QNN Loss for ODEs

docs/modules/classes.rst

@@ -65,9 +65,11 @@ Encoding Circuits
    encoding_circuit.MultiControlEncodingCircuit
    encoding_circuit.ChebyshevRx
    encoding_circuit.ParamZFeatureMap
+   encoding_circuit.KyriienkoEncodingCircuit
    encoding_circuit.QiskitEncodingCircuit
    encoding_circuit.QCNNEncodingCircuit
 
+
 Encoding Circuit Tools
 ------------------------------------
 
@@ -198,6 +200,7 @@ QNN Core
    qnn.lowlevel_qnn_base.LowLevelQNNBase
    qnn.loss.SquaredLoss
    qnn.loss.VarianceLoss
+   qnn.loss.ODELoss
    qnn.loss.ParameterRegularizationLoss
 
 Tools for training QNNs

src/squlearn/encoding_circuit/__init__.py

@@ -12,6 +12,7 @@
 from .circuit_library.chebyshev_rx import ChebyshevRx
 from .circuit_library.param_z_feature_map import ParamZFeatureMap
 from .circuit_library.qiskit_encoding_circuit import QiskitEncodingCircuit
+from .circuit_library.kyriienko_nonlinear_encoding_circuit import KyriienkoEncodingCircuit
 
 __all__ = [
     "PrunedEncodingCircuit",
@@ -30,4 +31,5 @@
     "ChebyshevRx",
     "ParamZFeatureMap",
     "QiskitEncodingCircuit",
+    "KyriienkoEncodingCircuit",
 ]

src/squlearn/encoding_circuit/circuit_library/kyriienko_nonlinear_encoding_circuit.py

