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Topological quantum memory
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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.
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Cited by 30 Pith papers
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Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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Ground state preparation in $(2+1)$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory via deterministic quantum imaginary time evolution
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Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel
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Tensor-network decoders for process tensor descriptions of non-Markovian noise
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Magic State Injection on IBM Quantum Processors Above the Distillation Threshold
Experimental demonstration of logical |H_L> and |T_L> magic states with fidelities 0.8806 and 0.8665 on IBM superconducting hardware using a qubit-efficient surface code embedding, with reported error thresholds above...
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The limits of erasure-based postselection for quantum error mitigation
Postselection on erasure qubits fully mitigates erasure noise in QFT for erasure-check error rates below 3% and enables dual-rail systems to exceed noise floors unreachable by single-rail at kiloquop scale.
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Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state...
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Quantum Error Correction and $Z(2)$ Lattice Gauge Theories
Monte Carlo simulations of mapped 3D Z(2) x Z(2) gauge theories yield preliminary toric/surface code thresholds of about 0.68%, 6%, and 1.44% for three circuit-level noise models.
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