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Chinese Physics B

Coherent-driving-assisted quantum speedup in Markovian channels*

Xiang Lu, Yingjie Zhang, Yun‐Jie Xia

Published Oct 15, 2020• 5 citations
Publisher

Abstract

As is well known, the quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system. The Hamiltonian corrections induced by the action of coherent driving forces are often used to fight dissipative and decoherence mechanisms in experiments. For this reason, considering three noisy channels (the phase-flip channel, the amplitude damping channel and the depolarizing channel), we propose a scheme of speedup evolution of an open system by controlling an external unitary coherent driving operator on the system. It is shown that, in the presence of the coherent driving, no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process. Additionally, under the fixed coherent driving strength in the above three noisy channels, the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles, respectively. Finally, we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.

DOI
10.1088/1674-1056/abc150

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As is well known, the quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system. The Hamiltonian corrections induced by the action of coherent driving forces are often used to fight dissipative and decoherence mechanisms in experiments. For this reason, considering three noisy channels (the phase-flip channel, the amplitude damping channel and the depolarizing channel), we propose a scheme of speedup evolution of an open system by controlling an external unitary coherent driving operator on the system. It is shown that, in the presence of the coherent driving, no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process. Additionally, under the fixed coherent driving strength in the above three noisy channels, the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles, respectively. Finally, we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.
Abstract In this study, we propose accelerating the qubit evolution using external classical driving fields in open systems. The results show that the quantum speed limit is determined by the driving strength, population of the initial excited state, and quantum coherence of the initial state. In the Markovian regime, the evolution of the open system will be accelerated by increasing the driving strength, while in non-Markovian regime, the evolution of the open system will present acceleration and deceleration periodically. Moreover, in both Markovian and non-Markovian regime, the population of the initial excited state and the initial-state coherence always can make the quantum speed limit bound tighter.
We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong system-environment couplings. By considering the relationship between non-Makovianity of environment and the classical field, we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of the classical field. That is the intrinsic physical reason that the classical field may induce the speed-up process. In addition, the role of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.
The maximal evolution speed of a quantum system can be represented by quantum speed limit time (QSLT). We investigate the QSLT of a two-qubit system passing through a correlated channel (amplitude damping, phase damping, and depolarizing). By adjusting the correlation parameter of the channel and the initial entanglement, a method to accelerate the evolution speed of the system for some specific channels is proposed. It is shown that, in the amplitude damping channel and the depolarizing channel, QSLT may be shortened in some cases by increasing the correlation parameter of the channel and the initial entanglement, which are in sharp contrast to the phase damping channel. In particular, under depolarizing channels, the transition from no-speedup evolution to speedup evolution for the system can be realized by changing the correlation strength of the channel.
A potential acceleration of a quantum open system is of fundamental interest in quantum computation, quantum communication, and quantum metrology. In this paper, we investigate the “quantum speed-up capacity” which reveals the potential ability of a quantum system to be accelerated. We explore the evolutions of the speed-up capacity in different quantum channels for two-qubit states. We find that although the dynamics of the capacity is varying in different kinds of channels, it is positive in most situations which are considered in the context except one case in the amplitude-damping channel. We give the reasons for the different features of the dynamics. Anyway, the speed-up capacity can be improved by the memory effect. We find two ways which may be used to control the capacity in an experiment:selecting an appropriate coefficient of an initial state or changing the memory degree of environments.
We illustrate a scheme for implementing a non-Markovian speedup evolution of an open system weakly interacting with a controllable environment: the coupled qubit-array. By controlling the environment, for instance by choosing a judicious nearest-neighbor excitation quanta hopping strength among the qubit-array or by changing the number of qubits coupled to the quantum system, two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved in the weak system-environment coupling regime. For the weaker system-environment coupling, the larger hopping strength (or the larger qubits number) should be tuned to drive the non-Markovian speedup evolution. Particularly, the controllable non-Markovian dynamics is the intrinsic physical reason for the speedup evolution of a quantum system.
In this work, we investigate the dynamical process of an open quantum system under the action of quantum cyclic nnn-switch in generalized amplitude-damping channels and depolarizing channels. The quantum cyclic nnn-switch operation is introduced by an external control system. Our results show that the quantum switch can regulate the dynamical behavior of the system dynamics and achieve non-Markovian speedup dynamics. Increasing the dimension of the control system can significantly enhance the evolution speed of the system's non-Markovian dynamics. For the generalized amplitude-damping channels, when the influence of thermal noise is intense, the greater the quantum cyclic nnn-switch is, the lower the initial coherence is, and the more conducive it is to the acceleration of the quantum state evolution speed. In the depolarizing channels, under the action of quantum cyclic nnn-switch, the evolution speed of the system dynamics is directly related to the non-Markovianity and is independent of the initial coherence of the system.