Operator quantum error correction for continuous dynamics
arXiv:0806.3145 · doi:10.1103/PhysRevA.78.022333
Abstract
We study the conditions under which a subsystem code is correctable in the presence of noise that results from continuous dynamics. We consider the case of Markovian dynamics as well as the general case of Hamiltonian dynamics of the system and the environment, and derive necessary and sufficient conditions on the Lindbladian and system-environment Hamiltonian, respectively. For the case when the encoded information is correctable during an entire time interval, the conditions we obtain can be thought of as generalizations of the previously derived conditions for decoherence-free subsystems to the case where the subsystem is time dependent. As a special case, we consider conditions for unitary correctability. In the case of Hamiltonian evolution, the conditions for unitary correctability concern only the effect of the Hamiltonian on the system, whereas the conditions for general correctability concern the entire system-environment Hamiltonian. We also derive conditions on the Hamiltonian which depend on the initial state of the environment, as well as conditions for correctability at only a particular moment of time. We discuss possible implications of our results for approximate quantum error correction.
11 pages, no figures, essentially the published version, includes a new section on correctability at only a particular moment of time
References in corpus (24)
- Mixed State Entanglement and Quantum Error Correction
- Decoherence Free Subspaces for Quantum Computation
- Noiseless Quantum Codes
- A Theory of Quantum Error-Correcting Codes
- Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
- Correcting Quantum Errors with Entanglement
- Resilient Quantum Computation: Error Models and Thresholds
- A Unified and Generalized Approach to Quantum Error Correction
- Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment
- Completely Positive Maps and Classical Correlations
- General entanglement-assisted quantum error-correcting codes
- Optimum Quantum Error Recovery using Semidefinite Programming
- Iterative Optimization of Quantum Error Correcting Codes
- Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
- Generalization of Quantum Error Correction via the Heisenberg Picture
- Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization
- Constructing Qubits in Physical Systems
- Robust Quantum Error Correction via Convex Optimization
- Quantum Computation using Decoherence-Free States of the Physical Operator Algebra
- On Protected Realizations of Quantum Information
- Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems
- Suboptimal quantum-error-correcting procedure based on semidefinite programming
- Approximate quantum error correction, random codes, and quantum channel capacity
- Robustness of operator quantum error correction with respect to initialization errors