Accurately Simulating the Time Evolution of an Ising Model with Echo Verified Clifford Data Regression on a Superconducting Quantum Computer

TL;DR

This paper introduces an error mitigation method combining Echo Verification and Clifford Data Regression, enabling accurate simulation of Ising model dynamics on superconducting quantum computers despite noise.

Contribution

The paper develops and demonstrates a novel error mitigation approach that effectively learns and compensates for noise in quantum simulations of many-body systems.

Findings

Accurate simulation of Ising model evolution with up to 35 sites.

Effective noise learning and mitigation via EVCDR.

Robust results at circuit depths up to 173 layers.

Abstract

We present an error mitigation strategy composed of Echo Verification (EV) and Clifford Data Regression (CDR), the combination of which allows one to learn the effect of the quantum noise channel to extract error mitigated estimates for the expectation value of Pauli observables. We analyse the behaviour of the method under the depolarizing channel and derive an estimator for the depolarization rate in terms of the ancilla purity and postselection probability. We also highlight the sensitivity of this probability to noise, a potential bottleneck for the technique. We subsequently consider a more general noise channel consisting of arbitrary Pauli errors, which reveals a linear relationship between the error rates and the estimation of expectation values, suggesting the learnability of noise in EV by regression techniques. Finally, we present a practical demonstration of Echo Verified Clifford Data Regression (EVCDR) on a superconducting quantum computer and observe accurate results for the time evolution of an Ising model over spin-lattices consisting of up to 35 sites and circuit depths up to 173 entangling layers.