When is randomization advantageous in quantum simulation?

arXiv (Cornell University)

Abstract

We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller contributions are sampled stochastically. Crucially, we analyze how stochastic and approximation errors propagate through block-encoding and QSVT procedures. To benchmark this approach, we construct ensembles of random Hamiltonians with controlled coefficient dispersion, locality, and number of terms, designed to favor randomization, and therefore providing an upper bound on its practical advantage. For Hamiltonians with many terms and highly inhomogeneous coefficient distributions, randomized methods reduce gate counts by up to an order of magnitude. However, this advantage is confined to moderate-precision regimes: as the target error decreases, deterministic methods become more efficient, with a crossover near $\varepsilon \sim 10^{-3}$. Although this regime partially overlaps with quantum chemistry Hamiltonians, realistic systems exhibit additional structure, such as commutation patterns, not captured by our model, which are expected to further favor deterministic approaches.

Authors 5

1. Francesco Paganelli Aachen Leiden Institute of Physics (LION)

   Leiden University · European Organization for Nuclear Research

   Affiliation as printed

   European Organization for Nuclear Research (CERN) , Geneva 1211 , Switzerland

   Leiden Institute of Physics (LION) , Leiden University , Leiden 2333 CA , The Netherlands

2. Michele Grossi

   European Organization for Nuclear Research

   Affiliation as printed

   European Organization for Nuclear Research (CERN) , Geneva 1211 , Switzerland

3. Andrea Giachero
4. T. E. O'Brien Aachen Leiden Institute of Physics (LION)

   Leiden University

   Affiliation as printed

   Google Quantum AI , Munich , Germany

   Leiden Institute of Physics (LION) , Leiden University , Leiden 2333 CA , The Netherlands

5. Oriel Kiss