Fault-tolerant gates via homological product codes

Tomas Jochym-O'Connor

doi:10.22331/q-2019-02-04-120

Fault-tolerant gates via homological product codes

Walter Burke Institute for Theoretical Physics, Institute for Quantum Information & Matter, California Institute of Technology, Pasadena, CA 91125, USA

Published:	2019-02-04, volume 3, page 120
Eprint:	arXiv:1807.09783v2
Doi:	https://doi.org/10.22331/q-2019-02-04-120
Citation:	Quantum 3, 120 (2019).

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Abstract

A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.

Popular summary

Quantum error correction provides a means to combat errors present in a physical realization of a quantum computer. However, one must also prevent errors from proliferating when computing on the stored quantum data. This is the central goal of fault tolerance. Unfortunately, there is no simple method to both protect and manipulate the data of a single code in a universal manner, that is exploit the full power of the quantum computer. Rather, additional tricks or resources are required.

We present a method to cross between different codes in a fault-tolerant manner, allowing one to exploit the desirable properties of both codes. The path between different codes may spread errors, but importantly it does so in a controlled manner that allows for the resulting code to clean up any noise that has propagated. Moreover, the method keeps the code simple and does not rely on preparing special resource states or measuring complicated objects. This provides a potential fruitful alternative to universal fault tolerance.

► BibTeX data

@article{JochymOConnor2019faulttolerantgates,
  doi = {10.22331/q-2019-02-04-120},
  url = {https://doi.org/10.22331/q-2019-02-04-120},
  title = {Fault-tolerant gates via homological product codes},
  author = {Jochym-O'Connor, Tomas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {120},
  month = feb,
  year = {2019}
}

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[3] Daryus Chandra, Zunaira Babar, Hung Viet Nguyen, Dimitrios Alanis, Panagiotis Botsinis, Soon Xin Ng, and Lajos Hanzo, "Quantum Topological Error Correction Codes are Capable of Improving the Performance of Clifford Gates", IEEE Access 7, 121501 (2019).

[4] Anirudh Krishna and David Poulin, "Fault-Tolerant Gates on Hypergraph Product Codes", Physical Review X 11 1, 011023 (2021).

[5] Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D. Bartlett, "Universal fault-tolerant quantum computing with stabilizer codes", Physical Review Research 4 1, 013092 (2022).

[6] Christopher Chamberland and Kyungjoo Noh, "Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits", npj Quantum Information 6 1, 91 (2020).

[7] Michael Newman, Leonardo Andreta de Castro, and Kenneth R. Brown, "Generating Fault-Tolerant Cluster States from Crystal Structures", Quantum 4, 295 (2020).

[8] Maxime A. Tremblay, Nicolas Delfosse, and Michael E. Beverland, "Constant-Overhead Quantum Error Correction with Thin Planar Connectivity", Physical Review Letters 129 5, 050504 (2022).

[9] Diego Ristè, Luke C. G. Govia, Brian Donovan, Spencer D. Fallek, William D. Kalfus, Markus Brink, Nicholas T. Bronn, and Thomas A. Ohki, "Real-time processing of stabilizer measurements in a bit-flip code", npj Quantum Information 6 1, 71 (2020).

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