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Laser Physics Letters

Efficient implementation of arbitrary quantum state engineering in four-state system by counterdiabatic driving

Song-Bai Wang, Ye‐Hong Chen, Qi‐Cheng Wu, Zhi‐Cheng Shi, Bi‐Hua Huang, Jie Song, Yan Xia

Published May 23, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/aabf19

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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.
A scheme for arbitrary quantum state engineering (QSE) in three-state systems is proposed. Firstly, starting from a set of complete orthogonal time-dependent basis with undetermined coefficients, a time-dependent Hamiltonian is derived via Counterdiabatic driving for the purpose of guiding the system to attain an arbitrary target state at a predefined time. Then, on request of the assumed target states, two single-mode driving protocols and a multi-mode driving protocol are proposed as examples to discuss the validity of the QSE scheme. The result of comparison between single-mode driving and multi-mode driving shows that multi-mode driving seems to have a wider rang of application prospect because it can drive the system to an arbitrary target state from an arbitrary initial state also at a predefined time even without the use of microwave fields for the transition between the two ground states. Moreover, for the purpose of discussion in the scheme's feasibility in practice, a polynomial ansatz as the simplest exampleis used to fix the pulses. The result shows that the pulses designed to implement the protocols are not hard to be realized in practice. At the end, QSE in higher-dimensional systems is also discussed in brief as a generalization example of the scheme.
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.
Local counterdiabatic driving (CD) provides a feasible approach for realizing approximate adiabatic or reversible processes like quantum state preparation using only local controls and without demanding excessively long protocol times. However, in many instances getting high accuracy of such CD protocols requires engineering very complicated new controls or pulse sequences. In this work, we describe a systematic method for altering the adiabatic path by adding extra local controls along which performance of local CD protocols is enhanced, both close to and far from the adiabatic limit. We also identify an iterative procedure to improve the performance of local counterdiabatic driving further without any knowledge of the quantum wave function. We then show that these methods provides dramatic improvement in the preparation of nontrivial Greenberger-Horne-Zeilinger ground states of several different spin systems with both short-range and long-range interactions.
Shortcuts to adiabaticity (STA) is a common protocol to realize high-fidelity and robust quantum control in various quantum systems. To date, STA has been widely applied in two- and three-level systems, whereas designing feasible strategies to achieve perfect quantum state engineering in multi-level systems still remains a challenging task. Here, we propose to use counterdiabatic (CD) driving and time-rescaling (TR) methods to construct multi-state stimulated Raman shortcut-to-adiabatic passage protocols for realizing robust and fast population transfer in chainwise-connected five-state systems. The first protocol is implemented by initially reducing the original five-state system to an equivalent two-state counterpart, and then designing the corresponding driving field by combining CD driving and unitary transformation. Further, we introduce the TR method to optimize the first protocol and thus offers an alternative solution. Numerical calculations show that both protocols can achieve complete population transfer and effectively suppress transient populations of all intermediate states. Compared with the first protocol, the optimized second exhibits better performance within a shorter evolution time.
Abstract We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcuts to adiabaticity aim to retain the adiabatic condition upon speed-up. We outline a new method which combines the two methodologies and takes advantage of the strengths of each. The new technique improves upon approximate local counterdiabatic driving with the addition of time-dependent control fields. We refer to this new method as counterdiabatic optimised local driving (COLD) and we show that it can result in a substantial improvement when applied to annealing protocols, state preparation schemes, entanglement generation and population transfer on a lattice. We also demonstrate a new approach to the optimisation of control fields which does not require access to the wavefunction or the computation of system dynamics. COLD can be enhanced with existing advanced optimal control methods and we explore this using the chopped randomised basis method and gradient ascent pulse engineering.