Quantum error correction for quantum memories

By Barbara M. Terhal. 2013

1,367 citations recorded by the source corpus.

It may seem inevitable that highly entangled quantum states are susceptible to disturbance through interaction with a decohering environment. However, certain multiqubit entangled states are well protected from common forms of decoherence as the quantum information is hidden in inherently nonlocal degrees of freedom. This review shows that this robustness is enabled by specific measurements on subsets of qubits, implementing a quantum version of an error correction process. Beginning with the basics, the latest understanding of the relation between this form of error correction and the concept of two-dimensional topological order in many-body physics is reviewed.

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

View Paper: https://www.semanticscholar.org/paper/3a0f4231bf931d1e3eb97b2ced99d0be0ca5c1c3

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Fracton Topological Order, Generalized Lattice Gauge Theory and Duality (2016, background): “Fracton topological order provides an exciting development in the search for new quantum phases of matter, for new schemes for quantum information processing [20], and in the investigation of glassy dynamics in interacting quantum systems [21].”
Demonstration of fault-tolerant universal quantum gate operations (2021, background): “SX (2) = X4X5X6X7 SZ (2) = Z4Z5Z6Z7 SX (3) = X2X3X6X7 SZ (3) = Z2Z3Z6Z7”
Sparse Blossom: correcting a million errors per core second with minimum-weight matching (2023, positive): “However, parallelisation of the decoder itself is important for real-time decoding, to prevent an exponentially increasing backlog of data building up within a single computation [Ter15], or to avoid the polynomial slowdown imposed by relying on parallel window decoding instead [Sko+23; Tan+23].”
Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory (2023, background): “A first step would be the realization of robust quantum memories [2–4].”
Realizing repeated quantum error correction in a distance-three surface code (2021, methodology): “We collectively process successive syndromes σm to determine which data and auxiliary qubits have most likely suffered an error [4, 14, 31].”
Fracton phases of matter (2020, background): “[17] Barbara M.”
Silicon CMOS architecture for a spin-based quantum computer (2016, methodology): “Individual qubit tuning is controlled electrically via g-factor control [1].”
Magic State Distillation: Not as Costly as You Think (2019, background): “sential part of a large-scale quantum computer [1–3].”
Quantum computing with atomic qubits and Rydberg interactions: progress and challenges (2016, background): “Roughly speaking larger codes can tolerate gates with higher errors[7, 8], with large scale surface codes that combine hundreds of physical qubits to create a single logical qubit having threshold error rates ∼ 0.”
Quantum error correction below the surface code threshold (2024, positive): “This is because some logical operations are non-deterministic; they depend on logical measurement outcomes that must be correctly interpreted on the fly [23].”
A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery (2018, methodology): “quantum information on large time scales, it is necessary to actively correct errors by combining many physical qubits into logical qubits using a quantum errorcorrecting code [3–5].”
Geometry and Response of Lindbladians (2015, methodology): “This recipe should prove useful in experimental quantum channel simulation [57] and autonomous or passive quantum error correction [58].”