Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation

• URL: http://arxiv.org/abs/2608.14002v1
• Date: Fri, 14 Aug 2026 06:45:48 GMT
• Title: Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation
• Abstract summary: We show that quantum phase estimation can be significantly compressed in depth by preprocessing the input operator.<n>We prove that this compression is exact, bounded by log2(1/(4w Delta_lambda) + 1, and impossible for exactly spectra.<n>A net resource advantage occurs when 4w2 (2Delta_m - 1) > Delta_lambda log (1/epsilon)
• Score: 1.2318267573115809
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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