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The frontiers collection

Dissipation in Quantum Mechanical Systems: Where Is the System and Where Is the Reservoir?

Joachim Ankerhold

Published Jan 1, 2015• 0 citations
Publisher
DOI
10.1007/978-3-662-43911-1_4

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The driven-dissipative many-body problem remains one of the most challenging unsolved problems in quantum mechanics. The advent of quantum computers may provide a unique platform for efficiently simulating such driven-dissipative systems. But, there are many choices for how one can engineer the reservoir. One can simply employ ancilla qubits to act as a reservoir and then digitally simulate them via algorithmic cooling. A more attractive approach, which allows one to simulate an infinite reservoir, is to integrate out the bath degrees of freedom and describe the driven-dissipative system via a master equation, that can also be simulated on a quantum computer. In this work, we consider the particular case of noninteracting electrons on a lattice driven by an electric field and coupled to a fermionic thermostat. Then, we provide two different quantum circuits: the first one reconstructs the full dynamics of the system using Trotter steps, while the second one dissipatively prepares the final nonequilibrium steady state in a single step. We run both circuits on the IBM quantum experience. For circuit (i), we achieved up to five Trotter steps. When partial resets become available on quantum computers, we expect that the maximum simulation time can be significantly increased. The methods developed here suggest generalizations that can be applied to simulating interacting driven-dissipative systems.

arXiv:1912.08310•Physical review. B./Physical review. B•Sep 10, 2020•67 citations
In a recent paper [Phys. Rev. E 48, 1547 (1993)] Li, Ford, and O'Connel argue that the power lost through dissipation by a system in equilibrium with a thermal reservoir is compensated by the action of a fluctuation force that the reservoir exerts on the system. Their analysis is quantum mechanical and their expression for the power supplied by the reservoir remains positive definite even at absolute zero. This Comment outlines an analysis of a harmonic oscillator coupled to a loss mechanism and shows how the quantum-mechanical formalism should be interpreted to avoid unphysical conclusions. An explicit distinction is made between thermal and zero-point fluctuations, and the physical significance of the latter is discussed.
Abstract Quality of charging and discharging of energy in quantum batteries are mostly affected by environmental dissipations, so the advantages of using such devices depend on the protection of them from the dissipations. In this work, we show that under a certain engineering of coupling strengths of each reservoir modes with elements of charging process (charger and battery), the extension of dissipative reservoir leads to a robust charging against the arisen dissipation. The extension of reservoir is provided by auxiliary systems each of which is similar to the coupled charger–battery system and has the same interactions with the reservoir modes as of the charger and battery constituents. It is demonstrated that the robustness of charging process is well controlled by the number of involved auxiliary systems. Furthermore, a method for stable charging is proposed which provides storing energy in a loss-free dark state of the battery. Also, we observe that the robustness of charging process is related to formation of bound state for the total system (charger–battery-extended reservoir) which in turns can be manipulated by the number of involved auxiliary systems.
The driven-dissipative many-body problem remains one of the most challenging unsolved problems in quantum mechanics. The advent of quantum computers may provide a unique platform for efficiently simulating such driven-dissipative systems. But, there are many choices for how one can engineer the reservoir. One can simply employ ancilla qubits to act as a reservoir and then digitally simulate them via algorithmic cooling. A more attractive approach, which allows one to simulate an infinite reservoir, is to integrate out the bath degrees of freedom and describe the driven-dissipative system via a master equation, that can also be simulated on a quantum computer. In this work, we consider the particular case of noninteracting electrons on a lattice driven by an electric field and coupled to a fermionic thermostat. Then, we provide two different quantum circuits: the first one reconstructs the full dynamics of the system using Trotter steps, while the second one dissipatively prepares the final nonequilibrium steady state in a single step. We run both circuits on the IBM quantum experience. For circuit (i), we achieved up to five Trotter steps. When partial resets become available on quantum computers, we expect that the maximum simulation time can be significantly increased. The methods developed here suggest generalizations that can be applied to simulating interacting driven-dissipative systems.