ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
권호 표지
DOI QR코드

DOI QR Code

Optimal execution of logical Hadamard with low-space overhead in rotated surface code

  • Sang-Min Lee (Future Computing Research Division, Electronics and Telecommunications Research Institute) ;
  • Ki-Sung Jin (Future Computing Research Division, Electronics and Telecommunications Research Institute) ;
  • Soo-Cheol Oh (Future Computing Research Division, Electronics and Telecommunications Research Institute) ;
  • Jin-Ho On (Future Computing Research Division, Electronics and Telecommunications Research Institute) ;
  • Gyu-Il Cha (Future Computing Research Division, Electronics and Telecommunications Research Institute)
  • Received : 2024.03.21
  • Accepted : 2024.08.19
  • Published : 2024.10.10
Download PDF
⟨ Previous Next ⟩

Abstract

Fault-tolerant quantum computation requires error-correcting codes that enable reliable universal quantum operations. This study introduces a novel approach that executes the logical Hadamard with low-space requirements while preserving the original definition of logical operators within the framework of the rotated surface codes. Our method leverages a boundary deformation method to rotate the logical qubit transformed by transversal Hadamard. Following this, the original encoding of the logical qubit is reinstated through logical flipand-shift operations. The estimated space-time cost for a logical Hadamard operation with a code distance d is 5d2 + 3d2 . The efficiency enhancement of the proposed method is approximately four times greater than those of previous approaches, regardless of the code distance. Unlike the traditional method, implementing a logical Hadamard requires only two patches instead of seven. Furthermore, the proposed method ensures the parallelism of quantum circuits by preventing interferences between adjacent logical data qubits.

Keywords

Acknowledgement

This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No. 2020-0-00014, A Technology Development of Quantum OS for Fault-tolerant Logical Qubit Computing Environment).

