Error Avoiding Quantum Codes

Abstract

The existence is proved of a class of open quantum systems that admits a linear subspace $\mathcal{C}$ of the space of states such that the restriction of the dynamical semigroup to the states built over $\mathcal{C}$ is unitary. Such subspace allows for error-avoiding (noiseless) enconding of quantum information.

9 pages, LaTeX

Cited by in corpus (79)

• Decoherence Free Subspaces for Quantum Computation
• Universal Quantum Computation with the Exchange Interaction
• Quantum Error Correction for Beginners
• Semiconductor Spin Qubits
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Quantum Decoherence
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• Symmetrizing Evolutions
• Decoherence-Free Subspaces and Subsystems
• Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes
• Stabilizing Quantum Information
• Quantum Information in Semiconductors: Noiseless Encoding in a Quantum-Dot Array
• Robustness of Decoherence-Free Subspaces for Quantum Computation
• Experimental detection of entanglement via witness operators and local measurements
• Calculating the Thermal Rate Constant with Exponential Speed-Up on a Quantum Computer
• Dynamical description of quantum computing: generic nonlocality of quantum noise
• Implementation of Universal Control on a Decoherence-Free Qubit
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Three-electron spin qubits
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
• Coherence-Preserving Quantum Bits
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation
• Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences
• Purity and State Fidelity of Quantum Channels via Hamiltonians
• Entanglement-Assisted Quantum Convolutional Coding
• Simulation of many-body interactions by conditional geometric phases
• Empirical Determination of Bang-Bang Operations
• Supersinglets
• Quantum Computation using Decoherence-Free States of the Physical Operator Algebra
• Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors
• Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Subdecoherent Information Encoding in a Quantum-Dot Array
• Self-consistent non-Markovian theory of a quantum state evolution for quantum information processing
• Computation on a Noiseless Quantum Code and Symmetrization
• Encoded Recoupling and Decoupling: An Alternative to Quantum Error Correcting Codes, Applied to Trapped Ion Quantum Computation
• An efficient high dimensional quantum Schur transform
• Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir
• Scrambling of Algebras in Open Quantum Systems
• Quantum Shift Register Circuits
• Universal Fault-Tolerant Quantum Computation in the Presence of Spontaneous Emission and Collective Dephasing
• Detected jump-error correcting quantum codes, quantum error designs and quantum computation
• Multi-particle decoherence free subspaces in extended systems
• Dynamically stabilized decoherence-free states in non-Markovian open fermionic systems
• Spin Bath Decoherence of Quantum Entanglement
• Refocusing schemes for holonomic quantum computation in presence of dissipation
• Solving non-Markovian open quantum systems with multi-channel reservoir coupling
• From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states
• Room-temperature storage of quantum entanglement using decoherence-free subspace in a solid-state spin system
• Concatenating dynamical decoupling with decoherence-free subspaces for quantum computation
• Two Qubit Quantum Computing in a Projected Subspace
• Universal Control Induced by Noise
• Quantum error avoiding codes versus quantum error correcting codes
• Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace
• Realization of decoherence-free subspace using Multiple-Quantum coherences
• Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model
• Repetition Versus Noiseless Quantum Codes For Correlated Errors
• Dynamical fidelity susceptibility of decoherence-free subspaces
• Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment
• Interaction-free evolving states of a bipartite system
• Possibility of Inhomogeneous Coupling Leading to Decoherence in an Electromagnetically-Induced-Transparency Quantum-Memory Process
• Decoherence-free quantum information in the presence of dynamical evolution
• Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
• Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras
• Protecting Quantum Information with Entanglement and Noisy Optical Modes
• Quantum Error Correction with Uniformly Mixed State Ancillae
• Generalized Interaction-Free Evolutions
• Combating quantum errors: an integrated approach
• Conditions for superdecoherence
• Coherence generation, symmetry algebras and Hilbert space fragmentation
• A Chain-Boson Model for the Decoherence and Relaxation of a Few Coupled SQUIDs in a Phonon Bath
• Many-Body Entanglement in Solid-State Emitters
• Entangling power of holonomic gates in atom-cavity systems
• Lie Algebras and Suppression of Decoherence in Open Quantum Systems
• Recursive encoding and decoding of the noiseless subsystem for qudits
• Identification of Decoherence-Free Subspaces Without Quantum Process Tomography
• Combating errors in propagation of orbital angular momentum modes of light in turbulent media
• Suppressing decoherence of quantum algorithms by jump codes
• On the number of representations providing noiseless subsystems