Surface codes: Towards practical large-scale quantum computation

By Austin G. Fowler, M. Mariantoni, John M. Martinis, A. Cleland. 2012

3,046 citations recorded by the source corpus.

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f9db7ae0a333ef8a21317d1a3126d75da9d43ff4

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Citations in the corpus

Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits (2021, methodology): “4 of the main paper we extracted an effectively global T1 time around 1 μs at the peak of large events, which is compatible with estimates based on similar device structures [1].”
Cryo-CMOS Circuits and Systems for Quantum Computing Applications (2018, positive): “Therefore, the classical controller is also responsible for implementing qubit corrections, such as echo techniques [16], [22]–[24] and quantum error correction (QEC) schemes [25], designed to maintain the quantum state over longer periods.”
Quantum error correction below the surface code threshold (2024, neutral): “We note there are other accurate decoders that would be interesting to test on this data, including beliefmatch-ing [13], BP+OSD [14], and tensor network decoding [1].”
Quantum Computing in the NISQ era and beyond (2018, background): “ for a while, because of the large number of physical qubits needed. To run algorithms involving thousands of protected qubits we’ll need a number of physical qubits which is in the millions, or more [50]. That’s a very large leap from where we will be for the next few years, with of order a hundred”
Flux-controlled quantum computation with Majorana fermions (2013, methodology): “Although we have calculated the improvements only for the 7-qubit Steane code, the advantages are characteristic for all error correction schemes, including surface codes [47, 48].”
Quantum simulation and computing with Rydberg-interacting qubits (2020, methodology): “The development of these techniques for the Rydberg platform should ultimately enable the realization of quantum error correcting codes with sizable numbers of logical qubits and logical gates for fault-tolerant quantum computing 321,322 .”
Fundamental limits of quantum error mitigation (2021, background): “NISQ devices often lack the capability to adaptively execute different quantum operations depending on measurement outcomes during a computation — an essential component necessary for general quantum error correction [3, 4].”
Quantum algorithms: an overview (2015, neutral): “We will also not cover the important topics of how to actually build a quantum computer [59] (in theory or in practice) and quantum error-correction [42], nor quantum communication complexity [23] or quantum Shannon theory [98].”
Qulacs: a fast and versatile quantum circuit simulator for research purpose (2020, methodology): “To construct a quantum computer large enough for Shor’s algorithm [60, 61], a quantum simulation for quantum many-body systems [33, 62], or algorithms for linear systems [63], quantum error correction [64] is necessary to reduce logical error rates to an arbitrarily small value.”
Digital zero noise extrapolation for quantum error mitigation (2020, background): “In the long run, fault-tolerance and quantum errorcorrection have the potential to arbitrarily reduce logical errors [2]–[4].”