_space.py
@@ -0,0 +1,206 @@
+from bloqade.emulate.ir.space import Space
+from bloqade.emulate.ir.atom_type import ThreeLevelAtom, TwoLevelAtom
+from bloqade.emulate.ir.emulator import Register
+import numpy as np
+
+
+def test_two_level_space():
+    positions = [(0, 0), (0, 1)]
+    register = Register(TwoLevelAtom, positions, 0)
+    space = Space.create(register)
+    print(space)
+    assert space.n_atoms == 2
+    assert space.size == 4
+    assert np.all(space.configurations == np.array([0, 1, 2, 3]))
+
+
+def test_two_level_subspace():
+    positions = [(0, 0), (0, 1)]
+    register = Register(TwoLevelAtom, positions, 1.1)
+    space = Space.create(register)
+    print(space)
+    assert space.n_atoms == 2
+    assert space.size == 3
+    assert np.all(space.configurations == np.array([0, 1, 2]))
+
+
+def test_two_level_subspace_2():
+    positions = [(0, 0), (0, 1), (1, 0), (1, 1)]
+    register = Register(TwoLevelAtom, positions, np.sqrt(2) + 0.1)
+    space = Space.create(register)
+    print(space)
+    assert space.n_atoms == 4
+    assert space.size == 5
+    assert np.all(space.configurations == np.array([0, 1, 2, 4, 8]))
+
+
+def test_three_level_space():
+    positions = [(0, 0), (0, 1)]
+    register = Register(ThreeLevelAtom, positions, 0)
+    space = Space.create(register)
+    print(space)
+    assert space.n_atoms == 2
+    assert space.size == 9
+    assert np.all(space.configurations == np.array([0, 1, 2, 3, 4, 5, 6, 7, 8]))
+
+
+def test_three_level_subspace():
+    positions = [(0, 0), (0, 1)]
+    register = Register(ThreeLevelAtom, positions, 1.1)
+    space = Space.create(register)
+    print(space)
+    assert space.n_atoms == 2
+    assert space.size == 8
+    assert np.all(space.configurations == np.array([0, 1, 2, 3, 4, 5, 6, 7]))
+
+
+def test_three_level_subspace_2():
+    positions = [(0, 0), (0.5, np.sqrt(3) / 2), (0, 1)]
+    register = Register(ThreeLevelAtom, positions, 1.1)
+    space = Space.create(register)
+    print(space)
+    assert space.n_atoms == 3
+    assert space.size == 20
+    assert np.all(
+        space.configurations
+        == np.array(
+            [0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22]
+        )
+    )
+
+
+def test_two_level_integer_to_string():
+    assert TwoLevelAtom.integer_to_string(0, 2) == "|gg>"
+    assert TwoLevelAtom.integer_to_string(1, 2) == "|rg>"
+    assert TwoLevelAtom.integer_to_string(2, 2) == "|gr>"
+    assert TwoLevelAtom.integer_to_string(3, 2) == "|rr>"
+
+
+def test_two_level_string_to_integer():
+    assert TwoLevelAtom.string_to_integer("|gg>") == 0
+    assert TwoLevelAtom.string_to_integer("|rg>") == 1
+    assert TwoLevelAtom.string_to_integer("|gr>") == 2
+    assert TwoLevelAtom.string_to_integer("|rr>") == 3
+
+
+def test_three_level_integer_to_string():
+    assert ThreeLevelAtom.integer_to_string(0, 2) == "|gg>"
+    assert ThreeLevelAtom.integer_to_string(1, 2) == "|hg>"
+    assert ThreeLevelAtom.integer_to_string(2, 2) == "|rg>"
+    assert ThreeLevelAtom.integer_to_string(3, 2) == "|gh>"
+    assert ThreeLevelAtom.integer_to_string(4, 2) == "|hh>"
+    assert ThreeLevelAtom.integer_to_string(5, 2) == "|rh>"
+    assert ThreeLevelAtom.integer_to_string(6, 2) == "|gr>"
+    assert ThreeLevelAtom.integer_to_string(7, 2) == "|hr>"
+    assert ThreeLevelAtom.integer_to_string(8, 2) == "|rr>"
+
+
+def test_three_level_string_to_integer():
