Codes for the Quantum Erasure Channel

Abstract

The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure, in contrast to five qubits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum BCH codes, that can be efficiently decoded is introduced.

6 pages, RevTeX, no figures, submitted to Physical Review A, code extended to encode 2 qubits, references added

References in corpus (4)

• Measurement of conditional phase shifts for quantum logic
• Multiple Particle Interference and Quantum Error Correction
• Quantum Computers and Dissipation
• Error Prevention Scheme with Four Particles

Cited by in corpus (222)

• Multi-photon entanglement and interferometry
• How to share a quantum secret
• Reliable Quantum Computers
• A Theory of Fault-Tolerant Quantum Computation
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Quantum Error Correction for Beginners
• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Capacities of Quantum Erasure Channels
• Quantum Error Correction: An Introductory Guide
• Quantum channels and memory effects
• A Survey on Quantum Channel Capacities
• Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
• Fundamentals of Quantum Information Theory
• Performance and structure of single-mode bosonic codes
• Quantum inseparability as local pseudomixture
• High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit
• Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
• Quantum channels and their entropic characteristics
• Efficient fault-tolerant quantum computing
• Fault-tolerant quantum error detection
• Optimizing Quantum Error Correction Codes with Reinforcement Learning
• Erasure conversion in a high-fidelity Rydberg quantum simulator
• A quantum network stack and protocols for reliable entanglement-based networks
• Entanglement-Assisted Quantum Networks: Mechanics, Enabling Technologies, Challenges, and Research Directions
• Quantum Computing: Pro and Con
• Experimental demonstration of a graph state quantum error-correction code
• Generalized Quantum Secret Sharing
• Entanglement-assisted communication of classical and quantum information
• Fundamental bound on the reliability of quantum information transmission
• On the strong converses for the quantum channel capacity theorems
• Decoherence limits to quantum computation using trapped ions
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Secret sharing of a quantum state
• Hardware-efficient quantum error correction via concatenated bosonic qubits
• Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel
• Continuous symmetries and approximate quantum error correction
• Robust quantum network architectures and topologies for entanglement distribution
• Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
• An Introduction to Quantum Error Correction
• Universal Limitations on Quantum Key Distribution over a Network
• Experimental quantum coding against photon loss error
• Principles of Quantum Communication Theory: A Modern Approach
• Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Correction
• Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
• High threshold codes for neutral atom qubits with biased erasure errors
• Dual-rail encoding with superconducting cavities
• Entropic proofs of Singleton bounds for quantum error-correcting codes
• Entanglement-Assisted Quantum Communication Beating the Quantum Singleton Bound
• Error Filtration and Entanglement Purification for Quantum Communication
• Overcoming erasure errors with multilevel systems
• Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes
• Deterministic correction of qubit loss
• Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons
• Heralded quantum gates with integrated error detection in optical cavities
• Quantum optical coherence can survive photon losses: a continuous-variable quantum erasure correcting code
• Stabilizing distinguishable qubits against spontaneous decay by detected-jump correcting quantum codes
• Quantum Reed-Solomon Codes
• Protecting an optical qubit against photon loss
• Emulating quantum teleportation of a Majorana zero mode qubit
• Resonant cancellation of off-resonant effects in a multilevel qubit
• Decoding algorithms for surface codes
• Experimentally feasible quantum erasure-correcting code for continuous variables
• An All Linear Optical Quantum Memory Based on Quantum Error Correction
• Entanglement cost and quantum channel simulation
• Entropy of a quantum channel
• Approximate quantum error correction for generalized amplitude damping errors
• All-microwave leakage reduction units for quantum error correction with superconducting transmon qubits
• The quantum dynamic capacity formula of a quantum channel
• Stabilizer quantum error correction toolbox for superconducting qubits
• Algebraic techniques in designing quantum synchronizable codes
• The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Quantum Error Correction of a Qubit Loss in an Addressable Atomic System
• Information-theoretic interpretation of quantum error-correcting codes
• Extendibility limits the performance of quantum processors
• Quantum Error Correction with Quantum Autoencoders
• Error detection on quantum computers improves accuracy of chemical calculations
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Distributed quantum error correction for chip-level catastrophic errors
• Deterministic quantum state transfer between remote qubits in cavities
• One way quantum repeaters with quantum Reed-Solomon codes
• Erasure-cooling, control, and hyper-entanglement of motion in optical tweezers
• Generalized Semi-Quantum Secret Sharing Schemes
• How many CNOT gates does it take to generate a three-qubit state ?
• Transmitting qubits through relativistic fields
• Public and private resource trade-offs for a quantum channel
• TASI Lectures on the Emergence of the Bulk in AdS/CFT
• Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement
• Causal order as a resource for quantum communication
• Fault-tolerant quantum computation using large spin cat-codes
• Testing quantum fault tolerance on small systems
• Subspace Confinement: How good is your qubit?
• On the distributed compression of quantum information
• Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)
• Universal programmable photonic architecture for quantum information processing
• Permutation-invariant quantum coding for quantum deletion channels
• Polar codes for degradable quantum channels
• Quantum error correction for continuously detected errors with any number of error channels per qubit
• Quantum control for high-fidelity multi-qubit gates
• Graphical Structures for Design and Verification of Quantum Error Correction
• Detecting lower bounds to quantum channel capacities
• Multi-Error-Correcting Amplitude Damping Codes
• Channel kets, entangled states, and the location of quantum information
• Resource theory of unextendibility and non-asymptotic quantum capacity
• Preserving Information from the Beginning to the End of time in a Robertson-Walker Spacetime
• Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
