2000 character limit reached
Graphical quantum Clifford-encoder compilers from the ZX calculus (2301.02356v3)
Published 6 Jan 2023 in quant-ph
Abstract: We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and prove canonicity as well as efficient reducibility of any Clifford encoder into the canonical form. The diagrams produced by our compiler visualize information propagation and entanglement structure of the encoder, revealing properties that may be obscured in the circuit or stabilizer-tableau representation. Consequently, our canonical representation may be an informative technique for the design of new stabilizer quantum codes via graph theory analysis.
- L. K. Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (1996) pp. 212–219.
- P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM review 41, 303 (1999).
- I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Reviews of Modern Physics 86, 153 (2014).
- H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nature Physics 16, 1050 (2020).
- A. Harrow, P. Hayden, and D. Leung, Superdense coding of quantum states, Physical review letters 92, 187901 (2004).
- M. A. Nielsen and I. Chuang, Quantum computation and quantum information (2002).
- A. Bouland and T. Giurgica-Tiron, Efficient universal quantum compilation: An inverse-free solovay-kitaev algorithm, arXiv preprint arXiv:2112.02040 10.48550/arXiv.2112.02040 (2021).
- V. Kliuchnikov, D. Maslov, and M. Mosca, Asymptotically optimal approximation of single qubit unitaries by clifford and t circuits using a constant number of ancillary qubits, Physical review letters 110, 190502 (2013).
- V. Kliuchnikov, D. Maslov, and M. Mosca, Fast and efficient exact synthesis of single qubit unitaries generated by clifford and t gates, arXiv preprint arXiv:1206.5236 10.48550/arXiv.1206.5236 (2012).
- N. J. Ross and P. Selinger, Optimal ancilla-free clifford+ t approximation of z-rotations, Quantum Inf. Comput. 16, 901 (2016).
- 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).
- P. Selinger, Efficient clifford+t approximation of single-qubit operators, arXiv preprint arXiv:1212.6253 10.48550/arXiv.1212.6253 (2012).
- D. Gottesman, Stabilizer codes and quantum error correction (California Institute of Technology, 1997).
- S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv preprint quant-ph/9811052 10.48550/arXiv.quant-ph/9811052 (1998).
- P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Physical review A 52, R2493 (1995).
- D. Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, arXiv preprint arXiv:0904.2557 10.48550/arXiv.0904.2557 (2009).
- A. T. Hu and A. B. Khesin, Improved graph formalism for quantum circuit simulation, Physical Review A 105, 022432 (2022).
- T. McElvanney and M. Backens, Complete flow-preserving rewrite rules for mbqc patterns with pauli measurements, arXiv preprint arXiv:2205.02009 10.4204/EPTCS.394.5 (2022).
- A. Kissinger, Phase-free zx diagrams are css codes (… or how to graphically grok the surface code), arXiv preprint arXiv:2204.14038 10.48550/arXiv.2204.14038 (2022).
- Z. Wu, S. Cheng, and B. Zeng, A zx-calculus approach to concatenated graph codes, arXiv preprint arXiv:2304.08363 10.48550/arXiv.2304.08363 (2023).
- T. Peham, L. Burgholzer, and R. Wille, Equivalence checking of quantum circuits with the zx-calculus, IEEE Journal on Emerging and Selected Topics in Circuits and Systems 12, 662 (2022).
- A. Cowtan and S. Majid, Quantum double aspects of surface code models, Journal of Mathematical Physics 63, 042202 (2022).
- J. van de Wetering, Constructing quantum circuits with global gates, New Journal of Physics 23, 043015 (2021).
- N. de Beaudrap and D. Horsman, The zx calculus is a language for surface code lattice surgery, Quantum 4, 218 (2020).
- A. Kissinger and J. van de Wetering, Reducing the number of non-clifford gates in quantum circuits, Physical Review A 102, 022406 (2020).
- M. Backens, The zx-calculus is complete for stabilizer quantum mechanics, New Journal of Physics 16, 093021 (2014).
- S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Physical Review A 70, 052328 (2004).
- A. Steane, Multiple-particle interference and quantum error correction, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 452, 2551 (1996).
- J. van de Wetering, Zx-calculus for the working quantum computer scientist, arXiv preprint arXiv:2012.13966 10.48550/arXiv.2012.13966 (2020).
- R. Duncan and M. Lucas, Verifying the steane code with quantomatic, arXiv preprint arXiv:1306.4532 10.48550/arXiv.1306.4532 (2013).
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
