Phase Estimation with Partially Randomized Time Evolution

2025/03/07 by Jakob Günther, Freek Witteveen, Günther, Jakob +10 · 1 voice · 20 citations
Engineering · Mathematics · #Estimation #Estimation theory #Extrapolation #Markov Chains and Monte Carlo Methods #Phase (matter) #Sparse and Compressive Sensing Techniques #Stability (learning theory) #Statistical Methods and Inference

paper · pdf · open access · doi:10.1103/ynxb-p2xq

published in PRX Quantum 7(2) (American Physical Society)

openalex publication_date 2026/03/31 · openalex created_date 2026/04/02 · openalex updated_date 2026/08/05

Abstract

Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground-state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation subroutine. In this paper we use randomization to speed up product formulas, one of the standard approaches to Hamiltonian simulation. We propose partially randomized Hamiltonian simulation methods in which some terms are kept deterministically and others are randomly sampled. We perform a detailed resource estimate for single-ancilla phase estimation using partially randomized product formulas for benchmark systems in quantum chemistry and obtain orders-of-magnitude improvements compared to other simulations based on product formulas. When applied to the hydrogen chain, we have numerical evidence that our methods exhibit asymptotic scaling with the system size that is competitive with the best known qubitization approaches.

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Discussions

• I love catching up on my “to read” list of papers on planes. And today found time to read some recent work on randomized phase estimation arxiv.org/abs/2503.05647 from Gunther et al [bsky, 19 points, 2 comments]

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