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arXiv:2410.02235 · Journal of the Physical Society of Japan

Fast-forward Scaling Theory for Quantum Dynamics on Curved Space-time

Yuji Ando, Shumpei Masuda

Published Aug 7, 2025• 0 citations
arXivHTMLPDF

Abstract

Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an essential role. We derive system parameters which realize speed-controlled dynamics. Moreover, we consider spatial scaling and derive system parameters which realize spatially-scaled quantum dynamics.

DOI
10.7566/jpsj.94.094002

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Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an essential role. We derive system parameters which realize speed-controlled dynamics. Moreover, we consider spatial scaling and derive system parameters which realize spatially-scaled quantum dynamics.
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There has been considerable interest over the past years in investigating the role of gravity in quantum phenomenon such as entanglement and decoherence. In particular, gravitational time dilation is believed to decohere superpositions of center of mass of composite quantum systems. Since true effects of gravity are encoded in the curvature of spacetime, the universality of such decoherence must be characterized through components of Riemann tensor RabcdR_{abcd}Rabcd​, with a clear separation from non-inertial kinematic effects. We obtain the reduced density matrix of a composite system in a generic curved spacetime and express the decoherence time scale explicitly in terms of curvature. The decoherence in an inertial frame is caused by tidal acceleration. We also analyze the effects of self-gravity and show that the coupling of gravitational interaction with external curvature can not be captured by the replacement m→m+Hint/c2m \to m + H_{\rm int}/c^2m→m+Hint​/c2.
Speed is the key to further advances in technology. For example, quantum technologies, such as quantum computing, require fast manipulations of quantum systems in order to overcome the effect of decoherence. However, controlling the speed of quantum dynamics is often very difficult due to both the lack of a simple scaling property in the dynamics and the infinitely large parameter space to be explored. Therefore, protocols for speed control based on understanding of the dynamical properties of the system, such as non-trivial scaling property, are highly desirable. Fast-forward scaling theory (FFST) was originally developed to provide a way to accelerate, decelerate, stop and reverse the dynamics of quantum systems. FFST has been extended in order to accelerate quantum and classical adiabatic dynamics of various systems including cold atoms, internal state of molecules, spins and solid-state artificial atoms. This paper describes the basic concept of FFST and reviews the recent developments and its applications such as fast state-preparations, state protection and ion sorting. We introduce a method, called inter-trajectory travel, recently derived from FFST. We also point out the significance of deceleration in quantum technology. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.
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Quantum information processing requires fast manipulations of quantum systems in order to overcome dissipative effects. We propose a method to accelerate quantum dynamics and obtain a target state in a shorter time relative to unmodified dynamics, and apply the theory to a system consisting of two linearly coupled qubits. We extend the technique to accelerate quantum adiabatic evolution in order to rapidly generate a desired target state, thereby realizing a shortcut to adiabaticity. Further, we address experimental limitations to the rate of change of control parameters for quantum devices which often limit one's ability to generate a desired target state with high fidelity. We show that an initial state following decelerated dynamics can reach a target state while varying control parameters more slowly, enabling more experimentally feasible driving schemes.