Continuous Hamiltonian dynamics on digital quantum computers without discretization error

TL;DR

This paper presents a quantum algorithm for simulating Hamiltonian dynamics with finite circuit depth and zero discretization error, suitable for noisy intermediate-scale quantum hardware, by controlling the number of gates and expectation value attenuation.

Contribution

The authors introduce a novel algorithm that achieves zero discretization error with finite circuit depth, independent of precision, and adapts well to non-sparse and time-dependent Hamiltonians.

Findings

Gate count scales as $O(t^2\,\mu^2)$, independent of precision

Algorithm is suitable for noisy hardware with moderate circuit depth

Generalizes to time-dependent Hamiltonians like in adiabatic processes

Abstract

We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number of gates comes at the cost of an attenuation of the measured expectation value by a known amplitude, requiring more shots per circuit. The gate count for simulation up to time $t$ is $O(t^2\mu^2)$ with $\mu$ the $1$-norm of the Hamiltonian, without dependence on the precision desired on the result, providing a significant improvement over previous algorithms. The only dependence in the norm makes it particularly adapted to non-sparse Hamiltonians. The algorithm generalizes to time-dependent Hamiltonians, appearing for example in adiabatic state preparation. These properties make it particularly suitable for present-day relatively noisy hardware that supports only circuits with moderate depth.