A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound

Abstract

I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$ error.

REVTeX, 22 pages; introduction clarified and corrected to explicitly include non-orthogonal codes, claim of appendix A restricted to possibly allow some 1-error degenerate codes, references added; to appear in Phys. Rev. A

References in corpus (2)

• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Good Quantum Error-Correcting Codes Exist

Cited by in corpus (618)

• Fault-tolerant quantum computation by anyons
• Decoherence, einselection, and the quantum origins of the classical
• Entanglement detection
• Topological quantum memory
• Dynamical suppression of decoherence in two-state quantum systems
• Encoding a qubit in an oscillator
• Improved Simulation of Stabilizer Circuits
• Quantum Computing
• How to share a quantum secret
• Noiseless Quantum Codes
• Reliable Quantum Computers
• A Theory of Fault-Tolerant Quantum Computation
• Quantum Error Correction and Orthogonal Geometry
• Quantum Error Correction for Beginners
• On mutually unbiased bases
• Topological Quantum Distillation
• Quantum computation with optical coherent states
• Quantum Entanglement Growth Under Random Unitary Dynamics
• On the Theory of Quantum Secret Sharing
• Measurement-driven entanglement transition in hybrid quantum circuits
• Fault-Tolerant Quantum Dynamical Decoupling
• Preserving coherence in quantum computation by pairing quantum bits
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Noise tailoring for scalable quantum computation via randomized compiling
• Simple Quantum Error Correcting Codes
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• Random Quantum Circuits
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Quantum enhanced measurements without entanglement
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Quantum error-correcting codes associated with graphs
• Discrete phase space based on finite fields
• Dynamical purification phase transitions induced by quantum measurements
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Higher-dimensional orbital angular momentum based quantum key distribution with mutually unbiased bases
• The Future of Quantum Computing with Superconducting Qubits
• Quantum tensor product structures are observable-induced
• Resilient Quantum Computation: Error Models and Thresholds
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• Valence Bond Solids for Quantum Computation
• Active stabilisation, quantum computation and quantum state synthesis
• A Survey on Quantum Channel Capacities
• Symmetrizing Evolutions
• Virtual Quantum Subsystems
• Fundamentals of Quantum Information Theory
• Information Scrambling in Computationally Complex Quantum Circuits
• Quantum Channel Capacity of Very Noisy Channels
• Decoherence-Free Subspaces and Subsystems
• Entanglement Detection in the Stabilizer Formalism
• Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes
• Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment
• Spin-based all-optical quantum computation with quantum dots: understanding and suppressing decoherence
• Bell Inequalities for Graph States
• Quantum error correction with only two extra qubits
• Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences
• Bosonic Quantum Codes for Amplitude Damping
• Implementation of the Five Qubit Error Correction Benchmark
• Statistical mechanics of quantum error correcting codes
• Measurement Protected Quantum Phases
• Stabilizing Quantum Information
• Practical issues in quantum-key-distribution post-processing
• Causal and localizable quantum operations
• Topological Computation without Braiding
• Nonlocality of cluster states of qubits
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Efficient fault-tolerant quantum computing
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Quantum circuits for strongly correlated quantum systems
• Analog quantum error correction
• Experimental application of decoherence-free subspaces in a quantum-computing algorithm
• Single-shot fault-tolerant quantum error correction
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Basics of Quantum Computation
• Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
• Entanglement Transition in the Projective Transverse Field Ising Model
• Quantum Information is Physical
• Experimental detection of entanglement via witness operators and local measurements
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Unified derivations of measurement-based schemes for quantum computation
• Not all pure entangled states are useful for sub shot-noise interferometry
• Universal transversal gates with color codes - a simplified approach
