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.
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An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
14 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum error-correcting code. The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value.
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UNVERDICTED 14roles
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A donor-cluster array architecture in silicon uses shared electrons and natural hyperfine distributions for individual spin addressability, tunable inter-cluster exchange, and high-fidelity gates to enable scalable quantum computing.
Dynamarq is a new scalable benchmarking framework that defines structural features for dynamic quantum circuits and uses statistical models to predict hardware fidelity with transferable parameters.
Postselection on typical syndromes in the toric code suppresses logical error rates from p_f to p_f^b with b approximately 3.1 via large-deviation arguments.
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.
A Hyperbolic Cycle Basis algorithm is introduced within a unified framework for constructing and benchmarking CSS quantum error correction codes on hyperbolic lattices, with performance metrics evaluated on two example codes.
Geometrical constructions map classical linear error correcting codes to purity testing protocols whose properties are fully determined by the codes, enabling applications in quantum communication.
GHZ states in X, Y, and Z bases form a maximally sensitive set allowing straightforward tests to identify coherent errors in quantum gates, measurements, and state preparation.
Neural decoders for surface-code QEC achieve practical microsecond FPGA latency when trained on large datasets with appropriate inductive biases and INT4 quantization, rather than relying on architectural complexity.
A graph-based bounded distance decoder corrects all errors up to a chosen weight in arbitrary stabilizer codes by representing stabilizers and syndromes as graphs and pruning the search space with a feed-forward structure.
SS-τ and AST scheduling policies for seam checks in distributed triangular color codes reduce remote-operation overhead and achieve lower logical error rates with fault-tolerant scaling in specific EGR regimes under circuit-level noise.
Superconducting circuit hosts fractional fluxon states (fraxons) in a tailored Josephson potential to realize protected qudits with a STIRAP gate protocol.
Null-result weak measurements are dynamically characterized for qubits and qutrits using Shannon entropy, mutual information, fidelity, and relative entropy to quantify information extraction amounts, rates, and reversibility.
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.
citing papers explorer
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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.
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Scalable Spin Qubit Architecture with Donor-Cluster Arrays in Silicon
A donor-cluster array architecture in silicon uses shared electrons and natural hyperfine distributions for individual spin addressability, tunable inter-cluster exchange, and high-fidelity gates to enable scalable quantum computing.
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Characterizing and Benchmarking Dynamic Quantum Circuits
Dynamarq is a new scalable benchmarking framework that defines structural features for dynamic quantum circuits and uses statistical models to predict hardware fidelity with transferable parameters.
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Scalable accuracy gains from postselection in quantum error correcting codes
Postselection on typical syndromes in the toric code suppresses logical error rates from p_f to p_f^b with b approximately 3.1 via large-deviation arguments.
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Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
Benchmarks gradient-ascent algorithms for constrained free energy minimization on quantum Heisenberg models and stabilizer codes, with applications to thermal state design and fixed-temperature quantum encoding.
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Systematic Approach to Hyperbolic Quantum Error Correction Codes
A Hyperbolic Cycle Basis algorithm is introduced within a unified framework for constructing and benchmarking CSS quantum error correction codes on hyperbolic lattices, with performance metrics evaluated on two example codes.
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Geometrical constructions of purity testing protocols and their applications to quantum communication
Geometrical constructions map classical linear error correcting codes to purity testing protocols whose properties are fully determined by the codes, enabling applications in quantum communication.
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Maximally Sensitive Sets of States
GHZ states in X, Y, and Z bases form a maximally sensitive set allowing straightforward tests to identify coherent errors in quantum gates, measurements, and state preparation.
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Rethink the Role of Neural Decoders in Quantum Error Correction
Neural decoders for surface-code QEC achieve practical microsecond FPGA latency when trained on large datasets with appropriate inductive biases and INT4 quantization, rather than relying on architectural complexity.
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A graph-aware bounded distance decoder for all stabilizer codes
A graph-based bounded distance decoder corrects all errors up to a chosen weight in arbitrary stabilizer codes by representing stabilizers and syndromes as graphs and pruning the search space with a feed-forward structure.
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Boundary-Aware Stabilizer Scheduling for Distributed Quantum Error Correction
SS-τ and AST scheduling policies for seam checks in distributed triangular color codes reduce remote-operation overhead and achieve lower logical error rates with fault-tolerant scaling in specific EGR regimes under circuit-level noise.
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Fraxonium: Fractional fluxon states for qudit encoding
Superconducting circuit hosts fractional fluxon states (fraxons) in a tailored Josephson potential to realize protected qudits with a STIRAP gate protocol.
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Information-Theoretic Analysis of Weak Measurements and Their Reversal
Null-result weak measurements are dynamically characterized for qubits and qutrits using Shannon entropy, mutual information, fidelity, and relative entropy to quantify information extraction amounts, rates, and reversibility.
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Graph-State Circuit Blocks control Entanglement and Scrambling Velocities
LC-inequivalent graph-state blocks in random Clifford circuits yield distinct entanglement velocities v_E and butterfly velocities v_B, correlated with internal entanglement distribution and graph connectivity.