A Clifford circuit is a pivotal tool in quantum computing and has extensive applications in quantum error correction codes and topological quantum computing. Hence, it is essential to benchmark and verify the effect of Clifford circuits against noise and errors. Standard quantum process tomography is a fundamental technique for fully characterizing quantum dynamics, but at the cost of exponential time, space, and computation with an increasing number of qubits. Here, we propose an efficient quantum process tomography method for Clifford circuits. Combining with the stabilizer formalism, we prove theoretically that, for an $n$-qubit Clifford circuit, our method merely needs $m$ ancillary qubits and $\lceil n/m\rceil$ input stabilizer states to obtain the quantum process. Numerical simulation results show that our method could perfectly rebuild the unknown Clifford quantum circuit with fidelity over $99.99\%$ to six qubit cases. Our work provides an efficient and practical approach to benchmark and verify Clifford circuits.

• Received 26 June 2022
• Revised 4 January 2023
• Accepted 5 September 2023

DOI:https://doi.org/10.1103/PhysRevA.108.032419