Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation

Quantum Physics arXiv:2608.14002 (quant-ph) [Submitted on 14 Aug 2026] Title:Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation Authors:Sk Mujaffar Hossain, Satadeep Bhattacharjee View a PDF of the paper titled Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation, by Sk Mujaffar Hossain and 1 other authors View PDF HTML (experimental) 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 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. Subjects: Quantum Physics (quant-ph); Materials Science (cond-mat.mtrl-sci) Cite as: 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) Submission history From: Sk Mujaffar Hossain [view email] [v1] Fri, 14 Aug 2026 06:45:48 UTC (471 KB) Full-text links: Access Paper: View a PDF of the paper titled Circuit Depth Compression via Spectral Gap Amplification in Quantum Phase Estimation, by Sk Mujaffar Hossain and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.mtrl-sci References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)