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Optimal verification of entangled states with local measurements
• Quantum Gates and Circuits
• Efficient Computations of Encodings for Quantum Error Correction
• Zeno effect for quantum computation and control
• Quantum computing by optical control of electron spins
• Topological Subsystem Codes
• Catalytic quantum error correction
• Mutually unbiased measurements in finite dimensions
• Calculating the Thermal Rate Constant with Exponential Speed-Up on a Quantum Computer
• Entanglement required in achieving entanglement-assisted channel capacities
• Spacetime duality between localization transitions and measurement-induced transitions
• Information-theoretic approach to quantum error correction and reversible measurement
• Partial separability and entanglement criteria for multiqubit quantum states
• Optimum Quantum Error Recovery using Semidefinite Programming
• A nonadditive quantum code
• Fault-tolerant logical gates in quantum error-correcting codes
• Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
• Quantum Measurements and Gates by Code Deformation
• Physical Optimization of Quantum Error Correction Circuits
• Holographic tensor network models and quantum error correction: A topical review
• Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes
• Commuting Pauli Hamiltonians as maps between free modules
• Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies
• Basic concepts in quantum computation
• No-Go Theorems for Quantum Resource Purification
• Quantum accuracy threshold for concatenated distance-3 codes
• Combined encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing
• Quantum Annealing Correction with Minor Embedding
• Asymptotically Good Quantum Codes
• Quantum Computation
• On the structure of the sets of mutually unbiased bases for N qubits
• Generalization of Quantum Error Correction via the Heisenberg Picture
• Quantum error correction for continuously detected errors
• Optical pumping into many-body entanglement
• Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes
• Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes
• Homological Error Correction: Classical and Quantum Codes
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
• Robust quantum metrological schemes based on protection of quantum Fisher information
• The black-hole/qubit correspondence: an up-to-date review
• Achievable rates for the Gaussian quantum channel
• Quantum error correction in the presence of spontaneous emission
• Feasibility of self-correcting quantum memory and thermal stability of topological order
• The ZX calculus is a language for surface code lattice surgery
• Introduction to Quantum Algorithms
• Experimental violation of multipartite Bell inequalities with trapped ions
• Topological order in 1D Cluster state protected by symmetry
• Linear Depth Stabilizer and Quantum Fourier Transformation Circuits with no Auxiliary Qubits in Finite Neighbor Quantum Architectures
• Quantum Error Correcting Codes From The Compression Formalism
• Graphical Nonbinary Quantum Error-Correcting Codes
• Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
• Efficient Quantum Transforms
• An Introduction to Quantum Error Correction
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Spin squeezing and entanglement for arbitrary spin
• Advantages of versatile neural-network decoding for topological codes
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Nonstabilizerness via matrix product states in the Pauli basis
• Fault-tolerant holonomic quantum computation
• Clifford Gates by Code Deformation
• Universal fault-tolerant gates on concatenated stabilizer codes
• Quantum codewords contradict local realism
• Multipulse Control of Decoherence
• Structure of 2D Topological Stabilizer Codes
• Quantum Error Correction of Observables
• Constructing finite dimensional codes with optical continuous variables
• Introduction to Quantum Error Correction
• Topological Protection and Quantum Noiseless Subsystems
• Universal Leakage Elimination
• Digital Quantum Simulation with Rydberg Atoms
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
• Preparing encoded states in an oscillator
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Robust Quantum Error Correction via Convex Optimization
• Cellular-automaton decoders with provable thresholds for topological codes
• Encoding Hypergraphs into Quantum States
• Prevention of dissipation with two particles
• Optimal quantum codes for preventing collective amplitude damping
• Purity and State Fidelity of Quantum Channels via Hamiltonians
• Magic State Distillation with Low Space Overhead and Optimal Asymptotic Input Count
• Entanglement-Assisted Quantum Convolutional Coding
