Compilation by stochastic Hamiltonian sparsification

TL;DR

This paper introduces a stochastic Hamiltonian sparsification method for quantum simulation that reduces the number of terms in the Hamiltonian, improving scalability and error suppression compared to existing methods.

Contribution

The paper proposes a novel stochastic sparsification scheme for Hamiltonians that interpolates between qDRIFT and randomized Trotter, enhancing efficiency and error control in quantum simulations.

Findings

Quadratic error suppression over deterministic methods.

Outperforms qDRIFT and randomized Trotter at intermediate gate budgets.

Provides an optimal probability distribution for Hamiltonian term selection.

Abstract

Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.