Leveraging state sparsity for more efficient quantum simulations

TL;DR

This paper introduces a new quantum simulation method that exploits state sparsity to significantly reduce memory and runtime, enabling the simulation of complex quantum algorithms on standard hardware.

Contribution

The authors present a novel simulation technique leveraging quantum state sparsity, including optimizations like gate scheduling, to efficiently simulate large quantum algorithms on classical hardware.

Findings

Successfully simulated a 20-bit factoring instance with 102 qubits in under 4 minutes.

Simulated elliptic curve discrete logarithm over a 10-bit curve with 110 qubits.

First to fully simulate a quantum algorithm for elliptic curve discrete logarithms.

Abstract

High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to special structure in the algorithm or even in the underlying problem. We thus introduce a new simulation method that exploits this sparsity to reduce memory usage and simulation runtime. Moreover, our prototype implementation includes optimizations such as gate (re)scheduling, which amortizes data structure accesses and reduces memory usage. To benchmark our implementation, we run quantum algorithms for factoring, computing integer and elliptic curve discrete logarithms, and for chemistry. Our simulator successfully runs a factoring instance of a 20-bit number using 102 qubits, and elliptic curve discrete logarithm over a 10-bit curve with 110 qubits. While previous work needed a supercomputer to simulate such instances of factoring, our approach succeeds in less than 4 minutes using a single core and less than 100 MB of memory. To the best of our knowledge, we are the first to fully simulate a quantum algorithm to compute elliptic curve discrete logarithms.