• A repetition code of 15 qubits
• Quantum Error Correction with the Semion Code
• Adiabatic quantum optimization with the wrong Hamiltonian
• Supersinglets
• Empirical Determination of Bang-Bang Operations
• QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
• Stabilizing distinguishable qubits against spontaneous decay by detected-jump correcting quantum codes
• Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
• Non-adiabatic geometrical quantum gates in semiconductor quantum dots
• Three-dimensional color code thresholds via statistical-mechanical mapping
• Two-setting Bell Inequalities for Graph States
• Nonadditive quantum error-correcting code
• Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors
• Resonant cancellation of off-resonant effects in a multilevel qubit
• Minimal qudit code for a qubit in the phase-damping channel
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Electron Spins in Artificial Atoms and Molecules for Quantum Computing
• Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
• Experimental exploration of five-qubit quantum error correcting code with superconducting qubits
• Algebraic Methods for Quantum Codes on Lattices
• Photon-number entangled states generated in Kerr media with optical parametric pumping
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
• EXIT-Chart Aided Near-Capacity Quantum Turbo Code Design
• Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
• Constructions and Noise Threshold of Topological Subsystem Codes
• Geometrical approach to mutually unbiased bases
• Quantum Error Correction via Convex Optimization
• Non-stabilizerness versus entanglement in matrix product states
• Simulating a measurement-induced phase transition for trapped ion circuits
• Approximate quantum error correction for generalized amplitude damping errors
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
• Algebraic and information-theoretic conditions for operator quantum error-correction
• Quantum error correction may delay, but also cause, entanglement sudden death
• A simple family of nonadditive quantum codes
• Triviality of quantum trajectories close to a directed percolation transition
• Fault-Tolerant Logical Gate Networks for CSS Codes
• On uncertainty relations and entanglement detection with mutually unbiased measurements
• Optimal preparation of graph states
• Quantum Computer Architecture: Towards Full-Stack Quantum Accelerators
• Entanglement-magic separation in hybrid quantum circuits
• Five Quantum Register Error Correction Code For Higher Spin Systems
• Overview of Quantum Error Prevention and Leakage Elimination
• Mermin inequalities for perfect correlations
• Quasi-Cyclic Constructions of Quantum Codes
• Time evolution and decoherence of a spin-1/2 particle coupled to a spin bath in thermal equilibrium
• Quantum Error Correction beyond the Bounded Distance Decoding Limit
• Dissipative Universal Lindbladian Simulation
• Surface Code Threshold in the Presence of Correlated Errors
• Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels
• Topological Quantum Error Correction with Optimal Encoding Rate
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Quantum Error-Correction-Enhanced Magnetometer Overcoming the Limit Imposed by Relaxation
• Quantum Stabilizer Codes and Classical Linear Codes
• The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
• Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
• Entanglement in eight-qubit graph states
• Uncertainty relations for general unitary operators
• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
• Algebraic geometric construction of a quantum stabilizer code
• Ability of stabilizer quantum error correction to protect itself from its own imperfection
• Optimally combining dynamical decoupling and quantum error correction
• Encoding One Logical Qubit Into Six Physical Qubits
• Statistical Mechanical Models and Topological Color Codes
• Coherent error threshold for surface codes from Majorana delocalization
• Logical operator tradeoff for local quantum codes
• Rank-2 Toric Code in Two Dimensions
• Level Reduction and the Quantum Threshold Theorem
• Measurement-Driven Phase Transition within a Volume-Law Entangled Phase
• Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
• Continuous variable encoding by ponderomotive interaction
• Quantum Convolutional Error Correcting Codes
• Protecting quantum memories using coherent parity check codes
• Mean Field Analysis of Quantum Annealing Correction
• Changing topology by topological defects in three-dimensional topologically ordered phases
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Multipartite entanglement detection with minimal effort
• Connectivity constrains quantum codes
