An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

TL;DR

This paper introduces an algebraic algorithm for compressing quantum circuits used in Hamiltonian simulation, resulting in shallow, topology-friendly circuits suitable for NISQ devices, with scalability to over a thousand spins.

Contribution

It develops a matrix analysis-based method for efficient circuit compression that maintains shallow depth and simple topology, advancing quantum simulation on near-term hardware.

Findings

Circuit depth is independent of simulation time.

Algorithm scales cubically with the number of spins.

Compressed circuits are suitable for NISQ devices.

Abstract

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in terms of chip size and error rates. Shallow quantum circuits with uncomplicated topologies are essential for successful applications in the NISQ era. Based on matrix analysis, we derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The depth of the compressed circuits is independent of simulation time and grows linearly with the number of spins. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $\mathcal{O}(10^3)$ spins. The resulting quantum circuits have a simple nearest-neighbor topology, which makes them ideally suited for NISQ devices.