Efficient Gaussian State Preparation in Quantum Circuits

[2507.20317] Efficient Gaussian State Preparation in Quantum Circuits Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2507.20317 (quant-ph) [Submitted on 27 Jul 2025] Title: Efficient Gaussian State Preparation in Quantum Circuits Authors: Yichen Xie , Nadav Ben-Ami View a PDF of the paper titled Efficient Gaussian State Preparation in Quantum Circuits, by Yichen Xie and Nadav Ben-Ami View PDF HTML (experimental) Abstract: Gaussian states hold a fundamental place in quantum mechanics, quantum information, and quantum computing. Many subfields, including quantum simulation of continuous-variable systems, quantum chemistry, and quantum machine learning, rely on the ability to accurately and efficiently prepare states that reflect a Gaussian profile in their probability amplitudes. Although Gaussian states are natural in continuous-variable systems, the practical interest in digital, gate-based quantum computers demands discrete approximations of Gaussian distributions over a computational basis of size \(2^n\). Because of the exponential scaling of naive amplitude-encoding approaches and the cost of certain block-encoding or Hamiltonian simulation techniques, a resource-efficient preparation of approximate Gaussian states is required. In this work, we propose and analyze a circuit-based approach that starts with single-qubit rotations to form an exponential amplitude profile and then applies the quantum Fourier transform to map those amplitudes into an approximate Gaussian distribution. We demonstrate that this procedure achieves high fidelity with the target Gaussian state while allowing optional pruning of small controlled-phase angles in the quantum Fourier transform, thus reducing gate complexity to near-linear in \(\mathcal{O}(n)\). We conclude that the proposed technique is a promising route to make Gaussian states accessible on noisy quantum hardware and to pave the way for scalable implementations on future devices. The implementation of this algorithm is available at the Classiq library: this https URL . Comments: 7 pages, 7 figures. To appear in Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE25) Subjects: Quantum Physics (quant-ph) MSC classes: 81P68, 81P40, 65Y20 Cite as: arXiv:2507.20317 [quant-ph] (or arXiv:2507.20317v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2507.20317 Focus to learn more arXiv-issued DOI via DataCite Journal reference: 2025 IEEE International Conference on Quantum Computing and Engineering (QCE), Albuquerque, NM, USA, 2025, pp. 242-248 Related DOI : https://doi.org/10.1109/QCE65121.2025.00035 Focus to learn more DOI(s) linking to related resources Submission history From: Eason Xie [ view email ] [v1] Sun, 27 Jul 2025 15:15:20 UTC (768 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Gaussian State Preparation in Quantum Circuits, by Yichen Xie and Nadav Ben-Ami View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-07 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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