• A Lower Bound on the Quantum Capacity of Channels with Correlated Errors
• All-Electrical Quantum Computation with Mobile Spin Qubits
• Fault Tolerant Quantum Computation with Constant Error
• Error suppression for Hamiltonian-based quantum computation using subsystem codes
• Generating continuous variable quantum codewords in the near-field atomic lithography
• Resource-efficient analyzer of Bell and Greenberger-Horne-Zeilinger states of multiphoton systems
• Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
• Framework for classifying logical operators in stabilizer codes
• Environment-Induced Decoherence and the Transition From Quantum to Classical
• Decoherence, Control, and Symmetry in Quantum Computers
• Effects of noise on quantum error correction algorithms
• Effective noise channels for encoded quantum systems
• Stabilizer quantum codes from $J$-affine variety codes and a new Steane-like enlargement
• Benchmarking near-term devices with quantum error correction
• Quantum Computing in the Presence of Detected Spontaneous Emission
• A universal set of qubit quantum channels
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
• Generalized X states of N qubits and their symmetries
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Mutually unbiased bases and generalized Bell states
• Entanglement properties of topological color codes
• Ignorance is bliss: General and robust cancellation of decoherence via no-knowledge quantum feedback
• Qubit stabilizer states are complex projective 3-designs
• Channel-Optimized Quantum Error Correction
• Universal Quantum Computation in a Neutral Atom Decoherence Free Subspace
• Perturbative expansions for the fidelities and spatially correlated dissipation of quantum bits
• Asymmetric entanglement-assisted quantum error-correcting codes and BCH codes
• Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies
• Particle-wave duality: a dichotomy between symmetry and asymmetry
• Universal quantum computation in decoherence-free subspaces with hot trapped-ions
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• Quantum Coding with Entanglement
• Distant entanglement protected through artificially increased local temperature
• Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors
• Coherence protection by the quantum Zeno effect and non-holonomic control in a Rydberg Rubidium isotope
• Entanglement-Assisted Quantum Error Correction with Linear Optics
• Optimal error correction in topological subsystem codes
• Additivity of decoherence measures for multiqubit quantum systems
• Quantum Goethals-Preparata Codes
• Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Analysis of the quantum Zeno effect for quantum control and computation
• Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes
• The multiplicative domain in quantum error correction
• Good Quantum Convolutional Error Correction Codes And Their Decoding Algorithm Exist
• Piggybacking on Quantum Streams
• Quantum error correction for continuously detected errors with any number of error channels per qubit
• Detection of multipartite entanglement with two-body correlations
• Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
• Conditional generation of error syndromes in fault-tolerant error correction
• The Minimum Distance Problem for Two-Way Entanglement Purification
• Stabilizer notation for Spekkens' toy theory
• The Veldkamp space of multiple qubits
• Quantum codes from affine variety codes and their subfield-subcodes
• Lower bound for the quantum capacity of a discrete memoryless quantum channel
• Single-shot decoding of good quantum LDPC codes
• On the distance of stabilizer quantum codes from $J$-affine variety codes
• Degenerate quantum codes and the quantum Hamming bound
• Quantum error correction with degenerate codes for correlated noise
• Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles
• Multiqubit entanglement witness
• Limits on Efficient Computation in the Physical World
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction
• Quantum Computing and Error Correction
• Multi-particle decoherence free subspaces in extended systems
• Quantum error correction on infinite-dimensional Hilbert spaces
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Quantum error suppression with commuting Hamiltonians: Two-local is too local
• Short Codes for Quantum Channels with One Prevalent Pauli Error Type
• Logical independence and quantum randomness
• Fault-tolerant qubit encoding using a spin-7/2 qudit
• Adaptive syndrome measurements for Shor-style error correction
• Conversion of a general quantum stabilizer code to an entanglement distillation protocol
• Error tolerance of topological codes with independent bit-flip and measurement errors
