Quantum Shapley Value Toolbox

Experimental Python toolbox for Shapley values with uncertain value functions in general (see Shapley Values with Uncertain Value Functions: arxiv.2301.08086) and quantum Shapley values in particular (see Explainable Quantum Machine Learning: arxiv.2301.09138). Quantum Shapley values provide a method to measure the influence of gates within quantum circuit with respect to a freely customizable value function, for example expressibility or entanglement capability.

Usage

For quantum Shapley values, the toolbox presumes a representation of quantum circuits via Qiskit.

Minimal working example:

from qiskit import Aer
from qiskit.utils import QuantumInstance
from qiskit.circuit.library import QAOAAnsatz
from qiskit.opflow import PauliSumOp
from qshap import QuantumShapleyValues
from qvalues import value_H
from tools import visualize_shapleys

# define circuit
H = PauliSumOp.from_list([('ZZI', 1), ('ZII', 2), ('ZIZ', -3)])
qc = QAOAAnsatz(cost_operator=H, reps=1)
qc = qc.decompose().decompose().decompose()
qc = qc.assign_parameters([0]*len(qc.parameters))

# define quantum instance
quantum_instance = QuantumInstance(backend=Aer.get_backend('statevector_simulator'))

# setup quantum Shapley values
qsv = QuantumShapleyValues(qc, value_fun=value_H, value_kwargs_dict=dict(H=H), quantum_instance=quantum_instance)
print(qsv)

# evaluate quantum Shapley values
qsv()

# show results
print(qsv.phi_dict)
visualize_shapleys(qc, phi_dict=qsv.phi_dict).draw()

As a result, the quantum Shapley values assigned to each gate are plotted:

📖 Citation

If you find this code useful in your research, please consider citing:

@misc{https://doi.org/10.48550/arxiv.2301.09138,
      doi = {10.48550/ARXIV.2301.09138},
      url = {https://arxiv.org/abs/2301.09138},
      author = {Heese, Raoul and Gerlach, Thore and Mücke, Sascha and Müller, Sabine and Jakobs, Matthias and Piatkowski, Nico},
      keywords = {Quantum Physics (quant-ph), Machine Learning (cs.LG), Machine Learning (stat.ML), FOS: Physical sciences, FOS: Physical sciences, FOS: Computer and information sciences, FOS: Computer and information sciences},
      title = {Explainable Quantum Machine Learning},
      publisher = {arXiv},
      year = {2023},
      copyright = {arXiv.org perpetual, non-exclusive license}
     }