Noiseless Quantum Codes

Abstract

In this paper we study a model quantum register $\mathcal{R}$ made of $N$ replicas (cells) of a given finite-dimensional quantum system S. Assuming that all cells are coupled with a common environment with equal strength we show that, for $N$ large enough, in the Hilbert space of $\mathcal{R}$ there exists a linear subspace ${\mathcal{C}}_N$ which is dynamically decoupled from the environment. The states in ${\mathcal{C}}_N$ evolve unitarily and are therefore decoherence-dissipation free. The space ${\mathcal{C}}_N$ realizes a noiseless quantum code in which information can be stored, in principle, for arbitrarily long time without being affected by errors.

Revised version (to make it accessible to a broader readership) to appear on PRL (4 pages, REVTEX)

References in corpus (1)

• Quantum Computers and Dissipation

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• Observation of multiple steady states with engineered dissipation
• Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource
• Robust engineering of maximally entangled states by identical particle interferometry
• Qubit-environment entanglement outside of pure decoherence: hyperfine interaction
• Universal collective rotation channels and quantum error correction
• Decoherence induced by electron accumulation in quantum measurement of charge qubits
• Possibility of Inhomogeneous Coupling Leading to Decoherence in an Electromagnetically-Induced-Transparency Quantum-Memory Process
• Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment
• Unitary Designs of Symmetric Local Random Circuits
• Two-qubit gates for decoherence-free qubits using a ring exchange interaction
• Using continuous measurement to protect a universal set of quantum gates within a perturbed decoherence-free subspace
• Decoherence-free subspaces and subsystems for a collectively depolarizing bosonic channel
• Dissipation-assisted quantum computation in atom-cavity systems
• Decoherence-free quantum information in Markovian systems
• Interaction-free evolving states of a bipartite system
• Decoherence-free quantum information in the presence of dynamical evolution
• Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's Algorithm
• Optimizing nonadiabatic geometric quantum gates against off-resonance error by dynamical correction in a silicon-based spin qubit
• Improved storage of coherent and squeezed states in imperfect ring cavity
• Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
• Entanglement and interference between different degrees of freedom of photons states
• Coherent population trapping in the stochastic limit
• Evaluation of Decoherence for Quantum Computing Architectures: Qubit System Subject to Time-Dependent Control
• Experimental implementation of quantum gates through actuator qubits
• Preparation of a single-photon dark state in a chiral quantum system
• Using quantum state protection via dissipation in a quantum-dot molecule to solve the Deutsch problem
• Non-Markovian decay and dynamics of decoherence in private and public environments
• Inhibiting decoherence via ancilla processes
• Dike states in multiple quantum dots
• Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
• Manipulation of spin cluster qubits by electric-field induced modulation of exchange coupling, $g$-factor, and axial anisotropy
• Controlled Quantum Open Systems
• Operational Quantum Mereology and Minimal Scrambling
• Quantumness and speedup limit of a qubit under transition frequency modulation
• Methods for Producing Decoherence-Free States and Noiseless Subsystems Using Photonic Qutrits
• Shielding quantum discord through continuous dynamical decoupling
• Error prevention scheme with two pairs of qubits
• Dynamical paths and universality in continuous variables open systems
• Protecting Two-Qubit Quantum States by $\pi$-Phase Pulses
• Quantum key distribution based on orthogonal state encoding
• On decoherence in noncommutative plane with perpendicular magnetic field
• Limitations of practical multi-photon decoherence-free states
• Analytic solution to N vs. M photon phase control in an open two-level system
• Number of steady states of quantum evolutions
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Observable geometric phase induced by a cyclically evolving dissipative process
• Protection of Logical Qubits via Optimal State Transfers
• A note on verification procedures for quantum noiseless subsystems
• Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras
• Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa
• Screening of qubit from zero-temperature reservoir
• Effects of imperfect noise correlations on decoherence-free subsystems: SU(2) diffusion model
