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Nonequilibrium Quantum Thermodynamics in the Process of Adiabatic Speedup

Zhao-Ming Wang, Feng-Hua Ren, Mark Byrd

Published Jun 17, 2021• 0 citations
OpenAlex

Abstract

Understanding heat transfer between a quantum system and its environment is of grave importance if reliable quantum devices are to be constructed. Here, the heat transfer between the system and bath in non-Markovian open quantum systems in the process of adiabatic speedup is investigated. Using the quantum state diffusion equation method, the heat current, energy current and the power are calculated during the free evolution and under external control of the system. While the heat current increases with increasing system-bath coupling strength and bath temperature, the non-Markovian nature of the bath can restrict the heat current. Without pulse control, the heat current is nearly equal to energy current. However, with pulse control, the energy current is nearly equal to the power. We show that more non-Markovian baths can be used to better approximate an adiabatic evolution and have a smaller heat current. Our results reveal that the non-Markovian nature of the bath significantly contributes to both the heat transfer rate as well as the effective adiabatic speedup.

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Understanding heat transfer between a quantum system and its environment is of grave importance if reliable quantum devices are to be constructed. Here, the heat transfer between the system and bath in non-Markovian open quantum systems in the process of adiabatic speedup is investigated. Using the quantum state diffusion equation method, the heat current, energy current and the power are calculated during the free evolution and under external control of the system. While the heat current increases with increasing system-bath coupling strength and bath temperature, the non-Markovian nature of the bath can restrict the heat current. Without pulse control, the heat current is nearly equal to energy current. However, with pulse control, the energy current is nearly equal to the power. We show that more non-Markovian baths can be used to better approximate an adiabatic evolution and have a smaller heat current. Our results reveal that the non-Markovian nature of the bath significantly contributes to both the heat transfer rate as well as the effective adiabatic speedup.
Abstract Adiabatic evolution has important applications in quantum information processing. In that context, the system has to be maintained in one of its instantaneous eigenstates. Normally the adiabaticity of the system will be ruined by its surrounding environment. Quantum control has been used widely to speed up the adiabatic process and thus reduces the effect of the environment. In this letter, we investigate the adiabatic speedup and the associated quantum heat current with and without pulse control. The system is immersed in a non-Markovian and finite-temperature heat bath. Our calculation results show that the effective adiabatic speedup can be obtained in a weak system-bath coupling and low-temperature heat bath. Specifically, non-Markovianity from the environment can be beneficial to the enhancement of the adiabatic fidelity. Furthermore, we calculate the quantum heat current between the system and bath in the process of adiabatic speedup. We find that the adiabatic fidelity decreases with increasing heat current. Our investigation paves the way for the design of quantum heat engines and quantum devices.
Adiabatic quantum computation requires keeping a system in a particular eigenstate. However, unwanted transitions can occur due to the interaction of the system with a noisy environment. The adiabatic evolution of the system will then be ruined. To reduce the effect of the environment, quantum control methods can be used. This allows one to speed up the adiabatic process. Here we present an effective control scheme to allow for a speedup of the adiabatic process by using a sequence of pulses on the system. Using the hierarchical functional derivative (HFD) approach, we calculate the fidelity evolution, which is a measure of the adiabaticity in an open system. By carefully choosing the pulse intensity and duration, an accelerated adiabatic path can be obtained for both a weak-coupling and a strong non-Markovian environment.
Control of the dynamics of an open quantum system is crucial in quantum information processing. Basically there are two ways: one is the control on the system and the other is tuning the bath parameters. In this paper, we use the latter to analyze the non-Markovian dynamics of the open system. The model is that the system is immersed in non-Markovian squeezed baths. For the dynamics, a non-Markovian master eqation is obtained using the quantum state diffusion (QSD) equation technique for the weak system-bath couplings. We use the adiabatic evolution or quantum state transmission as examples to analyze the effects of the bath parameters: non-Markovianity γγγ, the squeezed direction θθθ and squeezed strength rrr. For the adiabatic or state transmission fidelity, the calculation results show that they both can be enhanced by a smaller γγγ or bigger ppp-quadrature. Interestingly, when 0<θ<π/20<θ<π/20<θ<π/2, the squeezed quadrature is determined by the combination of rrr and θθθ, and by numerical simulation we find that the fidelity peak occurs at r=1−2θ/πr=1-2θ/πr=1−2θ/π. The fidelities increase with increasing rrr when r∈(0,1−2θ/π]r\in (0,1-2θ/π]r∈(0,1−2θ/π]. When θ≥π/2θ\geπ/2θ≥π/2, lower fidelities are obtained due to the squeezed bath. Our results show that the dynamics of the open systems can be effectively controlled by reservoir enginerring.
Adiabatic quantum computation requires that the system remains in its ground state. However, an adiabatic process often loses partly or entirely its quantumness, such as entanglement in its long runtime, due to the system-environment interactions. Here we put forward an effective quantum control technique to realize the adiabatic quantum search algorithm in a nonadiabatic regime and in the presence of environment. Using the non-Markovian quantum state diffusion equation approach, we numerically study the system dynamics characterized by the success probability. The results show that the probability increases with decreasing coupling strength and temperature. In particular, non-Markovianity from the environment can help to enhance the success probability. By choosing a suitable pulse intensity and period, a high success probability can be obtained in a short runtime for weak system-bath coupling, low temperature, and strong non-Markovian heat baths.
Precise and efficient control of quantum systems is essential to perform quantum information-processing tasks. In terms of adiabatic speedup via leakage elimination operator approach, for a closed system, the ideal pulse control conditions have been theoretically derived by P-Q partitioning technique. However, it is a challenge to design the corresponding control pulses for an open system, which requires noisy environments to be addressed. In this paper, we apply the stochastic search procedures to an open qutrit system and successfully obtain the optimal control pulses for significant adiabatic speedup. The calculation results show that these optimal pulses allow us to acquire higher fidelities than the ideal pulses. The improvement of fidelity is large for relatively strong system-bath coupling strength and high bath temperature. For certain coupling strength and bath temperature, the maximal improvement can be achieved for a critical characteristic frequency which represents the memory time of the environment. Our investigation indicates that the stochastic search procedures are powerful tools to design control pulses for combating the detrimental effects of the environment.
Abstract We generalize time-evolving matrix product operators method to nonequilibrium quantum transport problems. The nonequilibrium current is obtained via numerical differentiation of the generating functional which is represented as a tensor network. The approach is numerically exact and the non-Markovian effects are fully taken into account. In the transport process, a part of the heat that flows out from a bath flows into the system and other baths, and the rest is stored in the system-bath coupling part. We take the spin-boson model as a demonstration to show the details of this heat flowing and the establishment of a steady current between two baths.