%0 Journal Article
%J Phys. Rev. Lett.
%D 2010
%T Adiabatic Markovian Dynamics
%A Oreshkov, Ognyan
%A Calsamiglia, John
%K Quantum Physics
%X We propose a theory of adiabaticity in quantum Markovian dynamics based on a structural decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the underlying Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As an application of our theory, we propose a framework for decoherence-assisted computation in noiseless codes under general Markovian noise. We also formulate a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by non-dissipative means.
%B Phys. Rev. Lett.
%V 105
%P 050503
%U http://arxiv.org/abs/1002.2219
%R 10.1103/PhysRevLett.105.050503
%0 Journal Article
%J Physical Review Letters
%D 2009
%T Comment on “Nongeometric Conditional Phase Shift via Adiabatic Evolution of Dark Eigenstates: A New Approach to Quantum Computation”
%A Oreshkov, Ognyan
%A Calsamiglia, John
%B Physical Review Letters
%V 103
%P 188901
%G eng
%U http://prl.aps.org/abstract/PRL/v103/i18/e188901
%R 10.1103/PhysRevLett.103.188901
%0 Journal Article
%J Physical Review A (Atomic, Molecular, and Optical Physics)
%D 2009
%T Distinguishability measures between ensembles of quantum states
%A Oreshkov, Ognyan
%A Calsamiglia, John
%B Physical Review A (Atomic, Molecular, and Optical Physics)
%V 79
%P 032336–29
%G eng
%U http://link.aps.org/doi/10.1103/PhysRevA.79.032336
%R 10.1103/PhysRevA.79.032336
%0 Journal Article
%J Physical Review Letters
%D 2009
%T Holonomic Quantum Computation in Subsystems
%A Oreshkov, Ognyan
%X We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
%B Physical Review Letters
%V 103
%P 090502
%G eng
%U http://prl.aps.org/abstract/PRL/v103/i9/e090502
%R 10.1103/PhysRevLett.103.090502
%0 Journal Article
%J Physical Review A
%D 2009
%T Scheme for fault-tolerant holonomic computation on stabilizer codes
%A Oreshkov, Ognyan
%A Brun, Todd
%A Lidar, Daniel
%B Physical Review A
%V 80
%P 022325
%G eng
%U http://pra.aps.org/abstract/PRA/v80/i2/e022325
%R 10.1103/PhysRevA.80.022325
%0 Journal Article
%J Physical Review A (Atomic, Molecular, and Optical Physics)
%D 2008
%T Operator quantum error correction for continuous dynamics
%A Oreshkov, Ognyan
%A Lidar, Daniel A.
%A Brun, Todd A.
%K error correction codes
%K quantum noise
%B Physical Review A (Atomic, Molecular, and Optical Physics)
%V 78
%P 022333–10
%G eng
%U http://link.aps.org/abstract/PRA/v78/e022333
%R 10.1103/PhysRevA.78.022333