Shortcuts to Thermodynamic Quasistaticity

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 adiabaticity,” 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. Hence, in this Letter, we 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 quasiadiabatic driving, and by applying the method to the quantum Ising chain in the transverse field.

Figure 1

Magnetization of the TI chain in the entirely paramagnetic process with $N=100$ starting at zero temperature. The results were numerically obtained from the exact time-dependent dynamics. (a) State diagram of the TI chain for an adiabatic (quasistatic) evolution (EOS), the LIN, the FQA, and the FQ2 protocols for $J\tau =3$, starting from the top right corner. The inset shows the time dependence of each protocol. (b) Excess magnetization ${\mu }_{\mathrm{ex}}=\mu -{\mu }^{(0)}$ at the end of the process vs process duration.

Figure 2

Magnetization of the TI chain in the QCP crossing process starting at zero temperature with $N=100$. The results of both panels were numerically obtained from the exact time-dependent dynamics. (a) State diagram of the TI chain for an adiabatic (quasistatic) evolution (EOS), the LIN, the UQA, and the UQ2 protocols for $J\tau =50$, starting from the top right corner. The inset shows the time dependence of each protocol. (b) Excess magnetization ${\mu }_{\mathrm{ex}}=\mu -{\mu }^{(0)}$ at the end of the process vs process duration.