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arxiv: 2604.14921 · v1 · submitted 2026-04-16 · 🪐 quant-ph · physics.comp-ph

Recognition: unknown

Split-Evolution Quantum Phase Estimation for Particle-Conserving Hamiltonians

Megan Cerys Rowe , Carlo A. Gaggioli , Ludmila Szulakowska , David Mu\~noz Ramo , David Zsolt Manrique
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:58 UTC · model grok-4.3

classification 🪐 quant-ph physics.comp-ph
keywords split-evolution QPEquantum phase estimationparticle-conserving HamiltoniansCSWAP interferencequantum chemistry simulationTrotterized Hamiltoniansresource reductionhardware demonstration
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The pith

Split-evolution QPE replaces controlled time evolution with CSWAP interference between two registers for particle-conserving Hamiltonians.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces split-evolution quantum phase estimation (SE-QPE) as a modification to standard quantum phase estimation tailored to particle-conserving Hamiltonians. It substitutes controlled time evolution with CSWAP-based interference between a target register and a reference register, which preserves the phase-register outcome distribution when time-evolution factorizations share an eigenbasis. This approach eliminates controlled-simulation overhead, supports non-exact eigenstates, and allows parallel evolution on separate registers to reduce circuit depth. Resource analysis for Trotterized chemistry Hamiltonians shows growing savings at higher precision, with concrete reductions for FeMoco active spaces. A four-qubit ethylene demonstration on Quantinuum H2 hardware confirms distinct energies and auxiliary-register error detection.

Core claim

For particle-conserving Hamiltonians that admit factorizations of time evolution with a shared eigenbasis, SE-QPE replaces controlled time evolution with CSWAP-based interference between a target register and a reference register. This substitution preserves the phase-register outcome distribution of canonical QPE, remains compatible with non-exact eigenstates unlike compute-uncompute methods, removes controlled-simulation overhead, and enables parallel evolution on two registers, thereby reducing the depth of each phase-kickback block.

What carries the argument

CSWAP-based interference between target and reference registers that replicates phase kickback for shared-eigenbasis factorizations of time evolution.

If this is right

  • Resource analysis for Trotterized double-factorized chemistry Hamiltonians shows the substitution becomes increasingly favorable at higher phase powers.
  • Over a range of FeMoco active spaces, SE-QPE reduces time-evolution resources with asymptotic reductions of about 33% in CX count and 25% in T count, plus an asymptotic CX depth ratio of 3/N.
  • Combining QPE and SE-QPE implementations can serve as a useful option for chemistry simulations.
  • A hardware demonstration on Quantinuum H2-2 with a four-qubit ethylene model using explicit inverse QFT and up to 6 phase bits yields distinct energies while auxiliary registers provide error-detection filters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The parallel evolution on two registers could improve qubit utilization on hardware with limited connectivity or depth constraints.
  • Error detection from auxiliary registers might combine with other mitigation strategies to boost overall accuracy on noisy devices.
  • The approach may extend resource savings to other phase-estimation-based algorithms operating on particle-conserving systems.
  • Compatibility with non-exact states suggests the method could integrate with variational quantum eigensolvers without requiring perfect eigenstates.

Load-bearing premise

The Hamiltonians must be particle-conserving and admit time-evolution factorizations that share an eigenbasis so CSWAP interference can replicate the exact phase distribution.

What would settle it

An experiment comparing SE-QPE and canonical QPE on the same non-exact eigenstate of a particle-conserving Hamiltonian and finding a statistically significant difference in the phase-register probability distribution.

Figures

Figures reproduced from arXiv: 2604.14921 by Carlo A. Gaggioli, David Mu\~noz Ramo, David Zsolt Manrique, Ludmila Szulakowska, Megan Cerys Rowe.