@@ -0,0 +1,266 @@
+import numpy as np
+from typing import Union
+
+from qiskit.circuit import ParameterVector
+from qiskit import QuantumCircuit
+
+from ..encoding_circuit_base import EncodingCircuitBase
+from ..layered_encoding_circuit import LayeredEncodingCircuit, Layer
+
+
+class KyriienkoEncodingCircuit(EncodingCircuitBase):
+    r"""
+    Collection of encoding circuits introduced by Kyriienko et al. in reference [1].
+
+    The following circuits are implemented:
+
+    * ``chebyshev_tower`` encoding (Eq. 15),
+    * ``chebyshev_sparse`` encoding (Eq. 14)
+    * ``chebyshev_product`` encoding (Eq. 5).
+
+    Each encoding circuit is followed by a variational circuit as defined in reference [1],
+    RZ-RX-RZ layers followed by entangling layers. Two arrangements are possible:
+
+    * ``HEA``: Hardware Efficient Ansatz, with consecutive entangling layers
+      (See Figure 5a or Section IIIB in [1])
+    * ``ABA``: Alternating Block Ansatz with consecutive shifted entangling layers in
+      each block (See Figure 5b or Section IIIB in [1])
+
+    **Example: 4 qubits, a 2 dimensional feature vector, 1 encoding layer, 2 variational layers, variational arrangement ABA and Chebyshev tower encoding:**
+
+    .. plot::
+
+        from squlearn.encoding_circuit import KyriienkoEncodingCircuit
+        pqc = KyriienkoEncodingCircuit(4, 1, num_encoding_layers=1, num_variational_layers=2,
+                                       variational_arrangement="ABA")
+        pqc.draw(output="mpl", style={'fontsize':15,'subfontsize': 10})
+
+
+    Args:
+        num_qubits (int): Number of qubits of the encoding circuit
+        encoding_style (str): Style of the encoding. Options are ``'chebyshev_tower'`` (default),
+                              ``'chebyshev_sparse'`` and ``'chebyshev_product'``
+                              (see reference [1], Equation  15, 14 and 5 respectively)
+        variational_arrangement (str): Arrangement of the variational layers. Options are
+                                       ``'HEA'`` (default) and ``'ABA'`` (see reference [1],
+                                       section IIIB)
+        num_encoding_layers (int): Number of encoding layers (default: 1)
+        num_variational_layers (int): Number of variational layers (default: 1)
+        rotation_gate (str): Rotation gate to use. Either ``'rx'``, ``'ry'`` or
+                             ``'rz'`` (default: ``'ry'`` as in reference [1])
+        num_features (int): Dimension of the feature vector (default: 1)
+        block_width (int): Only necessary for arrangement ``'ABA'``. Width (vertical) of each
+                           blocks for the ABA arrangement (default: 2), also refered as Nb in
+                           the paper. Must be a divisor of the number of qubits
+        block_depth (int): Only necessary for arrangement ``'ABA'``. Depth (horizontal) of each
+                           blocks for the ABA arrangement (default: 1), also refered as b in
+                           the paper.
+
+    References
+    ----------
+    [1]: O. Kyriienko et al., "Solving nonlinear differential equations with differentiable
+    quantum circuits", `arXiv:2011.10395 (2021). <https://arxiv.org/pdf/2011.10395>`_
+    """
+
+    def __init__(
+        self,
+        num_qubits: int,
+        num_features: int = 1,
+        encoding_style: str = "chebyshev_tower",
+        variational_arrangement: str = "HEA",
+        num_encoding_layers: int = 1,
+        num_variational_layers: int = 1,
+        rotation_gate: str = "ry",
+        block_width: int = 2,
+        block_depth: int = 1,
+    ) -> None:
+        super().__init__(num_qubits, num_features)
+
+        self.num_encoding_layers = num_encoding_layers
+        self.num_variational_layers = num_variational_layers
+        self.variational_arrangement = variational_arrangement
+        self.encoding_style = encoding_style
+        self.block_width = block_width
+        self.block_depth = block_depth
+        self.alpha = 2.0
+        self.rotation_gate = rotation_gate
+        self.num_chebyshev = self.num_qubits
+        self.tower = True if encoding_style == "chebyshev_tower" else False
+
+        if self.variational_arrangement not in ("HEA", "ABA"):
+            raise ValueError("Arrangement must be either 'HEA' or 'ABA'")
+
+        if self.num_qubits < 2:
+            raise ValueError("Variational circuit HEE_rzrxrz requires at least two qubits.")
+
+        if self.rotation_gate not in ("rx", "ry", "rz"):
+            raise ValueError("Rotation gate must be either 'rx', 'ry' or 'rz'")
+
+    @property
+    def parameter_bounds(self) -> np.ndarray:
+        """The bounds of the trainable parameters of the HEE_rzrxrz encoding circuit."""
+        return np.array([[-2.0 * np.pi, 2.0 * np.pi]] * self.num_parameters)
+
+    @property
+    def num_parameters(self) -> int:
+        """The number of trainable parameters of the variational circuit."""
+        if self.variational_arrangement == "HEA":
+            num_param = 3 * self.num_qubits * self.num_variational_layers
+        elif self.variational_arrangement == "ABA":
+            num_param = 3 * self.num_qubits * self.block_depth * self.num_variational_layers
+        return num_param
+
+    def get_params(self, deep: bool = True) -> dict:
+        """
+        Returns hyper-parameters and their values of the Kyriienko encoding circuit
+
+        Args:
+            deep (bool): If True, also the parameters for
+                         contained objects are returned (default=True).
+
+        Return:
+            Dictionary with hyper-parameters and values.
+        """
+        params = super().get_params()
+        params["num_encoding_layers"] = self.num_encoding_layers
+        params["num_variational_layers"] = self.num_variational_layers
+        params["variational_arrangement"] = self.variational_arrangement
+        params["encoding_style"] = self.encoding_style
+        params["block_width"] = self.block_width
+        params["block_depth"] = self.block_depth
+        params["rotation_gate"] = self.rotation_gate
+
+        return params
+
+    def get_circuit(
+        self,
+        features: Union[ParameterVector, np.ndarray],
+        parameters: Union[ParameterVector, np.ndarray],
+    ) -> QuantumCircuit:
+        """
