Operator quantum error-correcting subsystems for self-correcting quantum memories

By D. Bacon. 2005

467 citations recorded by the source corpus.

The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures.

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

View Paper: https://www.semanticscholar.org/paper/d801c199effc8cbf0e7722e8adf231a69b264b83

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum error correction for quantum memories (2013, unknown): “(Bacon, 2006; Aliferis and Cross, 2007) whose qubits can be laid out in an n × n array as in Fig.”
Quantum memories at finite temperature (2014, background): “(Bacon, 2006), the Author considers a simple Pauli noise model and meanfield arguments to show that the model may demonstrate a macroscopic power-law energy barrier.”
Stim: a fast stabilizer circuit simulator (2021, background): “Figure 3: Delay until first sample on d×d×d Bacon-Shor code memory circuits [4].”
Sparse Blossom: correcting a million errors per core second with minimum-weight matching (2023, unknown): “Many related code families also have graphlike error models, such as repetition codes, 2D hyperbolic codes [BT16], some 2D subsystem codes [Bra+13; SBT11; Bac06; HB21] and Floquet codes [HH21; Gid+21], amongst others.”
Quantum computing and the entanglement frontier (2012, background): “66 Models realizing this vision are known in four spatial dimensions.”
Fault-tolerant quantum error correction for Steane’s seven-qubit color code with few or no extra qubits (2018, background): “One extra qubit is also enough for the [[9, 1, 3]] Bacon-Shor subsystem code [14, 20].”
Local stabilizer codes in three dimensions without string logical operators (2011, background): “Bacon subsystem code in 3D [11] which does not have string-like bare logical operator, might be self-correcting, but it is not yet affirmative since its Hamiltonian is hard to solve.”
Quantum memories based on engineered dissipation (2010, background): “Although the results above have no obvious practical implication, they suggest that local models may exist in spatial dimensions lower than 4 (for the search of quantum memories based on protecting Hamiltonians in lower dimension see [5, 7, 8]).”