• Twins Percolation for Qubit Losses in Topological Color Codes
• Location of quantum information in additive graph codes
• Heuristics for Quantum Compiling with a Continuous Gate Set
• Permutation-Invariant Quantum Codes for Deletion Errors
• Entropic bounds on coding for noisy quantum channels
• A hybrid classical-quantum approach to speed-up Q-learning
• Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel
• On the design and analysis of near-term quantum network protocols using Markov decision processes
• A Note on Non-Additive Quantum Codes
• Scalability of quantum computation with addressable optical lattices
• One-shot quantum error correction of classical and quantum information
• Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings
• Quantum reading capacity: General definition and bounds
• Algebraic Quantum Codes: Linking Quantum Mechanics and Discrete Mathematics
• Quantum multipartite maskers vs quantum error-correcting codes
• Error correction of transversal CNOT gates for scalable surface code computation
• Thresholds for Linear Optics Quantum Computing with Photon Loss at the Detectors
• Bounding the forward classical capacity of bipartite quantum channels
• Fast erasure decoder for hypergraph product codes
• Quantum Pin Codes
• Fault-tolerant quantum architectures based on erasure qubits
• A family of loss-tolerant quantum coin flipping protocols
• Resource-efficient fault-tolerant one-way quantum repeater with code concatenation
• Experimentally Realizable C-NOT Gate in a Flux Qubit/Resonator System
• Erasure Decoding for Quantum LDPC Codes via Belief Propagation with Guided Decimation
• Bell Gems: the Bell basis generalized
• Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
• Experimental observation of coherent-information superadditivity in a dephrasure channel
• Reversal of Photon-Scattering Errors in Atomic Qubits
• On quantum capacity of erasure channel assisted by back classical communication
• Capacities of Grassmann channels
• Using three-partite GHZ states for partial quantum error-detection in entanglement-based protocols
• The Floquet Fluxonium Molecule: Driving Down Dephasing in Coupled Superconducting Qubits
• Symmetry-protection of multiphoton states of light
• Enhanced Quantum Estimation via Purification
• Virtual quantum error detection
• A linear-time benchmarking tool for generalized surface codes
• Analytical percolation theory for topological color codes under qubit loss
• Quantum stabilizer codes and beyond
• New Genuine Multipartite Entanglement
• Entanglement generation with a quantum channel and a shared state
• Constructions of $\ell$-Adic $t$-Deletion-Correcting Quantum Codes
• Combinatorial Approaches in Quantum Information Theory
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction
• Surface Code with Imperfect Erasure Checks
• Logical multi-qubit entanglement with dual-rail superconducting qubits
• Some no-go results in Quantum Thermodynamics
• Experimental Implementation of a Codeword Stabilized Quantum Code
• Quantifying the unextendibility of entanglement
• Fault-tolerant conversion between stabilizer codes by Clifford operations
• Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
• Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements
• Information transmission with continuous variable quantum erasure channels
• Efficient Code for Relativistic Quantum Summoning
• Quantum codes from classical graphical models
• Degenerate quantum erasure decoding
• Efficiently decoding the 3D toric codes and welded codes on cubic lattices
• Coherent information of a quantum channel or its complement is generically positive
• Strong converse for the quantum capacity of the erasure channel for almost all codes
• Quantum error detection in qubit-resonator star architecture
• Decoherence and Quantum Error Correction for Quantum Computing and Communications
• Supercomputer simulations of transmon quantum computers
• Fundamental thresholds for computational and erasure errors via the coherent information
• Logical qubits with erasure conversion using metastable neutral atoms
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses
• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Parsing a sequence of qubits
• Codes for entanglement-assisted classical communication
• Adaptive measurement strategy for quantum subspace methods
• Shrinking of Operators in Quantum Error Correction and AdS/CFT
• Some Directions beyond Traditional Quantum Secret Sharing
• Unextendible entanglement of quantum channels
• Competing automorphisms and disordered Floquet codes
• Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
• Optomechanical resource for fault-tolerant quantum computing
• Optimizing quantum codes with an application to the loss channel with partial erasure information
• Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
• Error mitigation of entangled states using brainbox quantum autoencoders
• A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length
• On two maximally entangled couples
• Union-Intersection Union-Find for Decoding Depolarizing Errors in Topological Codes
• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Towards self-correcting quantum codes for neutral atom arrays
• Generation of frequency-bin-encoded dual-rail cluster states via time-frequency multiplexing of microwave photonic qubits
• Machine learning logical gates for quantum error correction
• Sparse Non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations
• Performance comparison of the two reconstruction methods for stabilizer-based quantum secret sharing
• Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
• Protecting Information Against Computational Errors and Quantum Erasures via Concatenation
• Codeword Stabilized Codes from m-Uniform Graph States
• A scheme to protect against multiple quantum erasures
• Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection
• Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics
• Hierarchical Generation and Design of Tree-Codes for Resource-Efficient Loss-Tolerant Quantum Communications
• On Quantum and Classical BCH Codes
• Relaxation times do not capture logical qubit dynamics
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Scalable and fault-tolerant preparation of encoded k-uniform states
• Detecting the event of a single photon loss on quantum signals
• Primitive Quantum BCH Codes over Finite Fields
• Structure Theorem for Quantum Replacer Codes
• Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems
• Quantum Bicyclic Hyperbolic Codes
• Dynamic LOCC Circuits for Automated Entanglement Manipulation
• Error detection without post-selection in adaptive quantum circuits
• Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
• Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• Proposal for erasure conversion in integer fluxonium qubits
• Impure codes exceeding the pure bounds for quantum local recovery
• Qubits through Queues: The Capacity of Channels with Waiting Time Dependent Errors
• Separable Operations, Graph Codes and the Location of Quantum Information