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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The sequence of classically controlled phase shifts can be combined into a single shift and implemented to a level of precision far below other sources of error without noticeable cost.
“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]
The circuit-synthesis discussion (p. 3) describes approximating an arbitrary phase to a chosen precision, and the Conclusions (p. 4) report that expected T-count grows logarithmically with inverse precision. The paper does not compare that cost with other sources of error in the citing algorithm, so it does not establish that the required precision incurs no noticeable cost. The combination into a single shift is presented as the citing authors’ step, not as a result attributed to this source. (LLM, conf=0.84)
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Wu, X.-C., Davis, M., Chong, F., & Iancu, C. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.09835 · Cited by 44 · see citing works
AutoQ 2.0: From Verification of Quantum Circuits to Verification of Quantum Programs
Chen, Y., Chung, K.-M., Hsieh, M.-H., Huang, W., Lengál, O., Lin, J.-A., & Tsai, W.-L. (2025) · Lecture notes in computer science · doi:10.1007/978-3-031-90660-2_5 · Cited by 9 · see citing works
Ancilla-driven quantum computation for qudits and continuous variables
Proctor, T. J., Giulian, M., Korolkova, N., Andersson, E., & Kendon, V. M. (2017) · Physical Review A · doi:10.1103/physreva.95.052317 · Cited by 9 · see citing works
Simulating Vibrational Dynamics on Bosonic Quantum Devices
Malpathak, S., Kallullathil, S. D., & Izmaylov, A. F. (2025) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.4c03480 · Cited by 12 · see citing works
Reinforcement-learning generation of four-qubit entangled states
Giordano, S., & Martin-Delgado, M. A. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.043056 · Cited by 8 · see citing works
Differentiable Quantum Programming with Unbounded Loops
Fang, W. S., Ying, M., & Wu, X. (2023) · ACM Transactions on Software Engineering and Methodology · doi:10.1145/3617178 · Cited by 7 · see citing works
Quantum circuit synthesis using Solovay-Kitaev algorithm and optimization techniques
Al-Ta'ani, O. (2015) · K-State Research Exchange (Kansas State University) · Cited by 7 · see citing works
Quantum Steering of Surface Error Correcting Codes
Volya, D., & Mishra, P. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00158 · Cited by 7 · see citing works
Alvertis, A. M., Khan, A., & Tubman, N. M. (2025) · Physical Review Applied · doi:10.1103/physrevapplied.23.044028 · Cited by 8 · see citing works
Efficient approximation of diagonal unitaries over the Clifford+T basis
Welch, J., Bocharov, A., & Svore, K. M. (2016) · Quantum Information and Computation · doi:10.26421/qic16.1-2-6 · Cited by 9 · see citing works
Self-citationStructural stability of the quantum Fourier transform
Nam, Y., & Blümel, R. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-0923-2 · Cited by 7 · see citing works
Digital quantum simulation for screening and confinement in gauge theory with a topological termPreprint
Honda, M., Itou, E., Kikuchi, Y., Nagano, L., & Okuda, T. (2021) · arXiv (Cornell University) · Cited by 7 · see citing works
TE-PAI: exact time evolution by sampling random circuits
Kiumi, C., & Koczor, B. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/ae1160 · Cited by 6 · see citing works
Predicting the Optimizability for Workflow Decisions
Mete, B., Schulz, M., & Ruefenacht, M. (2022) · IEEE/ACM International Workshop on Quantum Computing Software (QCS) · doi:10.1109/qcs56647.2022.00013 · Cited by 6 · see citing works
Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian
Mukhopadhyay, P., Stetina, T. F., & Wiebe, N. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.010345 · Cited by 6 · see citing works
- 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 · 2014: 1
- 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 › Computer Science › Artificial Intelligence › 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
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