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Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits
Open accessAbstract
Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize a RUS circuit to approximate any given single-qubit unitary to precision ϵ over the Clifford+T basis. Surprisingly, the T count of the synthesized RUS circuit surpasses the theoretical lower bound of 3 log_{2}(1/ϵ) that holds for purely unitary single-qubit circuit decomposition. By taking advantage of measurement and an ancilla qubit, RUS circuits achieve an expected T count of 1.15 log_{2}(1/ϵ) for single-qubit z rotations. Our method leverages the fact that the set of unitaries implementable by RUS protocols has a higher density in the space of all unitaries compared to the density of purely unitary implementations.
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“This sequence can be combined into a single shift, and implemented using e.g. the technique in [10], to a level of precision far below other sources of error in the algorithm without incurring a noticeable cost.”
From How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2021) · cites this paper as [10]
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Metadata
- Authors
- Bocharov, A., Roetteler, M., & Svore, K. M.
- Affiliations
- Microsoft (United States) (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2015-02-27
- Volume
- 114
- Issue
- 8
- Pages
- 080502-080502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1915167278
- Cited by
- 142
- References
- 22
- Citations by year
- 2026: 8 · 2025: 17 · 2024: 16 · 2023: 12 · 2022: 15 · 2021: 12 · 2020: 13 · 2019: 10 · 2018: 6 · 2017: 12 · 2016: 12 · 2015: 8
- FWCI
- 12.43
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum circuit synthesis, T-count, ancilla qubits, measurement, quantum resource reduction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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