• Non-Additive Quantum Codes from Goethals and Preparata Codes
• Generalized Toric Codes Coupled to Thermal Baths
• Noise Tolerance of the BB84 Protocol with Random Privacy Amplification
• Hierarchy of quasi-symmetries and degeneracies in chiral crystal materials CoSi
• Refocusing schemes for holonomic quantum computation in presence of dissipation
• Effect of system level structure and spectral distribution of the environment on the decoherence rate
• Landauer Principle and Thermodynamics of Computation
• Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes
• Simultaneous Discovery of Quantum Error Correction Codes and Encoders with a Noise-Aware Reinforcement Learning Agent
• Encoding graphs into quantum states: an axiomatic approach
• Multipartite unlockable bound entanglement in the stabilizer formalism
• Universally Optimal Verification of Entangled States with Nondemolition Measurements
• Experimental Implementation of Logical Bell State Encoding
• In-situ characterization of quantum devices with error correction
• Combined Error Correction Techniques for Quantum Computing Architectures
• Quantum codes from a new construction of self-orthogonal algebraic geometry codes
• Continuous quantum error correction for evolution under time-dependent Hamiltonians
• Efficient estimation of multipartite quantum coherence
• Parts and Wholes. An Inquiry into Quantum and Classical Correlations
• Scheme for fault-tolerant holonomic computation on stabilizer codes
• Efficient Quantum Key Distribution Scheme And Proof of Its Unconditional Security
• Simulating noisy variational quantum eigensolver with local noise models
• Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
• Compilation of algorithm-specific graph states for quantum circuits
• Simple quantum error detection and correction for superconducting qubits
• Activation of metrologically useful genuine multipartite entanglement
• Channel-Adapted Quantum Error Correction
• Quantum Interleaver: Quantum Error Correction for Burst Error
• Achieving fault tolerance on capped color codes with few ancillas
• Determination of the Semion Code Threshold using Neural Decoders
• Theory of multiwave mixing and decoherence control in qubit array system
• The Stability of Quantum Concatenated Code Hamiltonians
• Entanglement-Assisted Quantum Error Correcting Codes From RS Codes and BCH Codes with Extension Degree 2
• Entropic bounds on coding for noisy quantum channels
• Derandomizing quantum circuits with measurement based unitary designs
• Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
• Demonstration of quantum error correction for enhanced sensitivity of photonic measurements
• Quantum Complexity Fluctuations from Nuclear and Hypernuclear Forces
• Generalized Multiplicative Domains and Quantum Error Correction
• Mermin pentagrams arising from Veldkamp lines for three qubits
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Always-On Quantum Error Tracking with Continuous Parity Measurements
• Towards Large-Scale Quantum Computation
• Numerical method for finding decoherence-free subspaces and its applications
• Hyperentanglement witness
• Multi-qubit stabilizer and cluster entanglement witnesses
• Continuous Quantum Error Correction Through Local Operations
• Limits to error correction in quantum chaos
• Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations
• Algebraic Quantum Codes: Linking Quantum Mechanics and Discrete Mathematics
• Entanglement Transitions in Unitary Circuit Games
• Engineering complex topological memories from simple Abelian models
• $k$-uniform mixed states
• A proposal for a minimal surface code experiment
• A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices
• Analysis of Quantum Entanglement in Quantum Programs using Stabilizer Formalism
• Qubit state guidance without feedback
• Constructing quantum error-correcting codes for p^m-state systems from classical error-correcting codes
• An introduction to one-way quantum computing in distributed architectures
• Measuring the parity of an $N$-qubit state
• Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles
• Modular Quantum Information Processing by Dissipation
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• Quantum Error-Correcting Codes over Mixed Alphabets
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Perfect many-to-one teleportation with stabilizer states
• Criteria to detect genuine multipartite entanglement using spin measurements
• Quantum simulation of many-body spin interactions with ultracold polar molecules
• On preparing ground states of gapped Hamiltonians: An efficient Quantum Lovász Local Lemma
• Quantum coherence in mutually unbiased bases
