Surface code quantum computing by lattice surgery

By Clare Horsman, Austin G. Fowler, Simon J. Devitt, R. V. Meter. 2011

796 citations recorded by the source corpus.

In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c375e28f31864920ca0b867664e3819a577c87f7

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Citations in the corpus

Stim: a fast stabilizer circuit simulator (2021, background): “Figure 1: Delay until one thousandth sample on d × d × d surface code memory circuits [15].”
Freely Scalable Quantum Technologies using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links (2014, background): “…from errors: certain operations between encoded logical qubits can be performed merely by altering the patterns of parity measurements [22, 24] and together with a technique such as magic state distillation [25], all the operations required for universal quantum computation can be…”
Magic State Distillation: Not as Costly as You Think (2019, background): “The simplest protocol [27] starts with a physical state |ψ〉, i.”
A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery (2018, background): “Qubit initialization has no time cost, since, in case of X and Z eigenstates, it can be done simultaneously with the following lattice surgery [9, 12].”
Fusion-based quantum computation (2021, background): “Boundaries can be used to create patches on which lattice surgery can be performed [60].”
Realizing repeated quantum error correction in a distance-three surface code (2021, background): “The number of required cycles scales in general with d in planar architectures and in architectures allowing for transversal execution of logical two-qubit gates [5, 6, 23, 52, 53].”
Logical quantum processor based on reconfigurable atom arrays (2023, methodology): “Logic operations are implemented by changing stabilizer measurement patterns, enabling realization of techniques such as braiding 24 and lattice surgery 89 .”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, methodology): “The scheme we choose and review here is based on lattice surgery for the surface code [125–128], particularly its measurement-based version [88, 129].”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, methodology): “For example, the logical qubit representation used in lattice surgery [110] requires fewer physical qubits than the double-defect representation used in the estimates of this paper.”
Halving the cost of quantum addition (2017, background): “For example, qubits that are idle can be compressed into an inactive “memory” form that covers six times fewer physical qubits than the double-defect form [13].”
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2019, positive): “We assume distance-d logical qubits are stored using square patches of 2(d+1) physical qubits (see Figure 8) and are operated on via lattice surgery [12, 29] (see Figure 9).”
Quantum error correction: an introductory guide (2019, background): “Figure 8(a) shows the five-qubit surface code formed by tiling together four four-cycles in a square lattice [55].”