Shortcuts to Thermodynamic Quasistaticity

Abstract

The operation of near-term quantum technologies requires the development of feasible, implementable, and robust strategies of controlling complex many body systems. To this end, a variety of techniques, so-called "shortcuts to adiabaticty", have been developed. Many of these shortcuts have already been demonstrated to be powerful and implementable in distinct scenarios. Yet, it is often also desirable to have additional, approximate strategies available, that are applicable to a large class of systems. In this work, we hence take inspiration from thermodynamics and propose to focus on the macrostate, rather than the microstate. Adiabatic dynamics can then be identified as such processes that preserve the equation of state, and systematic corrections are obtained from adiabatic perturbation theory. We demonstrate this approach by improving upon fast quasi-adiabatic driving, and by applying the method to the quantum Ising chain in the transverse field.

Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems

“…Comparison of equation (24) to equation ( 15) leads to the conclusion that the FQA protocol distributes first-order transition probabilities uniformly throughout the entire duration of the process. As it is, equation (24) only works when considering a single pair of energy levels m and n, but we can use the expressions for the work in equations ( 10) and ( 21) to take every level pair into account. To this c), (e) and (f) depict numerical results obtained from the integration of the exact time-dependent dynamics, while the lines in (b) and (e) represent the lowest-order predictions from APT.…”

“…The external parameter is the magnetic field λ = B, to be compared with the fixed coupling J between neighboring spins. Here, for the sake of illustrating our results using this model as an exactly diagonalized testbed with a well defined thermodynamic limit, we consider only processes that do not cross the system's quantum critical point (at B = J), because it brings unwanted difficulties (that we have considered elsewhere [24,61,81]). The results for processes entirely contained in the paramagnetic phase (B > J) or in the ferromagnetic phase (B < J) can be seen in figure 1.…”

“…Since there is only one constant of integration, c must also be used to impose the boundary conditions, which ultimately leads to c ∝ τ −1 . Comparison of equation (24) to equation ( 15) leads to the conclusion that the FQA protocol distributes first-order transition probabilities uniformly throughout the entire duration of the process. As it is, equation (24) only works when considering a single pair of energy levels m and n, but we can use the expressions for the work in equations ( 10) and ( 21) to take every level pair into account.…”

“…The implementations often require additional control mechanisms [9][10][11] or specific characteristics of the control fields [17,20], restricting the possible setups in the laboratory. Extensions to many-body systems may also face some difficulties, although it has been proved possible in some cases [20][21][22][23][24]. The different shortcuts to adiabaticity have been mostly restricted to isolated systems, i.e., systems whose dynamics is Hamiltonian.…”

Many-body enhancement in a spin-chain quantum heat engine

“…For diabatic engine operation, quantum friction degrades performance. We have presented one counterdiabatic method that mitigates friction for weak interactions, however other methods could be explored [79,85,91,[94][95][96][97][98][99]. Modulating the phase and detuning of the drive profile may better isolate the two lowest energy eigenstates [100][101][102][103][104], limiting degradation due to thermal fluctuations and quantum friction.…”