Non-Markovian Quantum Process Tomography

TL;DR

This paper introduces process tensor tomography, a comprehensive method for characterizing non-Markovian quantum dynamics, enabling better diagnostics and control of correlated noise in quantum devices, with demonstrated improvements on superconducting qubits.

Contribution

It presents a formalism and practical algorithms for process tensor tomography, extending quantum process tomography to non-Markovian dynamics and improving device noise management.

Findings

Efficient process tensor tomography algorithms developed.

Application shows improved multi-time circuit fidelities.

Method aids in diagnostics and control of correlated noise.

Abstract

Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices: ones that can surpass classical computers for particular tasks -- but progress in characterisation must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a generalisation of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary post-processing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterisation is a pathway to diagnostics and informed control of correlated noise. As an example application of the hardware-agnostic technique, we show how its predictive control can be used to substantially improve multi-time circuit fidelities on superconducting quantum devices. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.