Error Crafting in Mixed Quantum Gate Synthesis
Abstract: In fault-tolerant quantum computing, errors in unitary gate synthesis is comparable with noise inherent in the gates themselves. While mixed synthesis can suppress such coherent errors quadratically, there is no clear understanding on its remnant error, which hinders us from designing a holistic and practical error countermeasure. In this work, we propose that the classical characterizability of synthesis error can be exploited; remnant errors can be crafted to satisfy desirable properties. We prove that we can craft the remnant error of arbitrary single-qubit unitaries to be Pauli and depolarizing errors, while the conventional twirling cannot be applied in general. For Pauli rotation gates, in particular, the crafting enables us to suppress the remnant error up to cubic order, which results in synthesis with a T-count of $\log_2(1/\varepsilon)$ up to accuracy of $\varepsilon=10{-9}$. Our work opens a novel avenue in quantum circuit design and architecture that orchestrates error countermeasures.
- P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995).
- D. Gottesman, Stabilizer codes and quantum error correction, arXiv preprint quant-ph/9705052 (1997).
- P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM review 41, 303 (1999).
- D. S. Abrams and S. Lloyd, Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors, Phys. Rev. Lett. 83, 5162 (1999).
- K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017).
- Y. Li and S. C. Benjamin, Efficient variational quantum simulator incorporating active error minimization, Phys. Rev. X 7, 021050 (2017).
- S. Endo, S. C. Benjamin, and Y. Li, Practical quantum error mitigation for near-future applications, Phys. Rev. X 8, 031027 (2018).
- B. Koczor, Exponential error suppression for near-term quantum devices, Phys. Rev. X 11, 031057 (2021a).
- E. van den Berg, Z. K. Minev, and K. Temme, Model-free readout-error mitigation for quantum expectation values, Phys. Rev. A 105, 032620 (2022).
- B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Phys. Rev. Lett. 102, 110502 (2009).
- K. Tsubouchi, T. Sagawa, and N. Yoshioka, Universal Cost Bound of Quantum Error Mitigation Based on Quantum Estimation Theory, Physical Review Letters 131, 210601 (2023), publisher: American Physical Society.
- R. Takagi, H. Tajima, and M. Gu, Universal sampling lower bounds for quantum error mitigation, Phys. Rev. Lett. 131, 210602 (2023).
- M. B. Hastings, Turning gate synthesis errors into incoherent errors, Quantum Info. Comput. 17, 488–494 (2017).
- E. Campbell, Shorter gate sequences for quantum computing by mixing unitaries, Phys. Rev. A 95, 042306 (2017).
- J. J. Wallman and J. Emerson, Noise tailoring for scalable quantum computation via randomized compiling, Physical Review A 94, 052325 (2016).
- S. Akibue, G. Kato, and S. Tani, Probabilistic unitary synthesis with optimal accuracy, arXiv preprint arXiv:2301.06307 (2023).
- S. Akibue, G. Kato, and S. Tani, Probabilistic state synthesis based on optimal convex approximation, npj Quantum Information 10, 1 (2024), publisher: Nature Publishing Group.
- N. J. Ross and P. Selinger, Optimal ancilla-free clifford+t approximation of z-rotations, Quantum Info. Comput. 16, 901–953 (2016).
- A. G. Fowler, Constructing arbitrary steane code single logical qubit fault-tolerant gates, Quantum Info. Comput. 11, 867–873 (2011).
- A. Bocharov and K. M. Svore, Resource-optimal single-qubit quantum circuits, Phys. Rev. Lett. 109, 190501 (2012).
- V. Kliuchnikov, D. Maslov, and M. Mosca, Fast and efficient exact synthesis of single-qubit unitaries generated by clifford and t gates, Quantum Info. Comput. 13, 607–630 (2013).
- A. Bocharov, M. Roetteler, and K. M. Svore, Efficient synthesis of universal repeat-until-success quantum circuits, Phys. Rev. Lett. 114, 080502 (2015).
- R. Takagi, Optimal resource cost for error mitigation, Phys. Rev. Res. 3, 033178 (2021).
- A. M. Dalzell, N. Hunter-Jones, and F. G. Brandão, Random quantum circuits transform local noise into global white noise, Communications in Mathematical Physics 405, 78 (2024).
- H. Morisaki, S. Akibue, and K. Fujii, Optimal ancilla-free clifford+t compilation of single qubit unitary, in preparation (2024).
- B. Koczor, The dominant eigenvector of a noisy quantum state, New Journal of Physics 23, 123047 (2021b).
- V. Kliuchnikov, D. Maslov, and M. Mosca, Practical approximation of single-qubit unitaries by single-qubit quantum clifford and t circuits, IEEE Transactions on Computers 65, 161 (2015).
- E. T. Campbell, Early fault-tolerant simulations of the hubbard model, Quantum Science and Technology 7, 015007 (2021).
- B. Regula, Probabilistic transformations of quantum resources, Phys. Rev. Lett. 128, 110505 (2022).
- J. Watrous, Semidefinite programs for completely bounded norms, arXiv preprint arXiv:0901.4709 (2009).
- J. Watrous, Simpler semidefinite programs for completely bounded norms, arXiv preprint arXiv:1207.5726 (2012).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.