References

  1. P. W. Shor, Schemes for reducing decoherence in quantum computer memory, Phys. Rev. A 52 (1995), no. 4, R2493-R2496.
  2. D. Gottesman, A theory of fault-tolerant quantum computation, Phys. Rev. A 57 (1998), 127-137.
  3. D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. Thesis, Caltech, 1997.
  4. M. H. Freedman and D. A. Meyer, Projective plane and planar quantum codes, Found. Comp. Math. 1 (2001), 325-332.
  5. D. Poulin, Stabilizer formalism for operator quantum error correction, Phys. Rev. Lett. 95 (2005), no. 23, 230504.
  6. A. M. Steane, A tutorial on quantum error correction, In Proc. International School of Physics "Enrico Fermi," Course CLXII, "Quantum Computers, Algorithms and Chaos", G. Casati, D. L. Shepelyansky, P. Zoller (eds.), IOS Press, Amsterdam, 2006, 1-32.
  7. D. Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, Quant. Info. Sci. Contr. Math., Proc. Symp. App. Math. 68 (2010), 513-588.
  8. Y. Wang, Quantum computation and quantum information, Stat. Sci. 27 (2012), no. 3, 373-394.
  9. S. J. Devitt, W. J. Munro, and K. Nemoto, Quantum error correction for beginners, Rep. Prog. Phys. 76 (2013), no. 7, 076001.
  10. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, J. Math. Phys. 43 (2002), 4452-4505.
  11. S. B. Bravyi, and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv preprint, 1998. DOI 10.48550/arXiv.quant-ph/9811052
  12. D. S. Wang, A. G. Fowler, and L. C. L. Hollenberg, Surface code quantum computing with error rates over 1%, Phys. Rev. A 83 (2011), 020302.
  13. A. G. Fowler, A. M. Stephens, and P. Groszkowski, Highthreshold universal quantum computation on the surface code, Phys. Rev. A 80 (2009), 052312.
  14. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: towards practical large-scale quantum computation, Phys. Rev. A 86 (2012), 032324.
  15. D. Horsman, A. G. Fowler, S. Devitt, and R. Van Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14 (2012), 123011.
  16. B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87 (2015), 307-346.
  17. B. J. Brown, K. Laubscher, M. S. Kesselring, and J. R. Wootton, Poking holes and cutting corners to achieve Clifford Gates with the surface code, Phys. Rev. X. 7 (2017), 021029.
  18. T. Tomaru, C. Yoshimura, and H. Mizuno, Surface code for low-density qubit array, Sci. Rep. 12 (2022), no. 1, 12946.
  19. B. Zeng, A. Cross, and I. L. Chuang, Transversality versus universality for additive quantum codes, Theory IEEE Trans. Info. 57 (2011), 6272-6284.
  20. D. Chandra, Z. Babar, H. V. Nguyen, D. Alanis, P. Botsinis, S. X. Ng, and L. Hanzo, Quantum topological error correction codes are capable of improving the performance of Clifford gates, IEEE Access. 7 (2019), 121501-121529.
  21. A. G. Fowler, Low overhead surface code logical Hadamard, Quantum Inf. Comput. 12 (2012), 970-982.
  22. D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and singlequbit operations, Nature 402 (1999), 390-393.
  23. A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Stadler, V. Negnevitsky, M. Ringbauer, P. Schindler, H. J. Briegel, R. Blatt, N. Friis, and T. Monz, Entangling logical qubits with lattice surgery, Nature 589 (2021), no. 7841, 220-224.
  24. H. Bombin and M. A. Martin-Delgado, Quantum measurements, and gates by code deformation, J. Phys. A. 42 (2009), 095302.
  25. H. Bombin, Clifford gates by code deformation, New J. Phys. 13 (2011), 043005.
  26. C. Vuillot, L. Lao, B. Criger, C. Garcia Almudever, K. Bertels, and B. M. Terhal, Code deformation and lattice surgery are gauge fixing, New J. Phys. 21 (2019), 033028.
  27. A.G. Fowler, and C. Gidney, Low overhead quantum computation using lattice surgery, arxiv preprint, 2018. DOI 10.48550/arXiv.1808.06709
  28. M. Beverland, V. Kliuchnikov, and E. Schoute, Surface code compilation via edge-disjoint paths, PRX Quantum. 3 (2022), no. 2, 020342.
  29. M. E. Beverland, S. Huang, and V. Kliuchnikov, Fault tolerance of stabilizer channels, arxiv preprint, 2024. DOI 10.48550/ arXiv.2401.12017
  30. X. Fu, L. Lao, K. Bertels, and C. G. Almudever, A control microarchitecture for fault-tolerant quantum computing, Microprocess. Microsyst. 70 (2019), 21-30.
  31. L. Lao, B. van Wee, I. Ashraf, J. Van Someren, N. Khammassi, K. Bertels, and C. G. Almudever, Mapping of lattice surgerybased quantum circuits on surface code architectures, Quantum Sci. Technol. 4 (2019), 015005.
  32. H. Daniel, N. Franco, and J. D. Simon, Lattice surgery translation for quantum computing, New J. Phys. 1 (2017), 013034.
  33. D. Litinski and F. von Oppen, Lattice surgery with a twist: simplifying Clifford gates of surface codes, Quantum 2 (2018), 62.
  34. C. Christopher and T. C. Earl, Universal quantum computing with a twist-free and temporally encoded lattice surgery, PRX Quan. 3 (2022), 010331.
  35. Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90 (2014), 062320.
  36. D. Litinski, A game of surface codes: large-scale quantum computing with lattice surgery, Quantum. 3 (2019), 128.
  37. K. S. Jin and G. I. Cha, Multilayered logical qubits and synthesized quantum bits, Quantum Sci. Technol. 8 (2023), 035008.
  38. S. Nagayama, A. G. Fowler, D. Horsman, S. J. Devitt, and R. V. Meter, Surface code error correction on a defective lattice, New J. Phys. 19 (2017), 023050.
  39. J. Edmonds, Paths, trees, and flowers, Can. J. Math. 17 (1965), 449-467.
  40. V. Kolmogorov, Blossom V: a new implementation of a minimum cost perfect matching algorithm, Math. Program. Comput. 1 (2009), 43-67.
  41. O. Higgott, PyMatching: a Python package for decoding quantum codes with minimum-weight perfect matching, ACM Quantum Comp. Trans. 3 (2022), no. 3, 1-16.
  42. T. E. O'Brien, B. Tarasinski, and L. DiCarlo, Density-matrix simulation of small surface codes under current and projected experimental noise, NPJ Quantum Info. 3 (2017), 39.
  43. J. H. On, C. Y. Kim, S. C. Oh, S. M. Lee, and G. I. Cha, A multilayered Pauli tracking architecture for lattice surgery-based logical qubits, ETRI J. 45 (2023), 462-478.
  44. E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature 549 (2017), no. 7671, 172-179.
  45. K. S. Jin and G. I. Cha, QPlayer: lightweight, scalable, and fast quantum simulator, ETRI J. 45 (2022), 304-317.