Stochastic Approach For Simulating Quantum Noise Using Tensor Networks

TL;DR

This paper introduces a stochastic ensemble method using tensor networks to simulate quantum noise more efficiently than traditional density matrix approaches, enabling larger system simulations with low error.

Contribution

The paper presents a novel stochastic simulation method with tensor networks for quantum noise, outperforming density matrix methods for larger qubit systems.

Findings

Stochastic ensemble approach achieves low error for up to 30 qubits.

Tensor slicing enables simulation of 100-qubit QAOA circuits.

Method is embarrassingly parallel and suitable for supercomputers.

Abstract

Noisy quantum simulation is challenging since one has to take into account the stochastic nature of the process. The dominating method for it is the density matrix approach. In this paper, we evaluate conditions for which this method is inferior to a substantially simpler way of simulation. Our approach uses stochastic ensembles of quantum circuits, where random Kraus operators are applied to original quantum gates to represent random errors for modeling quantum channels. We show that our stochastic simulation error is relatively low, even for large numbers of qubits. We implemented this approach as a part of the QTensor package. While usual density matrix simulations on average hardware are challenging at $n>15$, we show that for up to $n\lesssim 30$, it is possible to run embarrassingly parallel simulations with $<1\%$ error. By using the tensor slicing technique, we can simulate up to 100 qubit QAOA circuits with high depth using supercomputers.