Figure 1
Figure 1. Figure 1: FIG. 1. The CSWAP-gadget, a circuit-level construction of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. SE-QPE circuit with the CSWAP-gadget. A canonical [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Vacuum-reference substitution for a controlled- [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A compute–uncompute gadget marked with the dashed [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. FeMoco resource-estimation summary from compiled [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (Top) Noiseless SE-QPE simulations and statevector calculations for the exact evolution and Trotterization with [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Top) The proportion shots which returned the modal outcome for variants of SE-QPE and QPE in shot-based emulator [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison of bitstring results from measuring the [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The 2-qubit gate count (top) and depth (bottom), [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Ansatz circuit [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Diagonal one-body primitive [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Diagonal two-body primitive [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Controlled one-body primitive c [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Controlled two-body primitive c [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Basis rotation [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Spin-block basis rotation [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Resource metrics for circuit building blocks. Panels show [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Resource metrics for circuit building blocks. Panels show [PITH_FULL_IMAGE:figures/full_fig_p020_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Results from 50000 shot noiseless simulations of [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. A MR-cat-SE-QPE circuit to determine 2 digits of the ethylene PPP Hamiltonian ground-state energy phase bitstring, [PITH_FULL_IMAGE:figures/full_fig_p021_20.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents split-evolution quantum phase estimation (SE-QPE) as a modification to canonical QPE for particle-conserving Hamiltonians. Controlled time evolution is replaced by CSWAP-based interference between a target register and a reference register. For factorizations of time evolution that share an eigenbasis, the method is claimed to preserve the phase-register outcome distribution of standard QPE while remaining compatible with non-exact eigenstates. The substitution eliminates controlled-simulation overhead and permits parallel evolution, yielding resource reductions. Analysis for Trotterized double-factorized chemistry Hamiltonians shows asymptotic savings (approximately 33% in CX count, 25% in T count, and depth ratio 3/N for CX layers) over FeMoco active spaces. A hardware demonstration on Quantinuum H2-2 implements a four-qubit ethylene model with explicit inverse QFT and up to 6 phase bits, reporting distinct energies and auxiliary-register error detection.

Significance. If the preservation and compatibility claims hold under the stated assumptions, SE-QPE offers a concrete route to lower circuit depth and gate counts in quantum chemistry simulations on near-term devices. The explicit resource analysis for FeMoco active spaces and the hardware demonstration on a real device provide practical evidence of utility. The compatibility with non-exact eigenstates distinguishes the approach from compute-uncompute substitutions and supports its use as a hybrid option with standard QPE. These elements strengthen the contribution to quantum algorithms for many-body physics.

major comments (1)
  1. Hardware Demonstration section: the four-qubit ethylene run on Quantinuum H2-2 reports distinct energies and useful error detection from auxiliary registers but provides no quantitative details on shot counts, measurement statistics, variance, or explicit verification that the phase distribution matches canonical QPE, weakening support for the central preservation claim on hardware.
minor comments (2)
  1. Resource Analysis section: the asymptotic reductions (33% CX, 25% T, depth ratio 3/N) are stated for Trotterized double-factorized Hamiltonians; an explicit derivation or table showing the counting for increasing phase powers would clarify how the savings scale with the number of phase bits.
  2. The abstract and introduction would benefit from a short statement of the precise particle-conserving Hamiltonians for which the shared-eigenbasis factorization is assumed, beyond the ethylene and FeMoco examples.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the constructive comment on the hardware demonstration section. We address the point below and will incorporate revisions to strengthen the presentation.

read point-by-point responses

  1. Referee: [—] Hardware Demonstration section: the four-qubit ethylene run on Quantinuum H2-2 reports distinct energies and useful error detection from auxiliary registers but provides no quantitative details on shot counts, measurement statistics, variance, or explicit verification that the phase distribution matches canonical QPE, weakening support for the central preservation claim on hardware.

    Authors: We agree that additional quantitative details would improve the hardware demonstration section. The preservation of the phase-register outcome distribution is established theoretically in the manuscript for particle-conserving Hamiltonians with shared eigenbases (see Section III and the analysis of Trotterized double-factorized operators). The four-qubit ethylene experiment serves as a proof-of-principle implementation on Quantinuum H2-2, demonstrating distinct energies, explicit inverse QFT, repeated phase-kickback up to 6 bits, and the utility of auxiliary-register error detection filters. In the revised manuscript we will add the requested details: the number of shots per circuit, full measurement statistics and histograms, computed energy variances, and an explicit comparison of the observed phase bitstring distribution to the theoretical expectation from canonical QPE under identical conditions. This will provide stronger empirical support while clarifying that the hardware run illustrates feasibility rather than serving as the primary evidence for the preservation property. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper defines SE-QPE via a direct structural substitution (CSWAP interference replacing controlled evolution) for particle-conserving Hamiltonians admitting shared-eigenbasis factorizations. Phase-distribution preservation is asserted from the interference mechanism under that explicit condition, not derived from fitted parameters or self-referential equations. Resource counts (CX, T, depth) follow from standard Trotterized double-factorized analysis and are presented as asymptotic comparisons rather than predictions fitted to the target result. The hardware demonstration on the ethylene model is direct execution, not an extrapolation from internal fits. No self-citation chains, uniqueness theorems, or ansatzes are invoked as load-bearing premises for the central claims. The derivation remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard quantum computing primitives and the domain property that certain chemistry Hamiltonians are particle-conserving; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Particle-conserving Hamiltonians admit factorizations of time evolution with a shared eigenbasis.
    Invoked to guarantee that CSWAP interference reproduces the canonical QPE phase distribution.

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