+        Generates and returns the circuit of the Kyriienko encoding circuit
+
+        Args:
+            features (Union[ParameterVector, np.ndarray]): The features to encode
+            parameters (Union[ParameterVector, np.ndarray]): The parameters of the encoding circuit
+
+        Returns:
+            QuantumCircuit: The encoding circuit
+        """
+
+        def mapping(x, i):
+            """Non-linear mapping for x: alpha*i*arccos(x)"""
+            return self.alpha * i * np.arccos(x)
+
+        def variational_gate_block(
+            QC,
+            num_layers,
+            num_qubits,
+            shift_parameter=0,
+            index_offset=0,
+            variational_arrangement="HEA",
+        ):
+            """
+            Implements an Encoding circuit with layers of RZRXRZ followed by entangling layers.
+
+            """
+            qubit_starting_index = shift_parameter
+            num_qubits += shift_parameter
+            for layer in range(num_layers):
+                for i in range(qubit_starting_index, num_qubits):
+                    if i >= self.num_qubits:
+                        i -= self.num_qubits
+                    QC.rz(parameters[index_offset], i)
+                    QC.rx(parameters[index_offset + 1], i)
+                    QC.rz(parameters[index_offset + 2], i)
+                    index_offset += 3
+                if variational_arrangement == "HEA":
+                    for start in (0, 1):
+                        for i in range(start, num_qubits - 1, 2):
+                            QC.cx(i, i + 1)
+
+                elif variational_arrangement == "ABA":
+                    for start in (qubit_starting_index, qubit_starting_index + 1):
+                        for i in range(start, num_qubits - 1, 2):
+                            if i + 1 < self.num_qubits:
+                                QC.cx(i, i + 1)
+                            else:
+                                QC.cx(i, 0)
+            return QC, index_offset
+
+        nfeature = len(features)
+
+        if self.encoding_style == "chebyshev_product":
+            QC = LayeredEncodingCircuit(num_qubits=self.num_qubits, num_features=self.num_features)
+            layer = Layer(QC)
+            {"rx": layer.Rx, "ry": layer.Ry, "rz": layer.Rz}[self.rotation_gate](
+                "x", encoding=np.arcsin
+            )
+            QC.add_layer(layer, num_layers=self.num_encoding_layers)
+
+        elif self.encoding_style in ("chebyshev_tower", "chebyshev_sparse"):
+            QC = QuantumCircuit(self.num_qubits)
+            for layer in range(self.num_encoding_layers):
+                index_offset_encoding = 0
+                iqubit = 0
+                icheb = 1
+
+                inner = self.num_features
+                outer = self.num_chebyshev
+
+                for outer_ in range(outer):
+                    for inner_ in range(inner):
+                        {"rx": QC.rx, "ry": QC.ry, "rz": QC.rz}[self.rotation_gate](
+                            mapping(features[index_offset_encoding % nfeature], icheb),
+                            iqubit % self.num_qubits,
+                        )
+                        iqubit += 1
+                        index_offset_encoding += 1
+                    icheb = 1 + icheb if self.tower else 1
+
+        index_offset_variational = 0
+        if self.variational_arrangement == "HEA":
+            QC = variational_gate_block(QC, self.num_variational_layers, self.num_qubits)[0]
+        elif self.variational_arrangement == "ABA":
+            if self.num_qubits % self.block_width != 0:
+                raise ValueError("Block width must be a divisor of the number of qubits.")
+
+            number_of_blocks = int(np.ceil(self.num_qubits / self.block_width))  # vertical blocks
+            shifting_factor = np.floor(self.block_width / 2)
+            for layer in range(self.num_variational_layers):
+                if layer % 2 == 0:  # even layer
+                    for block in range(number_of_blocks):
+                        QC, index_offset_variational = variational_gate_block(
+                            QC,
+                            self.block_depth,
+                            self.block_width,
+                            int(block * self.block_width),
+                            index_offset_variational,
+                            variational_arrangement="ABA",
+                        )
+                else:
+                    for block in range(number_of_blocks):
+                        if (
+                            shifting_factor + block * self.block_width + self.block_width
+                            <= self.num_qubits
+                        ):
+                            QC, index_offset_variational = variational_gate_block(
+                                QC,
+                                self.block_depth,
+                                self.block_width,
+                                int(shifting_factor + block * self.block_width),
+                                index_offset_variational,
+                                variational_arrangement="ABA",
+                            )
+                        else:  # if the block is out of the range of the qubits, we need to wrap around
+                            QC, index_offset_variational = variational_gate_block(
+                                QC,
+                                self.block_depth,
+                                self.block_width,
+                                int(shifting_factor + block * self.block_width),
+                                index_offset_variational,
+                                variational_arrangement="ABA",
+                            )
+                QC.barrier()
+
+        return QC

src/squlearn/qnn/__init__.py

@@ -1,6 +1,6 @@
 """QNN module for classification and regression."""
 
-from .loss import SquaredLoss, VarianceLoss, ConstantLoss, ParameterRegularizationLoss
+from .loss import SquaredLoss, VarianceLoss, ConstantLoss, ParameterRegularizationLoss, ODELoss
 from .qnnc import QNNClassifier
 from .qnnr import QNNRegressor
 from .training import get_variance_fac, get_lr_decay, ShotsFromRSTD
@@ -9,6 +9,7 @@
     "SquaredLoss",
     "VarianceLoss",
     "ConstantLoss",
+    "ODELoss",
     "ParameterRegularizationLoss",
     "QNNClassifier",
     "QNNRegressor",