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New Journal of Physics

Nonadiabatic quantum state engineering by time-dependent decoherence-free subspaces in open quantum systems

Qi‐Cheng Wu, Y. H. Zhou, Biao‐Liang Ye, Tong Liu, Chui‐Ping Yang

Published Oct 19, 2021• 20 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/ac309d

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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.
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 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 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.
Abstract A scheme is proposed to implement quantum state engineering (QSE) in a four-state system via counterdiabatic driving. In the scheme, single- and multi-mode driving methods are used respectively to drive the system to a target state at a predefined time. It is found that a fast QSE can be realized by utilizing simply designed pulses. In addition, a beneficial discussion on the energy consumption between the single- and multi-mode driving protocols shows that the multi-mode driving method seems to have a wider range of applications than the single-mode driving method with respect to different parameters. Finally, the scheme is also helpful for implementing the generalization QSE in high-dimensional systems via the concept of a dressed state. Therefore, the scheme can be implemented with the present experimental technology, which is useful in quantum information processing.
We propose schemes to design and control a time-dependent decoherence-free subspace (DFS) in a dissipative atom-cavity system. These schemes use atoms with three internal energy levels, which allows for the DFS to be multidimensional---a condition important for quantum sensing, simulation, and computation. We consider the use of tunable external driving lasers to transfer the system from a coherent spin state to a highly degenerate DFS. We find that the typical state in the DFS is highly entangled. Throughout evolution the state is kept in an instantaneous DFS, thereby allowing for pure states to be prepared. We develop adiabatic shortcuts to carry out this evolution with higher purity and fidelity than standard adiabatic and dissipative methods.
We propose a method to adiabatically control an atomic ensemble using a decoherence-free subspace (DFS) within a dissipative cavity. We can engineer a specific eigenstate of the system's Lindblad jump operators by injecting a field into the cavity which deconstructively interferes with the emission amplitude of the ensemble. In contrast to previous adiabatic DFS proposals, our scheme creates a DFS in the presence of collective decoherence. We therefore have the ability to engineer states that have high multiparticle entanglements which may be exploited for quantum information science or metrology. We further demonstrate a more optimized driving scheme that utilizes the knowledge of possible diabatic evolution gained from the so-called adiabatic criteria. This allows us to evolve to a desired state with exceptionally high fidelity on a timescale that does not depend on the number of atoms in the ensemble. By engineering the DFS eigenstate adiabatically, our method allows for faster state preparation than previous schemes that rely on damping into a desired state solely using dissipation.