Warm-Start Quantum Computation: Spectral-Weight Resources for Energy Readout and State Preparation
Abstract
Estimating a ground-state energy and preparing a ground state both split into a front-end that supplies an approximate state |χ⟩ and a back-end that reads or refines it. We argue, and measure at every step, that the only thing crossing that split is the front-end's spectral weight distribution pn=|⟨ En|χ⟩|2 over the eigenstates of the problem Hamiltonian HP. Everything downstream is priced in it, so the front-end is a swappable module, and we swap it seven times without altering anything to its right. We call the arrangement WARP. Four back-ends spend that distribution. A readout (A) samples g(t)=⟨χ|e−iHPt|χ⟩ on the device and extracts true eigenvalues by classical signal processing, returning an energy below the variational bound of the state it was handed, from a signal 50× shorter than a Fourier transform needs. Three routes spend the same account on a state instead. An adiabatic schedule (B) has a minimum gap set by the overlap; a discrete amplification (C) is cheaper in depth but must halt at an index the overlap fixes, so it needs a measured value and not a bound; a recursion (D) of depth 𝒪(3m) raises the question of whether it can be run at all. The interactions are the substance. On stretched N2 a sample-based diagonalisation reports a variational bound 79 mHa high, fifty times outside chemical accuracy; reading the state it has already prepared returns E0 to 1.4×10−6 Ha, three orders of magnitude inside it, and needs no new front-end and no new circuit. And because the weights price everything, they must be measurable when scarce, so we beat a weak reference against a strong one and recover overlaps four orders of magnitude below the shot-noise floor. We map the operating envelope throughout, and state the limitations.
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BibTeX
@misc{kieu2026warmstart,
title = {{Warm-Start Quantum Computation: Spectral-Weight Resources for Energy Readout and State Preparation}},
author = {Tien D. Kieu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12485},
eprint = {2610.12485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12485},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Warm-Start Quantum Computation: Spectral-Weight Resources for Energy Readout and State Preparation
AU - Tien D. Kieu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.12485
UR - https://arxiv.org/abs/2610.12485
AB - Estimating a ground-state energy and preparing a ground state both split into a front-end that supplies an approximate state |χ⟩ and a back-end that reads or refines it. We argue, and measure at every step, that the only thing crossing that split is the front-end's spectral weight distribution p_n=|⟨ E_n|χ⟩|^2 over the eigenstates of the problem Hamiltonian H_P. Everything downstream is priced in it, so the front-end is a swappable module, and we swap it seven times without altering anything to its right. We call the arrangement WARP. Four back-ends spend that distribution. A readout (A) samples g(t)=⟨χ|e^−iH_Pt|χ⟩ on the device and extracts true eigenvalues by classical signal processing, returning an energy below the variational bound of the state it was handed, from a signal 50× shorter than a Fourier transform needs. Three routes spend the same account on a state instead. An adiabatic schedule (B) has a minimum gap set by the overlap; a discrete amplification (C) is cheaper in depth but must halt at an index the overlap fixes, so it needs a measured value and not a bound; a recursion (D) of depth 𝒪(3^m) raises the question of whether it can be run at all. The interactions are the substance. On stretched N_2 a sample-based diagonalisation reports a variational bound 79 mHa high, fifty times outside chemical accuracy; reading the state it has already prepared returns E_0 to 1.4×10^−6 Ha, three orders of magnitude inside it, and needs no new front-end and no new circuit. And because the weights price everything, they must be measurable when scarce, so we beat a weak reference against a strong one and recover overlaps four orders of magnitude below the shot-noise floor. We map the operating envelope throughout, and state the limitations.
ER -