• Investigating a Class of $2\otimes 2\otimes d$ Chessboard Density Matrices via Linear and Non-linear Entanglement Witnesses Constructed by Exact Convex Optimization
• Quantum error avoiding codes versus quantum error correcting codes
• Identification of a reversible quantum gate: assessing the resources
• Benchmarking quantum gates and circuits
• The attractor mechanism as a distillation procedure
• Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
• Compact set of invariants characterizing graph states of up to eight qubits
• Qudit hypergraph states and their properties
• Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm
• On defining the Hamiltonian beyond quantum theory
• Benchmarking quantum logic operations relative to thresholds for fault tolerance
• Bacon-Shor code with continuous measurement of non-commuting operators
• Finding good quantum codes using the Cartan form
• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
• Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial
• Non-perturbative Dynamical Decoupling Control: A Spin Chain Model
• Delayed commutation in quantum computer networks
• Multipartite Entanglement and Hypergraph states of three qubits
• Entanglement-assisted Coding Theory
• Quantum phase transition in the $Z_3$ Kitaev-Potts model
• Classical and Quantum Evaluation Codes at the Trace Roots
• Dynamically Generated Decoherence-Free Subspaces and Subsystems on Superconducting Qubits
• Arbitrary-time error suppression for Markovian adiabatic quantum computing using stabilizer subspace codes
• Low-depth Clifford circuits approximately solve MaxCut
• Two Gilbert-Varshamov Type Existential Bounds for Asymmetric Quantum Error-Correcting Codes
• Lattice quantum codes and exotic topological phases of matter
• Characterizing measurement-based quantum gates in quantum many-body systems using correlation functions
• Conjugate Codes and Applications to Cryptography
• Decoding the Projective Transverse Field Ising Model
• Classicality of quantum information processing
• Teleportation and entanglement distillation in the presence of correlation among bipartite mixed states
• Fault-tolerant breathing pattern in optical lattices as a dynamical quantum memory
• Minimal noise subsystems
• Macroscopic features of quantum fluctuations in large N qubit system
• Gottesman Types for Quantum Programs
• Optimal noise estimation from syndrome statistics of quantum codes
• Magic State Distillation at Intermediate Size
• Systematic Design and Optimization of Quantum Circuits for Stabilizer Codes
• Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment
• A finite geometric toy model of space-time as an error correcting code
• Robustness of channel-adapted quantum error correction
• Quantum Reed-Muller Codes
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Optimized Entanglement-Assisted Quantum Error Correction
• Generalized Concatenation for Quantum Codes
• On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes
• Constructions of $\ell$-Adic $t$-Deletion-Correcting Quantum Codes
• Parafermion stabilizer codes
• Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's Algorithm
• How to correct small quantum errors
• Stability of topologically-protected quantum computing proposals as seen through spin glasses
• GHZ and W Entanglement Witnesses for the Non-interacting Fermi gas
• Error-correcting one-way quantum computation with global entangling gates
• Deterministic distributed dense coding with stabilizer states
• Composite anyon coding and the initialization of a topological quantum computer
• Quantum stabilizer codes and beyond
• Improved storage of coherent and squeezed states in imperfect ring cavity
• Homological invariants of Pauli stabilizer codes
• Evolving Quantum Circuits
• Quantum Error Correction and Fault-Tolerance
• Stabilizer Formalism for Operator Algebra Quantum Error Correction
• Quantum Ruzsa Divergence to Quantify Magic
• Quantum Error Correction and One-Way LOCC State Distinguishability
• Screening of qubit from zero-temperature reservoir
• On Quantum and Classical Error Control Codes: Constructions and Applications
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Bell inequality violations with random mutually unbiased bases
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Quantum 2-Body Hamiltonian for Topological Color Codes
• Limitations on transversal gates for hypergraph product codes
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• Quantum Capacity of Partially Corrupted Quantum Network
• Optical implementation of a unitarily correctable code
• Optimized Quantum Error Correction Codes for Experiments
• Effect of ancilla's structure on quantum error correction using the 7-qubit Calderbank-Shor-Steane code
• Construction of optimal resources for concatenated quantum protocols
