Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.
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Quantum codes on a lattice with boundary
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abstract
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of alternating pieces with two different types of boundary conditions. Logical operators are described in terms of relative homology groups.
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representative citing papers
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
Lattice-surgery scheduling is mapped to 3D path embedding and solved with look-ahead Dijkstra projection, yielding 3.8x lower execution time on quantum phase estimation benchmarks versus greedy scheduling.
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
Partial QEC on superpositions of code states suppresses local noise in quantum metrology with fewer checks than full QEC, achieving p to the power floor((l+1)/2) suppression for weight-l noise.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
KOVAL-Q uses SAT solving to optimize and verify surface-code logical operations with general encodings, finding d-cycle CNOTs and 2d-cycle rotations that reduce FTQC application runtime by about 10 percent.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
XYZ planar code with pMWPM decoder achieves higher and more stable thresholds under biased noise than standard surface codes, with a 36% improvement in the infinite-bias limit.
Concatenating quantum Reed-Solomon outer codes over the gross code using Galois qudits reaches teraquop regime at 10^{-3} physical noise with lower overhead than prior two-gross-code constructions.
The paper introduces concrete code deformation procedures for dense surface code packing, proposes hook-error-avoiding CNOT scheduling for syndrome extraction, and reports Monte Carlo simulations showing lower logical error rates than standard surface codes at large distances and low physical error,
Local syndrome-based preprocessing accelerates BP decoders for quantum LDPC codes, delivering up to 10x speedup on the [[144,12,12]] code while maintaining or improving logical error rates.
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 prior values.
Degenerate BP decoders achieve capacity-achieving or near-capacity performance for quantum erasure correction in linear time on bicycle, product, and topological stabilizer codes.
VGQEC codes embed tunable parameters in Quon graphs to enable noise-tailored quantum error correction, bridging repetition and stabilizer codes and showing experimental results under amplitude damping on a photonic system.
Synchronizable hybrid subsystem codes are built from classical cyclic codes C and D with C^perp subset C subset D via CSS construction to correct Pauli and synchronization errors, tolerate gauge errors, and carry both classical and quantum information, with explicit trade-offs.
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
Two new constructions of quantum dual-containing CSS LDPC codes from quasi-dyadic matrices achieve improved finite-length error performance over existing DC codes.
A programmable 2D toric oscillator network enables efficient routing for bivariate bicycle LDPC codes, reducing long-range couplers to O(sqrt(n)) and achieving 3.06% logical error rate per cycle in simulations for the [[18,4,4]] code.
The five-qubit code outperforms Steane and toric codes in preserving fidelity for low-temperature open quantum systems at weak-to-moderate couplings, with a critical time for entangled states beyond which correction helps.
Catalyst towers reduce runtime and spacetime volume for continuous rotations in surface codes at small and medium distances in phase oracle and variational state preparation circuits for option pricing.
Power-law divergence of fidelity susceptibility and logarithmic divergence of an entanglement witness mark the topological-to-non-topological transitions in locally perturbed Kitaev and color codes; critical points are located by finite-size scaling and confirmed by mapping to the 2D Ising model.
citing papers explorer
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Holographically Emergent Gauge Theory in Symmetric Quantum Circuits
Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.
-
Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
-
Non-linear Sigma Model for the Surface Code with Coherent Errors
A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.
-
The Structure of Circle Graph States
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
-
Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice
Lattice-surgery scheduling is mapped to 3D path embedding and solved with look-ahead Dijkstra projection, yielding 3.8x lower execution time on quantum phase estimation benchmarks versus greedy scheduling.
-
Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
-
Quantum metrology via partial quantum error correction
Partial QEC on superpositions of code states suppresses local noise in quantum metrology with fewer checks than full QEC, achieving p to the power floor((l+1)/2) suppression for weight-l noise.
