Optimising Matrix Product State Simulations of Shor's Algorithm

TL;DR

This paper presents optimized classical simulation techniques for Shor's quantum factoring algorithm using matrix product states, significantly reducing resource requirements by exploiting entanglement properties.

Contribution

It introduces a novel entanglement mapping approach that depends on the factors of the order, enabling simulation of larger instances of Shor's algorithm.

Findings

Successfully simulated a 60-qubit instance of Shor's algorithm

Demonstrated improved efficiency over previous methods

Showed that entanglement structure can be exploited for better simulation

Abstract

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.