Split-Evolution Quantum Phase Estimation for Particle-Conserving Hamiltonians

TL;DR

This paper demonstrates a modified quantum phase estimation method called SE-QPE on a quantum computer, showing resource savings and practical advantages for particle-conserving Hamiltonians in quantum chemistry.

Contribution

The paper introduces SE-QPE, a resource-efficient variant of QPE compatible with non-exact eigenstates, and provides experimental and resource analysis on a real quantum device.

Findings

SE-QPE reduces CX count by about 33% and T count by 25% in resource estimates.

Experimental demonstration on a four-qubit system yields consistent energy estimates.

SE-QPE's resource advantages grow with higher phase powers, especially in chemistry Hamiltonians.

Abstract

We present a hardware demonstration and resource analysis of split-evolution quantum phase estimation (SE-QPE) on a Quantinuum System Model H2 quantum computer. SE-QPE is a modification to canonical QPE for particle-conserving Hamiltonians in which controlled time evolution is replaced by CSWAP-based interference between a target register and a reference register. For factorizations of time evolution with a shared eigenbasis, SE-QPE preserves the phase-register outcome distribution of canonical QPE and, unlike with compute--uncompute substitutions, it remains compatible with non-exact eigenstates. The substitution removes controlled-simulation overhead and enables parallel evolution on two registers, reducing the depth of each phase-kickback block. Resource analysis for Trotterized double-factorized chemistry Hamiltonians shows that the substitution becomes increasingly favorable at higher phase powers, as such combining QPE and SE-QPE implementations can be a useful option. Over a range of FeMoco active spaces, SE-QPE reduces time evolution resources, with asymptotic reductions of about 33% in CX count, 25% in $T$ count, and an asymptotic depth ratio of $3/N$ for CX layers. On Quantinuum H2-2, a four-qubit model ethylene demonstration with explicit inverse QFT and repeated phase-kickback steps up to 6 phase bits yields distinct energies and shows the auxiliary registers provide useful error detection filters.