Online Convex Optimization of Programmable Quantum Computers to Simulate Time-Varying Quantum Channels

TL;DR

This paper introduces an online convex optimization approach using matrix exponentiated gradient descent to simulate time-varying quantum channels with sublinear regret, validated through experiments on dephasing channels.

Contribution

It presents a novel application of MEGD for adaptive quantum channel simulation, addressing the challenge of time-varying channels in programmable quantum processors.

Findings

Achieves sublinear regret in simulating adversarially changing quantum channels

Validates the approach experimentally on dephasing channels

Demonstrates effectiveness of online convex optimization in quantum simulation

Abstract

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.