pyXBM: Python Extended Bell Measurement

pyXBM efficiently evaluates $<\psi_0|A|\psi_1>$ for arbitrary $A\in\mathbb{C}^{2^n\times2^n}$ and $|\psi_0>,|\psi_1>\in\mathbb{C}^{2^n}$ by reducing the number of unique quantum circuits required.

Paper: https://quantum-journal.org/papers/q-2022-04-13-688/

Requirements

Software	Version
Python	3.6.9
Qiskit	0.25.0
SciPy	1.5.4

To run Jupyter Notebooks,

Software	Version
SymPy	1.7.1
OpenFermion	1.1.0
PyYAML	5.4.1
Matplotlib	3.3.4
seaborn	0.11.1
tqdm	4.57.0

Download term_grouping.py from https://www.github.com/teaguetomesh/vqe-term-grouping/
Rewrite line 257
- return max_cliques
+ return max_cliques, term_reqs

Usage

see sample.ipynb

from xbm import get_all_meas_circs_bits_coefs
from utils import eval_expectation

psi_0 = ... # qiskit.QuantumCircuit
psi_1 = ... # qiskit.QuantumCircuit
psi_2 = ... # qiskit.QuantumCircuit
mat_A = ... # numpy.ndarray
qins  = ... # qiskit.aqua.QuantumInstance
p_vec = ... # qiskit.circuit.parametervector.ParameterVector, parameter vectors for psi_0, psi_1 and psi_2

meas_1 = get_all_meas_circs_bits_coefs(psi_0, psi_1, mat_A) # <psi_0|A|psi_1>
meas_2 = get_all_meas_circs_bits_coefs(psi_2, None, mat_A @ np.conjugate(mat_A).T) # <psi_2|A^2|psi_2>

params = ... # numpy.ndarray, initial parameters for psi_0, psi_1 and psi_2
for loop in range(nb_loops):
    exp = eval_expectation(meas_1+meas_2, qins, params_dict={p_vec: params})
    params = ... # parameter update

Citing pyXBM

If you find it useful to use this module in your research, please cite the following paper.

Kondo, R., Sato, Y., Koide, S., Kajita, S. and Takamatsu, H., Computationally Efficient Quantum Expectation with Extended Bell Measurements, Quantum, Vol.6, (2022), p.688.

In Bibtex format:

@article{Kondo2022computationally,
  doi = {10.22331/q-2022-04-13-688},
  url = {https://doi.org/10.22331/q-2022-04-13-688},
  title = {Computationally {E}fficient {Q}uantum {E}xpectation with {E}xtended {B}ell {M}easurements},
  author = {Kondo, Ruho and Sato, Yuki and Koide, Satoshi and Kajita, Seiji and Takamatsu, Hideki},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {688},
  month = apr,
  year = {2022}
}

License

This project is licensed under the Apache License Version 2.0 - see the LICENSE.txt file for details