Quantum accuracy threshold for concatenated distance-3 codes

By Panos Aliferis, Daniel Gottesman, John Preskill. Quantum information & computation, 2005

535 citations recorded by the source corpus.

We prove a new version of the quantum threshold theorem that applies to concatenationof a quantum code that corrects only one error, and we use this theorem to derive arigorous lower bound on the quantum accuracy" threshold e0. Our proof also appliesto concatenation of higher-distance codes, and to noise models that allow faults to becorrelated in space and in time. The proof uses new criteria for assessing the accuracy" offault-tolerant circuits, which are particularly conducive to the inductive analysis of recur-sire simulations. Our lower bound on the threshold, e0 ≥ 2.73 × 10-5 for an adversarialindependent stochastic noise model, is derived from a computer-assisted combinatorialanaly sis; it is the best lower bound that has been rigorously proven so far.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fe6af917bcff5807c7574831b726b49fb20b7283

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Citations in the corpus

Quantum error correction for quantum memories (2013, unknown): “F) has developed a framework that allows one to establish the results of quantum error correction and fault tolerance for very general quantum dynamics obeying physical locality assumptions [see the comprehensive results by Aliferis, Gottesman, and Preskill (2006)].”
Quantum computation and quantum-state engineering driven by dissipation (2009, methodology): “where the Lk acts locally and has a steady state, ρ0: (1) that is unique; (2) that can be reached in a time poly(T ); (3) such that ψT can be extracted from it in a time poly(T ).”
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning (2013, methodology): “By contrast, we report a scalable automated tool for the optimization of T -depth that functions with or without ancillae, and is not limited to a few qubits or a specific class of circuits.”
High-threshold and low-overhead fault-tolerant quantum memory (2023, background): “008(3) 4× 10−8 2× 10−13 [[288, 12, 18]] 1/48 ≤ 18 0.”
Fault-tolerant quantum computation with constant overhead (2013, background): “The argument I have described above uses a somewhat different approach from the threshold proof in [4]; in terms of the tools from that paper, one could phrase the argument here as a process that replaces”
Demonstration of fault-tolerant universal quantum gate operations (2021, unknown): “E σ σ k l I I ∈ { ⊗ , ∀ , ∈ {0, 1, 2, 3}} \ { ⊗ } (5) k l 2”
Measurement-based quantum computation (2009, background): “This important result is called the threshold theorem of quantum computatio”
Superconducting nanocircuits for topologically protected qubits (2008, background): “Because of the local nature of noises, the task of large-scale quantum computation is considered to be realisti”
An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation (2009, methodology): “To deﬁne these properties rigorously, we need to ﬁrst introduce the notions of an r -ﬁlter and an ideal decoder [ 3 ].”
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.”
Quantum memories at finite temperature (2014, background): “This is due to the celebrated accuracy threshold theorem (Aharonov and Ben-Or, 1997; Aliferis and Cross, 2007; Aliferis et al., 2006; Kitaev, 1997; Knill et al., 1998; Preskill, 1998; Shor, 1996).”
Quantum computing and the entanglement frontier (2012, background): “44,48,49 If the noise Hamiltonian includes terms that act on k >> 1 qubits in the quantum computer (and in some complicated way on the environment), the proof of scalability works if these terms decay exponentially with k , and also decay rapidly enough as the qubits separate in space.”
A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits (2012, methodology): “5 for each controlled-H gate a cost of [2, 2, 1, 2] and for each controlled-P gate a cost of [0, 0, 2, 3].”
Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography (2016, background): “The bestknown proof of fault tolerance against general noise [20] derived a threshold of 2.”