• Dissipative Encoding of Quantum Information
• Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
• Discrete phase-space mappings, tomographic condition and permutation invariance
• Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
• Designing quantum error correction codes for practical spin qudit
• Advance sharing of quantum shares for classical secrets
• Separability Lindblad equation for dynamical open-system entanglement
• Quantitative Treatment of Decoherence
• Transition of D- Level Quantum Systems Through Quantum Channels with Correlated Noise
• Concatenated Conjugate Codes
• Automated searching for quantum subsystem codes
• Molecular machines for quantum error correction
• Information Rates Achievable with Algebraic Codes on Quantum Discrete Memoryless Channels
• Area laws and efficient descriptions of quantum many-body states
• Improvement of stabilizer based entanglement distillation protocols by encoding operators
• Group structures and representations of graph states
• Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Error correction for mutually interacting qubits
• All-versus-nothing proofs with n qubits distributed between m parties
• An anyon model in a toric honeycomb lattice
• Subsystem Code Constructions
• Stabilizer Codes with Exotic Local-dimensions
• Stabilizer quantum codes defined by trace-depending polynomials
• On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes
• Theory of homotopes in application to mutually unbiased bases, harmonic analysis on graphs and perverse sheaves
• Encoding Classical Information in Gauge Subsystems of Quantum Codes
• Role of quantum state texture in probing resource theories and quantum phase transition
• Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics
• Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
• Scalable noncontextuality inequalities and certification of multiqubit quantum systems
• A New Model for Fractons, Fluxons, and Freeons
• Quantum $(r,\delta )$-locally recoverable codes
• Unconditionally Secure Quantum Key Distribution In Higher Dimensions
• Deterministic Dense Coding and Faithful Teleportation with Multipartite Graph States
• Decoherence and Quantum Error Correction for Quantum Computing and Communications
• Entropic measure and hypergraph states
• Quantum MacWilliams Identities
• Information Theoretical Approach to Control of Quantum Mechanical Systems
• Decoherence suppression for oscillator-assisted geometric quantum gates via symmetrization
• Quantum Logical States and Operators for Josephson-like Systems
• Universal Simulation of Hamiltonians Using a Finite Set of Control Operations
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction
• Quantum Communication and Decoherence
• Quantum error pre-compensation for quantum noisy channels
• Self-Correcting Quantum Computers
• Information flow at the quantum-classical boundary
• Conditions for degradability of tripartite quantum states
• Quantum Property Preservation
• Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning
• Robust universal Hamiltonian quantum computing using two-body interactions
• Demonstration of teleportation-based error correction in the IBM quantum computer
• Dynamical Aspects of Information Storage in Quantum-Mechanical Systems
• A fermionic code related to the exceptional group $E_8$
• Quantum Cyclic Code
• 5-qubit quantum error correction in a charge qubit quantum computer
• Fidelity of a t-error correcting quantum code with more than t errors
• Several Classes of Concatenated Quantum Codes: Constructions and Bounds
• Nonbinary Quantum Stabilizer Codes
• Macroscopic approach to N-qudit systems
• Semidefinite programming bounds on the size of entanglement-assisted codeword stabilized quantum codes
• An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve
• Nonbinary stabilizer codes over finite fields
• Lie Algebras and Suppression of Decoherence in Open Quantum Systems
• Probabilistic quantum error correction
• Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
• Quantum Codes for Controlling Coherent Evolution
• Quantum Computing: Linear Optics Implementations
• Error Channels and the Threshold for Fault-tolerant Quantum Computation
• A Note on Quantum Hamming Bound
• Clifford Manipulations of Stabilizer States: A graphical rule book for Clifford unitaries and measurements on cluster states, and application to photonic quantum computing
• Single-shot quantum error correction with the three-dimensional subsystem toric code
• Asynchronous Operations on Qubits in Distributed Simulation Environments using QooSim
• MUB-like structures and tomographic reconstruction for N-ququart systems
• Channel Identification and its Impact on Quantum LDPC Code Performance
