Dissipation and Decoherence in a Quantum Register

Abstract

A model for a quantum register $\mathcal{R}$ made of $N$ replicas of a $d$-dimensional quantum system (cell) coupled with the environment, is studied by means of a Born-Markov Master Equation (ME). Dissipation and decoherence are discussed in various cases in which a sub-decoherent enconding can be rigorously found. For the qubit case ($d=2$) we have solved, for small $N,$ the ME by numerical direct integration and studied, as a function of the coherence length ${\xi }_c$ of the bath, fidelity and decoherence rates of states of the register. For large enough ${\xi }_c$ the singlet states of the global $su(2)$ pseudo-spin algebra of the register (noiseless at ${\xi }_c=\infty$) are shown to have a much smaller decoherence rates than the rest of the Hilbert space.

minor corrections, references added, to appear in PRA (10 pages + 5 figures LaTeX)

References in corpus (3)

• Noiseless Quantum Codes
• Quantum Computers and Dissipation
• Dissipative dynamics in a quantum register

Cited by in corpus (79)

• Decoherence, einselection, and the quantum origins of the classical
• Decoherence Free Subspaces for Quantum Computation
• Energy loss in perturbative QCD
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Quantum Decoherence
• Symmetries and conserved quantities in Lindblad master equations
• Decoherence-Free Subspaces and Subsystems
• Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes
• Towards a theory of metastability in open quantum dynamics
• 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
• Electro-optical properties of semiconductor quantum dots: Application to quantum information processing
• Coherent quantum dynamics in steady-state manifolds of strongly dissipative systems
• Implementation of Universal Control on a Decoherence-Free Qubit
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Bloch-Redfield equations for modeling light-harvesting complexes
• Two - Level Atom - Field Interaction: Exact Master Equations for Non-Markovian Dynamics, Decoherence and Relaxation
• Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
• Quantum Computer with Mixed States and Four-Valued Logic
• Coherence generating power of quantum unitary maps and beyond
• Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal
• Criteria for dynamically stable decoherence-free subspaces and incoherently generated coherences
• Supersinglets
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Quantum Computation using Decoherence-Free States of the Physical Operator Algebra
• Decay of highly-correlated spin states in a dipolar-coupled solid
• Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors
• Derivation of Markovian master equations for spatially correlated decoherence
• Boosting the performance of small autonomous refrigerators via common environmental effects
• Microscopic description for the emergence of collective dissipation in extended quantum systems
• Subdecoherent Information Encoding in a Quantum-Dot Array
• Long-lived spin entanglement induced by a spatially correlated thermal bath
• Computation on a Noiseless Quantum Code and Symmetrization
• Geometry, robustness, and emerging unitarity in dissipation-projected dynamics
• Decoherence control: Universal protection of two-qubit states and two-qubit gates using continuous driving fields
• Numerical and Analytical Approach to the Quantum Dynamics of Two Coupled Spins in Bosonic Baths
• Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment
• Optimal Control for Closed and Open System Quantum Optimization
• Decoherence of an $n$-qubit quantum memory
• Super- and subradiant emission of two-level systems in the near-Dicke limit
• Measurement of Two-Qubit States by a Two-Island Single Electron Transistor
• 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
• Solving non-Markovian open quantum systems with multi-channel reservoir coupling
• Numerical method for finding decoherence-free subspaces and its applications
• Universal Control Induced by Noise
• Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace
• Realization of decoherence-free subspace using Multiple-Quantum coherences
• Tensorial dynamics on the space of quantum states
• Dissipative remote-state preparation in an interacting medium
• Decoherence and Entanglement Dynamics of Coupled Qubits
• Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model
• Symmetry-protected adiabatic quantum transistors
• Minimal noise subsystems
• Possibility of Inhomogeneous Coupling Leading to Decoherence in an Electromagnetically-Induced-Transparency Quantum-Memory Process
• Neutrino Decoherence from Generalised Uncertainty
• Dynamical fidelity susceptibility of decoherence-free subspaces
• Decoherence-free quantum information in the presence of dynamical evolution
• Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's Algorithm
• Geometry of local quantum dissipation and fundamental limits to local cooling
• No-go theorem and optimization of dynamical decoupling against noise with soft cutoff
• Error prevention scheme with two pairs of qubits
• Quantum Error Correction with Uniformly Mixed State Ancillae
• Coherence generation, symmetry algebras and Hilbert space fragmentation
• A proposal of noise suppression for quantum annealing
• Localizable quantum coherence
• Quantum Property Preservation
• Decoherence of Two-Level Systems Can Be Very Different From Brownian Particles
• Recursive encoding and decoding of the noiseless subsystem for qudits
• Lie Algebras and Suppression of Decoherence in Open Quantum Systems
• Polarizing electron spins with a superconducting flux qubit
• Approaches to Quantum Error Correction
• Experimental implementation of leakage elimination operators
• On the number of representations providing noiseless subsystems
• Open n-Qubit System as a Quantum Computer with Four-Valued Logic
• Diffusion in quantum state preparation: From passive cooling to system-bath engineering