-
Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
-
Design automation and space-time reduction for surface-code logical operations using a SAT-based EDA kernel compatible with general encodings
KOVAL-Q uses SAT solving to optimize and verify surface-code logical operations with general encodings, finding d-cycle CNOTs and 2d-cycle rotations that reduce FTQC application runtime by about 10 percent.
-
Magic state cultivation: growing T states as cheap as CNOT gates
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
-
A Posterior MWPM Decoding Boosts the XYZ Planar Code
XYZ planar code with pMWPM decoder achieves higher and more stable thresholds under biased noise than standard surface codes, with a 36% improvement in the infinite-bias limit.
-
Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes
Concatenating quantum Reed-Solomon outer codes over the gross code using Galois qudits reaches teraquop regime at 10^{-3} physical noise with lower overhead than prior two-gross-code constructions.
-
Dense packing of the surface code: code deformation procedures and hook-error-avoiding gate scheduling
The paper introduces concrete code deformation procedures for dense surface code packing, proposes hook-error-avoiding CNOT scheduling for syndrome extraction, and reports Monte Carlo simulations showing lower logical error rates than standard surface codes at large distances and low physical error,
-
Accelerating BP-based decoders for QLDPC Codes with Local Syndrome-Based Preprocessing
Local syndrome-based preprocessing accelerates BP decoders for quantum LDPC codes, delivering up to 10x speedup on the [[144,12,12]] code while maintaining or improving logical error rates.
-
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 prior values.
-
Degenerate quantum erasure decoding
Degenerate BP decoders achieve capacity-achieving or near-capacity performance for quantum erasure correction in linear time on bicycle, product, and topological stabilizer codes.
-
Variational Graphical Quantum Error Correction Codes
VGQEC codes embed tunable parameters in Quon graphs to enable noise-tailored quantum error correction, bridging repetition and stabilizer codes and showing experimental results under amplitude damping on a photonic system.
-
Synchronizable hybrid subsystem codes
Synchronizable hybrid subsystem codes are built from classical cyclic codes C and D with C^perp subset C subset D via CSS construction to correct Pauli and synchronization errors, tolerate gauge errors, and carry both classical and quantum information, with explicit trade-offs.
-
Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.
-
Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices
Two new constructions of quantum dual-containing CSS LDPC codes from quasi-dyadic matrices achieve improved finite-length error performance over existing DC codes.
-
Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures
A programmable 2D toric oscillator network enables efficient routing for bivariate bicycle LDPC codes, reducing long-range couplers to O(sqrt(n)) and achieving 3.06% logical error rate per cycle in simulations for the [[18,4,4]] code.
-
Noise-Resilient Quantum Evolution in Open Systems through Error-Correcting Frameworks
The five-qubit code outperforms Steane and toric codes in preserving fidelity for low-temperature open quantum systems at weak-to-moderate couplings, with a critical time for entangled states beyond which correction helps.
-
Space and Time Cost of Continuous Rotations in Surface Codes
Catalyst towers reduce runtime and spacetime volume for continuous rotations in surface codes at small and medium distances in phase oracle and variational state preparation circuits for option pricing.
-
Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
Power-law divergence of fidelity susceptibility and logarithmic divergence of an entanglement witness mark the topological-to-non-topological transitions in locally perturbed Kitaev and color codes; critical points are located by finite-size scaling and confirmed by mapping to the 2D Ising model.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
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Dimensioning of Quantum Memories for Distilled Quantum EPR Packets
A Markov chain framework is introduced to model and optimize quantum memory dimensioning for preserving distilled EPR pairs in quantum networks.
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Maximum Likelihood Decoding of Quantum Error Correction Codes
A topical review unifying statistical mechanics, tensor network, and AI approaches to approximate maximum likelihood decoding for quantum error correction codes.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
- LightStim: A Framework for QEC Protocol Evaluation and Prototyping with Automated DEM Construction
- AI-Enabled Decoding of Qubit Loss for Quantum Error-Correcting Codes