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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.
Forward citations
Cited by 31 Pith papers
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Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
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Chiral edge codes have local-erasure robustness governed by power-law exponents with hierarchy γ≥α≥min{α,β}, so the 2D code is at least as robust as its 1D CFT reduction.
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A trapped-ion experiment demonstrates adaptive measurement-based simulation of real-time Z2 lattice gauge theory dynamics, with one-form-symmetry syndromes used for postselection.
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A quantum bus connects many logical qubits through a gauge-code strip, with a claimed factor O(d) reduction in qubit overhead for long-range logical interactions.
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In windowed quantum decoding, a wrong speculative boundary guess stays inside one window, and the predict-verify-recover loop removes the serial stall with negligible penalty.
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The Delayed Stabilizer ZX-Calculus
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Zero-weight percolation at pc = 0.1000(2) is argued to set the ferromagnetic phase boundary in the 2D ±J Ising model, making the boundary vertical below the Nishimori point.
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Confinement as Decoding: Higher Form Codes and Lattice Yang-Mills Theory
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Arbitrary-Distance Quantum Error Correction with Gauss's Law for $\mathbb Z_2$ Lattice Gauge Theory
Gauss's law constraints in Z2 lattice gauge theory can be made into quantum error-correcting codes of arbitrary distance, with provably optimal encoding rate within the constructed family.
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Realizing Error Suppression in Partially Fault-Tolerant Quantum Simulations with IBM Quantum Computers
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A conditional no-go for resource-free magic-axis measurement on a static surface code
Under three stated assumptions, a resource-free static surface-code patch cannot sharply measure the magic axis at polynomial acceptance; it must pay with a resource, leave the dilute regime, or accept exponentially rarely.
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LUCI on IBM Hardware: Error Suppression with Almost Half Syndrome Density
Hardware experiment on IBM devices shows reset-free LUCI achieves logical X and Z error suppression ratios of 1.75(10) and 1.93(12), competitive with surface code despite halved syndrome density.
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Static features from mixing in short- and long-range Lindbladians: Markov property and correlations
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Gauging Time Reversal Symmetry in Quantum Gravity: Arrow of Time from a Confinement--Deconfinement Transition
The emergence of the cosmological arrow of time is identified with a confinement-deconfinement transition in a Z2 lattice gauge theory on LQG spin networks, with the deconfined phase corresponding to a CZX-type SPT phase.
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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
Deterministic QITE with a Gauss-law-reduced Pauli pool reproduces DMRG ground-state energies of (2+1)-D pure Z2 lattice gauge theory to within 0.1% for ladders of up to 32 qubits and coupling λ ∈ [0.5, 5].
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Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel
Bivariate bicycle codes achieve an asymptotic threshold of approximately 0.488 on the quantum erasure channel with BP-OSD decoding, offering modest threshold edge and 12x lower overhead than toric codes under fair baselines.
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Dissipative quantum circuits with periodic qubit resets provably avoid both unitary and noise-induced barren plateaus for gates near the final measurement.
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Tensor-network decoders for process tensor descriptions of non-Markovian noise
A tensor-network-based maximum likelihood decoder is constructed for quantum error correction under process-tensor noise, with an MPS approximation demonstrated on the five-qubit and Steane codes.
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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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Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
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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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