Quantum-circuit design for efficient simulations of many-body quantum dynamics

TL;DR

This paper introduces an autonomous quantum-circuit design algorithm that efficiently simulates many-body quantum dynamics with optimal space and near-optimal time complexity, including parallelization and error analysis.

Contribution

It presents a novel algorithm for constructing efficient quantum circuits for many-body dynamics, optimizing space, time, and parallel execution, with applications to complex models.

Findings

Constructs circuits for Kitaev's honeycomb model and BCS superconductivity.

Provides numerical evidence that error bounds may overestimate actual errors.

Demonstrates near-optimal circuit sequences with optimized parallel execution.

Abstract

We construct an efficient autonomous quantum-circuit design algorithm for creating efficient quantum circuits to simulate Hamiltonian many-body quantum dynamics for arbitrary input states. The resultant quantum circuits have optimal space complexity and employ a sequence of gates that is close to optimal with respect to time complexity. We also devise an algorithm that exploits commutativity to optimize the circuits for parallel execution. As examples, we show how our autonomous algorithm constructs circuits for simulating the dynamics of Kitaev's honeycomb model and the Bardeen-Cooper-Schrieffer model of superconductivity. Furthermore we provide numerical evidence that the rigorously proven upper bounds for the simulation error here and in previous work may sometimes overestimate the error by orders of magnitude compared to the best achievable performance for some physics-inspired simulations.