Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation

Abstract:We show that quantum phase estimation (QPE) circuits can be significantly compressed in depth by preprocessing the input operator with a sigmoid spectral filter before estimation. For systems with small spectral gaps Delta_lambda, standard QPE requires m = ceil(log2(1/Delta_lambda)) precision qubits and depth Theta(2^m). Applying a soft-step transformation f(lambda; tau,w) amplifies the effective gap to Delta_f > Delta_lambda (for w < 1/4), reducing the required precision to m_f = ceil(log2(1/Delta_f)) and compressing circuit depth by 2^(alpha Delta_m), where alpha = 1 for the LMR density-matrix exponentiation framework and alpha is in [0.11,0.42] for controlled-phase-gate circuits. We prove that this compression is exact, bounded above by log2(1/(4w Delta_lambda)) + 1, and impossible for exactly degenerate spectra. We further show that the threshold parameter tau requires only O(w) accuracy, so classical preprocessing such as covariance diagonalisation or CASSCF avoids circularity. A net resource advantage occurs when 4w^2(2^Delta_m - 1) > Delta_lambda log(1/epsilon). Validation on LiH and BeH2 bond-stretch calculations, classical covariance datasets, and synthetic near-degenerate cases demonstrates depth reductions of up to 27x and CX-gate reductions of up to 21x. For LiH, QPE output fidelity improves from 0.66 to 0.98 at a 1% hardware error rate. The method preserves the principal subspace to machine precision, requires no modification of QPE, and can be combined with readout-stage and state-preparation filtering. Negative-control tests establish the benefit condition: m_raw >= 2 and Delta_lambda > 0.

Quantum Physics (quant-ph); Materials Science (cond-mat.mtrl-sci)

arXiv:2608.14002 [quant-ph]

(or arXiv:2608.14002v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.14002 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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