Quantum Computation using Decoherence-Free States of the Physical Operator Algebra

Abstract

The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction Hamiltonian, and the system Hamiltonian is the sum of arbitrary terms either commuting with or belonging to the physical algebra, then its states are decoherence free. One of the considered examples shows that, for a uniform collective coupling to the environment, the smallest number of physical qubits encoding a decoherence free logical qubit is reduced from four to three.

16 pages, LATEX/REVTEX, expanded version to appear in Phys. Rev. A

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Cited by in corpus (33)

• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
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• Nature and Measure of Entanglement in Quantum Phase Transitions
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Implementation of Universal Control on a Decoherence-Free Qubit
• Constructing Qubits in Physical Systems
• A decoherence-free subspace in a charge quadrupole qubit
• Chirality of triangular antiferromagnetic clusters as a qubit
• Adiabatic Markovian Dynamics
• Exploring Noiseless Subsystems via Nuclear Magnetic Resonance
• Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions
• From Davydov solitons to decoherence-free subspaces: self-consistent propagation of coherent-product states
• Nonunitary HD gravity classically equivalent to Einstein gravity and its Newtonian limit
• Operator quantum error correction for continuous dynamics
• Realization of decoherence-free subspace using Multiple-Quantum coherences
• Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace
• Quantum superpositions of a mirror for experimental tests for nonunitary Newtonian gravity
• Universal Continuous Variable Quantum Computation Without Cooling
• Robustness of operator quantum error correction with respect to initialization errors
• Suppression of decoherence in quantum registers by entanglement with a nonequilibrium environment
• A Unified Picture of Decoherence Control
• Universal collective rotation channels and quantum error correction
• Protected Solid-State Qubits
• Sudden death of entanglement in fermionic systems under collective decoherence
• Symmetric construction of reference-frame-free qudits
• Subsystem Pseudo-pure States
• Quantum Error Correction with Uniformly Mixed State Ancillae
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
• Lie Algebras and Suppression of Decoherence in Open Quantum Systems
• Noiseless subsystems for collective rotation channels in quantum information theory
• Decoherence suppression via environment preparation
• The Representation of Numbers in Quantum Mechanics
• Qubit subalgebra and tensor product in Weyl algebra of angular momentum system