Fault-tolerant quantum computation with constant overhead

By Daniel Gottesman. Quantum information & computation, 2013

346 citations recorded by the source corpus.

What is the minimum number of extra qubits needed to perform a large fault-tolerant quantum circuit? Working in a common model of fault-tolerance, I show that in the asymptotic limit of large circuits, the ratio of physical qubits to logical qubits can be a constant. The construction makes use of quantum low-density parity check codes, and the asymptotic overhead of the protocol is equal to that of the family of quantum error-correcting codes underlying the fault-tolerant protocol.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6c5e0c8408394e6e9bb622c0702e1aa18c11ef76

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Citations in the corpus

Fusion-based quantum computation (2021, methodology): “We can introduce a notion of low-density parity check (LDPC) fusion networks that is analogous to other similar constructions in error correction [45, 46].”
High-threshold and low-overhead fault-tolerant quantum memory (2023, methodology): “This spurred interest in more general quantum codes known as low-density parity-check (LDPC) codes 6 .”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, background): “The existence of such thresholds for qubitbased architectures has been a subject of extensive research for over twenty years [51, 73, 74, 104, 148–156] but the existence of thresholds for CV-based architectures [1] is less well understood.”
The future of quantum computing with superconducting qubits (2022, background): “Most of the codes designed for quantum computing are of the LDPC type 16,43,44 , meaning that each stabilizer acts on only a small number of qubits and each qubit participates in a small number of stabilizers, where small means a constant independent of the code size.”
Quantum error correction for quantum memories (2013, neutral): “This question was analyzed and answered in the affirmative by Gottesman (2014).”
Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, background): “Although the logN scaling implies that the encoding is unlikely to be fully fault-tolerant, such low-depth codes with high code rates may be crucial in improving the performance and flexibility of intermediate-scale quantum devices [82].”
Quantum error correction (2001, neutral): “Developing a full scheme that is fault tolerant is possible with quantum LDPC codes [Got14], but is beyond the scope of these lecture notes.”
The XZZX surface code (2020, neutral): “[65] D.”
Quantum error mitigation (2022, background): “There is ongoing theoretical research to find alternative codes with a more favourable overhead, and recent progress gives reasons to be optimistic (Breuckmann and Eberhardt, 2021; Dinur et al. , 2022; Gottesman, 2014; Panteleev and Kalachev, 2022).”
Quantum error correction: an introductory guide (2019, background): “Efforts are also in progress to develop code constructions with non-vanishing rates based on principles from high-performance classical codes [45,59].”