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Laser Physics Letters

Classical driving-assisted quantum evolution speedup

Hu-Ping Peng, Zhi-guang Tan, Hai-jie Peng, You-neng Guo

Published Sep 16, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ad771b

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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.
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.
The generic bound of quantum speed limit time (the minimal evolution time) for a qubit system interacting with a structural environment is investigated. We define a new bound for the quantum speed limits. It is shown that the non-Markovianity and the population of the excited state can fail to signal the quantum evolution acceleration, but the initial-state dependence is an important factor. In particular, we find that different quantum speed limits could produce contradictory predictions on the quantum evolution acceleration.
A unified bound on the quantum speed limit is obtained for open quantum systems with a mixed initial state by utilizing the function of relative purity proposed by F. Campaioli et al. [Phys. Rev. Lett. 120, 060409 (2018)]. As applications, it is found that the quantum speed limit bound for the damped Jaynes-Cummings model is determined by the competition among the non-Markovianity, the population of the initial excited state, and the initial-state coherence, which shows that the population of the initial excited state and the coherence of the initial state can make the quantum speed limit bound tighter even though the non-Markovian effects can accelerate the evolution of open quantum system. For the dephasing model, a simple factorization law with the initial-state coherence shows that the quantum speed limit is governed by only the competition between the non-Markovianity and the coherence of the initial state.
We present a method to accelerate the dynamical evolution of multiqubit open system by employing dynamical decoupling pulses (DDPs) when the qubits are initially in W-type states. It is found that this speed-up evolution can be achieved in both of the weak-coupling regime and the strong-coupling regime. The physical mechanism behind the acceleration evolution is explained as the result of the joint action of the non-Markovianity of reservoirs and the excited-state population of qubits. It is shown that both of the non-Markovianity and the excited-state population can be controlled by DDPs to realize the quantum speed-up.
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.