• Steady Schrödinger cat state of a driven Ising chain
• Immunity of information encoded in decoherence-free subspaces to particle loss
• Entanglement classes of symmetric Werner states
• Quantum Error Correction with Uniformly Mixed State Ancillae
• Dynamical Decoupling of Qubits in Spin Bath under Periodic Quantum Control
• Generalized Interaction-Free Evolutions
• Proposal for high-fidelity quantum simulation using a hybrid dressed state
• Non-Markovian quantum dissipative processes with the same positive features as Markovian dissipative processes
• Protected State Transfer via an Approximate Quantum Adder
• Entanglement Protection via Periodic Environment Resetting in Continuous Time Quantum Dynamical Processes
• Classifying quantum data by dissipation
• Intermittent decoherence blockade in a chiral ring environment
• Dissipative Encoding of Quantum Information
• Time-optimal universal quantum gates on superconducting circuits
• Quantum entanglement and Bell violation of two coupled cavity fields in dissipative environment
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Entanglement production by quantum error correction in the presence of correlated environment
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• Improving the purity of one- and two-qubit gates by AC fields
• Adapted-operator representations: Selective versus collective properties of quantum networks
• Subsystem Pseudo-pure States
• Protecting Quantum Information with Entanglement and Noisy Optical Modes
• Optical implementation of a unitarily correctable code
• Indistinguishability-assisted two-qubit entanglement distillation
• Conditions for superdecoherence
• Entanglement-assisted communication in the absence of shared reference frame
• Decoherence Rates in Large Scale Quantum Computers and Macroscopic Systems
• Robustness of Decoherence-Free States for Charge Qubits under Local Non-uniformity
• Perfect Function Transfer in two- and three- dimensions without initialization
• Generality of the concatenated five-qubit code
• Coherence generation, symmetry algebras and Hilbert space fragmentation
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• Decoherence-Insensitive Quantum Communication by Optimal C^*-Encoding
• Errors in quantum optimal control and strategy for the search of easily implementable control pulses
• Robustness of the concatenated quantum error-correction protocol against noise for channels affected by fluctuation
• Quantitative Treatment of Decoherence
• Transition of D- Level Quantum Systems Through Quantum Channels with Correlated Noise
• Hybrid noise protection of logical qubits for universal quantum computation
• Quantum Computers and Decoherence: Exorcising the Demon from the Machine
• Pre-management of Disentanglement
• Partial decoherence in mesoscopic systems
• Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians
• Long-time Quantum Scrambling and Generalized Tensor Product Structures
• Subsystem Code Constructions
• The Role of Rotational Invariance in the Properties of Hamiltonians
• Deformed versus undeformed cat states encoding qubit
• Decoherence suppression for oscillator-assisted geometric quantum gates via symmetrization
• Enhanced exciton transmission by quantum-jump-based feedback
• General approach to find steady-state manifolds in Markovian and non-Markovian systems
• Diffusive lossless energy and coherence transfer by noisy coupling
• Localizable quantum coherence
• Liouville invariance in quantum and classical mechanics
• Pauli Spin Blockade in a Resonant Triple Quantum Dot Molecule
• Entangling Nuclear Spins by Dissipation in a Solid-state System
• Information flow at the quantum-classical boundary
• Non-Hamiltonian modeling of squeezing and thermal disorder in driven oscillators
• Optimal encoding of two dissipative interacting qubits
• Dynamical Aspects of Information Storage in Quantum-Mechanical Systems
• Quantum Resource Theory for Charge-Parity-Time Inversion
• Optimal state transfer of a single dissipative two-level system
• Decoherence-enhanced measurements
• Protecting coherence from the environment via Stark many-body localization in a Quantum-Dot Simulator
• Quantum Property Preservation
• Entangling power of holonomic gates in atom-cavity systems
• Mitigating decoherence in molecular spin qudits
• Robustness of Charge-Qubit Cluster States to Double Quantum Point Contact Measurement
• Brain neurons as quantum computers: {\it in vivo} support of background physics
• Robust projective measurements through measuring code-inspired observables
• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps
• Targeting qubit states using open-loop control
