I recently posted a new paper on arXiv! Titled Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers, I alongside Di Luo and Bryan Clark develop a way to bring classical shadows [1] to process tomography. Check it out!
Abstract
Ryan Levy, Di Luo, Bryan K. Clark
Quantum process tomography is a powerful tool 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 classical shadow method, ShadowQPT, for quantum process tomography. ShadowQPT allows for the reconstruction of the Choi matrix for unitary and non-unitary processes including an efficient reconstruction of fixed-sized reduced processes; we also show how to predict the overlap between any arbitrary state and the output of the quantum channel on a different arbitrary state. We introduce both a scheme using ancilla qubits as well as a two-sided scheme with unitaries before and after the channel. A number of additional approximations and improvements are developed including the use of a pair-factorized Clifford shadow and a series of post-processing techniques which significantly enhance the accuracy for recovering the quantum channel. Both the theoretical scaling for large systems and the practicality of using shadow tomography on NISQ-era hardware are considered. Our algorithms have been implemented with both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to n=4 qubits (equivalent to the experimental complexity of n=8 qubits for quantum state tomography) and achieved good performance.