+    assert ThreeLevelAtom.string_to_integer("|gg>") == 0
+    assert ThreeLevelAtom.string_to_integer("|hg>") == 1
+    assert ThreeLevelAtom.string_to_integer("|rg>") == 2
+    assert ThreeLevelAtom.string_to_integer("|gh>") == 3
+    assert ThreeLevelAtom.string_to_integer("|hh>") == 4
+    assert ThreeLevelAtom.string_to_integer("|rh>") == 5
+    assert ThreeLevelAtom.string_to_integer("|gr>") == 6
+    assert ThreeLevelAtom.string_to_integer("|hr>") == 7
+    assert ThreeLevelAtom.string_to_integer("|rr>") == 8
+
+
+def test_two_level_swap_indices():
+    positions = [(0, 0), (0, 1), (1, 0)]
+    register = Register(TwoLevelAtom, positions, 0)
+    space = Space.create(register)
+    print(space)
+
+    row_indices, col_indices = space.swap_state_at(0, 0, 1)
+
+    row_indices_expected = slice(None, None, None)
+    col_indices_expected = np.array([1, 0, 3, 2, 5, 4, 7, 6])
+
+    assert row_indices == row_indices_expected
+    assert np.all(col_indices == col_indices_expected)
+
+    row_indices, col_indices = space.swap_state_at(1, 0, 1)
+
+    row_indices_expected = slice(None, None, None)
+    col_indices_expected = np.array([2, 3, 0, 1, 6, 7, 4, 5])
+
+    assert row_indices == row_indices_expected
+    assert np.all(col_indices == col_indices_expected)
+
+    row_indices, col_indices = space.swap_state_at(2, 0, 1)
+
+    row_indices_expected = slice(None, None, None)
+    col_indices_expected = np.array([4, 5, 6, 7, 0, 1, 2, 3])
+
+    assert row_indices == row_indices_expected
+    assert np.all(col_indices == col_indices_expected)
+
+
+def test_three_level_swap_indices():
+    positions = [(0, 0), (0, 1)]
+    register = Register(ThreeLevelAtom, positions, 0)
+    space = Space.create(register)
+    print(space)
+
+    # 0. |gg>
+    # 1. |hg>
+    # 2. |rg>
+    # 3. |gh>
+    # 4. |hh>
+    # 5. |rh>
+    # 6. |gr>
+    # 7. |hr>
+    # 8. |rr>
+
+    row_indices, col_indices = space.swap_state_at(0, 0, 1)
+
+    row_indices_expected = np.array(
+        [True, True, False, True, True, False, True, True, False]
+    )
+    col_indices_expected = np.array(
+        [
+            ThreeLevelAtom.string_to_integer("|hg>"),
+            ThreeLevelAtom.string_to_integer("|gg>"),
+            ThreeLevelAtom.string_to_integer("|hh>"),
+            ThreeLevelAtom.string_to_integer("|gh>"),
+            ThreeLevelAtom.string_to_integer("|hr>"),
+            ThreeLevelAtom.string_to_integer("|gr>"),
+        ]
+    )
+
+    assert np.all(row_indices == row_indices_expected)
+    assert np.all(col_indices == col_indices_expected)
+
+    # 0. |gg>
+    # 1. |hg>
+    # 2. |rg>
+    # 3. |gh>
+    # 4. |hh>
+    # 5. |rh>
+    # 6. |gr>
+    # 7. |hr>
+    # 8. |rr>
+
+    row_indices, col_indices = space.swap_state_at(0, 1, 2)
+
+    row_indices_expected = np.array(
+        [False, True, True, False, True, True, False, True, True]
+    )
+    col_indices_expected = np.array(
+        [
+            ThreeLevelAtom.string_to_integer("|rg>"),
+            ThreeLevelAtom.string_to_integer("|hg>"),
+            ThreeLevelAtom.string_to_integer("|rh>"),
+            ThreeLevelAtom.string_to_integer("|hh>"),
+            ThreeLevelAtom.string_to_integer("|rr>"),
+            ThreeLevelAtom.string_to_integer("|hr>"),
+        ]
+    )
+
+    assert np.all(row_indices == row_indices_expected)
+    assert np.all(col_indices == col_indices_expected)
+
+
+test_three_level_swap_indices()