• A unification of the coding theory and OAQEC perspective on hybrid codes
• The correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares
• MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes
• No quantum Ramsey theorem for stabilizer codes
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• Decoder for Nonbinary CWS Quantum Codes
• Quantum LDPC codes from intersecting subsets
• Design of Quantum Stabilizer Codes From Quadratic Residues Sets
• Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface Codes
• Notes on the Fidelity of Symplectic Quantum Error-Correcting Codes
• Beyond Stabilizer Codes I: Nice Error Bases
• Beyond Stabilizer Codes II: Clifford Codes
• Quantum Complementarity and Operator Structures
• Thermal stability of two-dimensional Topological Color Code
• Performance comparison of the two reconstruction methods for stabilizer-based quantum secret sharing
• Quantum Synchronizable Codes From Quadratic Residue Codes and Their Supercodes
• Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC
• Universal Quantum Computation with Abelian Anyon Models
• No More Perfect Codes: Classification of Perfect Quantum Codes
• Decoherence-Free Communication over Multiaccess Quantum Channels
• Approaches to Quantum Error Correction
• Demonstration of High-Fidelity Entangled Logical Qubits using Transmons
• Revisiting thermodynamics in computation and information theory
• Finding the disjointness of stabilizer codes is NP-complete
• Homology of Generic Stabilizer States
• Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
• Towards the Classical Communication Complexity of Entanglement Distillation Protocols with Incomplete Information
• Entanglement of stabilizer codewords
• Random access codes via quantum contextual redundancy
• Quantum LDPC Codes Constructed from Point-Line Subsets of the Finite Projective Plane
• Geometric Graph-Theoretic Aspects of Quantum Stabilizer Codes
• Non-Pauli Observables for CWS Codes
• Families of $d=2$ 2D subsystem stabilizer codes for universal Hamiltonian quantum computation with two-body interactions
• Entropy of a quantum error correction code
• Topological approach toward quantum codes with realistic physical constraints
• Abstract Error Groups Via Jones Unitary Braid Group Representations at q=i
• Is A Quantum Stabilizer Code Degenerate or Nondegenerate for Pauli Channel?
• Concatenation of Error Avoiding with Error Correcting Quantum Codes for Correlated Noise Models
• Enlargement of Calderbank Shor Steane quantum codes
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
• A Quantum Logic Array Microarchitecture: Scalable Quantum Data Movement and Computation
• Entropy density benchmarking of near-term quantum circuits
• A new approach to codeword stabilized quantum codes using the algebraic structure of modules
• Progress on Problem about Quantum Hamming Bound for Impure Quantum Codes
• Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
• On Ergotropic Gap of Tripartite Separable Systems
• Mapping Surface Code to Superconducting Quantum Processors
• Hoare meets Heisenberg: A Lightweight Logic for Quantum Programs
• Preparation and manipulation of a fault-tolerant superconducting qubit
• Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics
• Mutually unbiased measurements with arbitrary purity
• Impure codes exceeding the pure bounds for quantum local recovery
• New quantum codes from homothetic-BCH codes
• Quantum Key Distribution: Bridging Theoretical Security Proofs, Practical Attacks, and Error Correction for Quantum-Augmented Networks
• Improved Quantum LDPC Decoding Strategies For The Misidentified Quantum Depolarizing Channel
• QKD parameter estimation by two-universal hashing
• Coherence Conservation of a Qubit Coupled to a Thermal Dissipating Environment
• Entanglement witnesses for stabilizer states and subspaces beyond qubits
• Unified Framework for Quantum Code Embedding
• $t$-Frobenius Negacyclic Codes
• Certification of multi-qubit quantum systems with temporal inequalities
• Noncontextual Pauli Hamiltonians
• Codeword Stabilized Codes from m-Uniform Graph States
• Automorphisms of stabilizer codes
• The Fourier Transform Approach to Quantum Coding
• Higher Rank Matricial Ranges and Hybrid Quantum Error Correction
• Fidelity as a figure of merit in quantum error correction
• N-qubit entanglement via the $J_y^2$-type collective interaction
• On the number of representations providing noiseless subsystems
• Non stabilizer Clifford codes with qupits
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• Quantum Error Detection I: Statement of the Problem
• Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes
• Structure Theorem for Quantum Replacer Codes
• Remarks on Clifford codes