• Controlling dephasing of coupled qubits via shared-bath coherence
• Correlated and Critical Phenomena in Multipartite Quantum Non-Markovianity
• Enhanced Quantum Parameter Estimation via Dynamical Modulation
• Reductions in finite-dimensional quantum mechanics: from symmetries to operator algebras and beyond
• Universality of swap for qudits: a representation theory approach
• Decoherence of Two-Level Systems Can Be Very Different From Brownian Particles
• Quantum Error Correction in Loop Quantum Gravity
• Lie Algebras and Suppression of Decoherence in Open Quantum Systems
• Coherence in quantum estimation
• Quantum channel for light based on integrals of motion
• Relative information encoded in the degree of entanglement to discriminate bipartite states
• A unification of the coding theory and OAQEC perspective on hybrid codes
• Quantum Codes for Controlling Coherent Evolution
• Protection of entanglement between two two-level atoms
• Error correction with orbital angular momentum of multiple photons propagating in a turbulent atmosphere
• Singlet States Preparation for Three $\Lambda$-type Atoms with Rydberg Blockade Mechanism
• Protecting entangled states of two ions by engineering reservoir
• Decoherence of encoded quantum registers
• Casimir Invariants for Systems Undergoing Collective Motion
• Recursive encoding and decoding of the noiseless subsystem for qudits
• Relativistically invariant encoding of quantum information revisited
• Decoherence suppression via environment preparation
• Identification of Decoherence-Free Subspaces Without Quantum Process Tomography
• Symmetry and decoherence-free subspaces in quantum neural networks
• Asymptotic dynamics in the Heisenberg picture: attractor subspace and Choi-Effros product
• Suppressing decoherence in quantum state transfer with unitary operations
• Ancilla-Assisted Protection of Information: Application to Atom-Cavity Systems
• Error Crafting in Mixed Quantum Gate Synthesis
• Sensing microscopic noise events by frequent quantum measurements
• Entanglement preservation in tripartite quantum systems under dephasing dynamics
• On fixed-gap adiabatic quantum computation
• A two reservoir model of quantum error correction
• Mitigation of systematic amplitude error in nonadiabatic holonomic operations
• Encoding the information in relative parameters
• Two qubit gate with macroscopic singlet-triplet qubits in synthetic spin-one chains in InAsP quantum dot nanowires
• Quantum Mechanics in symmetry language
• Quantum Zero-error Capacity
• Noiseless subsystems for collective rotation channels in quantum information theory
• The Effect of Local Structure and Non-uniformity on Decoherence-Free States of Charge Qubits
• Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes
• Decoherence and fidelity enhancement during shuttling of entangled spin qubits
• Implementation of a two-qubit controlled-U gate based on unconventional geometric phase with a constant gating time
• Degenerate Landau-Zener model in the presence of quantum noise
• On the number of representations providing noiseless subsystems
• Indirect decoherence in optical lattices and cold gases
• Majorana-like oscillation for edge states in one-dimensional topological chain with dissipative couplings
• Decoherence Cancellation through Noise Interference
• Complete Weight Distribution and MacWilliams Identities for Asymmetric Quantum Codes
• Relaxation times do not capture logical qubit dynamics
• Control-Induced Decoherence-Free Manifolds
• Experimental Quantum Error-Free Transmission
• Quantum Markovian Subsystems: Invariance, Attractivity, and Control
• Coherence Conservation of a Qubit Coupled to a Thermal Dissipating Environment
• Non-normality and dissipation in Markovian quantum dynamics: Implications for quantum simulation
• Protected Rabi oscillation induced by natural interactions among physical qubits
• Geometric and holonomic quantum computation
• Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions
• Information storage and transmission under Markovian noise
• Local phase damping of single qubits sets an upper bound on the phase damping rate of entangled states
• Synthesis of Energy-Conserving Quantum Circuits with XY interaction
• Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems
• Entropy of a quantum error correction code
• Synchronizing two superconducting qubits through a dissipating resonator
• A quantum repeater based on decoherence free subspaces
• Adiabatic Generation of N-quNit Singlet States with Cavity QED
• Creating Quantum Cluster States embedded in ancillary baths
• Pulse Control of Decoherence with Population Decay
• Experimental implementation of leakage elimination operators