Approximation Algorithm for Noisy Quantum Circuit Simulation

TL;DR

This paper presents a new tensor network-based approximation algorithm that significantly extends the size of noisy quantum circuits that can be simulated, achieving up to 225 qubits, and offers speed improvements over existing methods.

Contribution

It introduces a novel tensor network diagram and SVD-based approximation method for simulating noisy quantum circuits, enhancing scalability and efficiency.

Findings

Simulates circuits with up to 225 qubits and 20 noises within 1.8 hours.

Provides a speedup over the quantum trajectories method.

Reduces the number of samples needed when noise rate is small.

Abstract

Simulating noisy quantum circuits is vital in designing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical counterpart because of the quantum state explosion problem (the dimension of state space is exponential in the number of qubits) and the complex (non-unitary) representation of noises. Consequently, only noisy circuits with up to about 50 qubits can be simulated approximately well. This paper introduces a novel approximation algorithm for simulating noisy quantum circuits when the noisy effectiveness is insignificant to improve the scalability of the circuits that can be simulated. The algorithm is based on a new tensor network diagram for the noisy simulation and uses the singular value decomposition to approximate the tensors of quantum noises in the diagram. The contraction of the tensor network diagram is implemented on Google's TensorNetwork. The effectiveness and utility of the algorithm are demonstrated by experimenting on a series of practical quantum circuits with realistic superconducting noise models. As a result, our algorithm can approximately simulate quantum circuits with up to 225 qubits and 20 noises (within about 1.8 hours). In particular, our method offers a speedup over the commonly-used approximation (sampling) algorithm -- quantum trajectories method. Furthermore, our approach can significantly reduce the number of samples in the quantum trajectories method when the noise rate is small enough.