Topological quantum memory

By E. Dennis, Alexei Y. Kitaev, A. Landahl, John Preskill. 2001

2,121 citations recorded by the source corpus.

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z(2) lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.

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

View Paper: https://www.semanticscholar.org/paper/8ba3a176211e3e9959c36cbb2e22dbdee84d3b00

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Sparse-graph codes for quantum error correction (2003, background): “Several constructions and decoding algorithms have been proposed for quantum codes that are associated with sparse graphs [5], [6], [13], [27].”
Topological order in an exactly solvable 3D spin model (2010, background): “It is important to emphasize the essential difference between membranes describing logical operators in our code and the ones in the 4D toric code [14].”
Fusion-based quantum computation (2021, background): “The syndrome graph picture makes it easier to interpret the underlying structure of the code and enables the application of existing decoders such as minimum-weight matching and unionfind decoders [53, 54].”
Confinement Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory (2002, methodology): “For the sort of error model described in [9], the qubit error rate and the measurement error rate are comparable, so the isotropic model with p 1⁄4 q provides useful guidance.”
A CMOS silicon spin qubit (2016, neutral): “Surface-code quantum computing architectures, possibly the only viable option to date, require large numbers (eventually millions) of qubits individually controlled with tunable nearest-neighbour couplings 17,18 .”
Silicon CMOS architecture for a spin-based quantum computer (2016, methodology): “Small variations can be expected depending on the design considerations, but these quantum dots size are consistent with experimental realizations of quantum dot qubits [1, 2].”
Surface code quantum computing by lattice surgery (2011, methodology): “The general procedure was given for the planar code in [2], and a worked example for general surface codes in [4, section VI(C)].”
On thermalization in Kitaev's 2D model (2008, methodology): “quantum spin systems which exhibit topological order, such as the 2D [1] and 4D Kitaev models [2].”
A Race-Track Trapped-Ion Quantum Processor (2023, methodology): “The decoding uses a minimumweight perfect-matching algorithm [95, 96], which is performed online at the end of the circuit as part of the control-system software execution of each shot (i.”
Quantum computing and the entanglement frontier (2012, background): “40 A topologically ordered medium on a topologically nontrivial surface is a special type of quantum error-correcting code, one that can be realized as the ground state of a system with a geometrically local Hamiltonian; in this respect its status is similar to that of the ferromagnet in classical…”
High-threshold and low-overhead fault-tolerant quantum memory (2023, background): “The sources of noise include imperfections in qubits, materials used, controlling apparatus, state preparation and measurement errors and a variety of external factors ranging from local man-made, such as stray electromagnetic fields, to those inherent to the Universe, such as cosmic rays.”
Quantum memories based on engineered dissipation (2010, methodology): “[3] Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory.”