Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers*

Quantum process tomography is crucial for understanding quantum channels and characterizing properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [1], we have developed a method using classical shadows for quantum process tomography, ShadowQPT. We have proved rigorous measurement complexity for ShadowQPT and provided new post-processing techniques for improving the accuracy. Furthermore, our approach has been implemented on the IonQ trapped ion quantum computer; we benchmark reconstructions for unitary and non-unitary processes of a channel of up to n=4 qubits (equivalent to the complexity of n=8 qubits in state tomography) as well as determining input-output state overlaps. We show that ShadowQPT is efficient and provides new advancement on quantum process tomography in near-term and future quantum devices.

[1] H.-Y. Huang, R. Kueng, and J. Preskill, Nature Physics 16, 1050 (2020)