High-threshold universal quantum computation on the surface code

By Austin G. Fowler, A. Stephens, Peter Groszkowski. 2008

476 citations recorded by the source corpus.

We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction and low overhead arbitrarily long-range logical gates. These features make it by far the best and most practical quantum computing scheme devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f2be031978dd8b4baca39461c7d4411e888c9bbb

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Roads towards fault-tolerant universal quantum computation (2016, methodology): “In addition, the [[15, 1, 3]] code is now recognized as the smallest member of the family of 3D colour codes.”
Surface code quantum computing by lattice surgery (2011, background): “The price of maintaining NN interactions is over three times the number of physical qubits per logical qubit [3, 4].”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, background): “The surface code [76, 77] is a commonly used code because it has both these properties, enjoying a high threshold of ∼ 1% [78–80] and only needing nearest-neighbor connectivity of qubits in two spatial dimensions.”
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning (2013, background): “Given the high cost of the fault tolerant implementations of the T gate [1, 14], exceeding the cost of Clifford group gates by as much as a factor of a hundred or more, it has recently been proposed that efficient circuits should minimize the number of T gates, and more specifically the number of T…”
Quantum error correction for quantum memories (2013, unknown): “Details of hole moving schemes are discussed in, e.g., Fowler, Stephens, and Groszkowski (2009) and Fowler, Mariantoni et al. (2012).”
A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits (2012, background): “We then store only one minimal depth circuit implementing the representative of each unitary equivalence class; specifically, we define a canonical representative for each unitary equivalence class, then when a new circuit is generated we find the unitary representative and determine whether a…”
Elucidating reaction mechanisms on quantum computers (2016, methodology): “The surface code is currently the most popular code due in part to its relatively high threshold of 1% [15].”
Coherent Conversion Between Microwave and Optical Photons—An Overview of Physical Implementations (2019, unknown): “[23] A.”
High-threshold and low-overhead fault-tolerant quantum memory (2023, methodology): “This resulted in the development of the surface code [19, 20, 21, 22] that offers a high error threshold close to 1%, fast decoding algorithms, and compatibility with the existing quantum processors relying on 2-dimensional (2D) square lattice qubit connectivity.”