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arXiv:1502.07967 · Physical Review A

Engineering of a quantum state by time-dependent decoherence-free subspaces

S. L. Wu

Published Mar 3, 2015• 9 citations
arXivHTMLPDF

Abstract

We apply the time-dependent decoherence-free subspace theory to a Markovian open quantum system in order to present a proposal for a quantum-state engineering program. By quantifying the purity of the quantum state, we verify that the quantum-state engineering process designed via our method is completely unitary within any total engineering time. Even though the controls on the open quantum system are not perfect, the asymptotic purity is still robust. Owing to its ability to completely resist decoherence and the lack of restraint in terms of the total engineering time, our proposal is suitable for multitask quantum-state engineering program. Therefore, this proposal is not only useful for achieving the quantum-state engineering program experimentally, it also helps us build both a quantum simulation and quantum information equipment in reality.

DOI
10.1103/physreva.91.032104

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We apply the time-dependent decoherence-free subspace theory to a Markovian open quantum system in order to present a proposal for a quantum-state engineering program. By quantifying the purity of the quantum state, we verify that the quantum-state engineering process designed via our method is completely unitary within any total engineering time. Even though the controls on the open quantum system are not perfect, the asymptotic purity is still robust. Owing to its ability to completely resist decoherence and the lack of restraint in terms of the total engineering time, our proposal is suitable for multitask quantum-state engineering program. Therefore, this proposal is not only useful for achieving the quantum-state engineering program experimentally, it also helps us build both a quantum simulation and quantum information equipment in reality.
We extend the theory of quantum state engineering (QSE) to the open quantum systems which simultaneously suffer time-dependent decoherence and time-independent decoherence. A hybrid approach is proposed to effectively realize QSE by combination of time-dependent decoherence-free subspaces and shortcuts to adiabaticity theories. As an application, a concrete single-qubit QSE example with an open five-level system is presented. Numerical simulations confirm that the approach is reliable and robust against both of time-dependent decoherence and time-independent decoherence. Certain dissipation effects are no longer harmful but play a positive role in the QSE. In addition, the approach can be generalized to realize QSE in high-dimensional quantum systems. Therefore, this proposal is quite useful for quantum computation and quantum information processing in open systems.
Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the kkk-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality k≥5k \geq 5k≥5, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.
The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.
We propose a protocol to construct shortcuts of adiabaticity for open quantum systems in unitary evolution. Using the dynamical invariants of open quantum systems, we design a convenient form of the driver Hamiltonian to accelerate the adiabatic decoherence free subspaces scheme (TDFs) and engineer a quantum state from the initial state into the target state. Since the trajectory of TDFSs is determined by the incoherent control process, we would like to call it as the inverse incoherent engineering protocol. We apply the method to a two-qubits system which interacts with a time-dependent vacuum squeezed field to prepare some maximally entangled states of it. The results illustrate that our protocol can be used both in the adiabatic and nonadiabatic regime with perfect fidelity.
We develop a novel framework to engineer persistent oscillatory modes in Markovian open quantum systems governed by a time-independent Lindblad master equation. We show that oscillatory modes can be created when the Hamiltonian and jump operator can be expressed in the same block-diagonal form. A key feature of the framework is that the dissipator of the Lindblad master equation are generally non-zero. We identify the weak and strong conditions, where the onset of the oscillatory modes is dependent and independent of the parameters of the system, respectively. Our method extends beyond the typical decoherence-free subspace approach, in which the dissipator is zero. We demonstrate the applicability of this framework using various models, showing how carefully tailored system-environment interactions can produce sustained coherent oscillations.
This paper discusses the concept of controllable subspace for open quantum dynamical systems.It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable.This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable.To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.