Symmetry-Adjusted Classical Shadows

Open-source codes for performing classical shadows, particularly for noisy quantum simulations of fermions and qubits. Based primarily on the following papers:

• https://arxiv.org/abs/2310.03071 - Develops an error-mitigation strategy using symmetries to introduce robustness to noise in the quantum computer. Also introduces a number of modifications and extensions of the above protocols, including an optimal circuit design for fermionic Gaussian unitaries
• https://arxiv.org/abs/2002.08953 - Introduces the concept of classical shadows, particularly demonstrates the application to local qubit (Pauli) measurements (random single-qubit Clifford gates)
• https://arxiv.org/abs/2010.16094 - Constructs classical shadows protocols for local fermion measurements (random fermionic Gaussian unitary (matchgate) & Clifford circuits)

The base implementation in Python requires OpenFermion and Cirq. The numerical examples additionally require qsimcirq, ReCirq, and the Julia package ITensor.

The files are organized as follows. For either fermion_shadows or pauli_shadows, codes in the prediction directory provide the routines to postprocess the quantum measurement data (description of random unitary and bit string) into numerical estimates of desired observables (using either a Pauli or Majorana operator decomposition). Included are also the robust estimators, using either Symmetry-Adjusted Classical Shadows if the system obeys a U(1) symmetry, or Robust Shadow Estimation from separately obtained calibration data. Codes in the simulation directory provide examples for running the protocol (i.e., numerically simulating the quantum circuits to obtain samples, which are then postprocessed into observable predictions).

Working examples/test codes are provided for each protocol. If you have any questions, please do not hesitate to reach out.