Related papers: Topological Speed Limit

Topological Speed Limit

URL: http://arxiv.org/abs/2207.03319v3
Date: Tue, 6 Dec 2022 15:11:32 GMT
Title: Topological Speed Limit
Authors: Tan Van Vu and Keiji Saito
Abstract summary: We derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.

Related papers

Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
arXiv Detail & Related papers (2024-09-24T04:58:28Z)
Reaction dynamics with qubit-efficient momentum-space mapping [42.408991654684876]
We study quantum algorithms for response functions, relevant for describing different reactions governed by linear response. We consider a qubit-efficient mapping on a lattice, which can be efficiently performed using momentum-space basis states.
arXiv Detail & Related papers (2024-03-30T00:21:46Z)
Quantum geometry and bounds on dissipation in slowly driven quantum systems [0.0]
We show that heat production in slowly driven quantum systems is linked to the topological structure of the driving protocol. Our results bridge topological phenomena and energy dissipation in slowly driven quantum systems.
arXiv Detail & Related papers (2023-06-29T18:00:03Z)
Fundamental speed limits on entanglement dynamics of bipartite quantum systems [0.0]
We derive the speed limits on entanglement using the relative entropy of entanglement and trace-distance entanglement. We find a lower bound on the time required to generate or degrade a certain amount of entanglement by arbitrary quantum dynamics.
arXiv Detail & Related papers (2023-03-13T18:54:56Z)
Exact universal bounds on quantum dynamics and fast scrambling [0.0]
We show that the spectral form factor sets a universal state-independent bound on the quantum dynamics of a complete set of initial states over arbitrarily long times. We use this result to constrain the scrambling of information in interacting many-body systems.
arXiv Detail & Related papers (2022-12-28T18:47:20Z)
Quantum Speed Limit for Change of Basis [55.500409696028626]
We extend the notion of quantum speed limits to collections of quantum states. For two-qubit systems, we show that the fastest transformation implements two Hadamards and a swap of the qubits simultaneously. For qutrit systems the evolution time depends on the particular type of the unbiased basis.
arXiv Detail & Related papers (2022-12-23T14:10:13Z)
Fast-forward scaling theory [0.0]
Fast-forward scaling theory (FFST) was originally developed to provide a way to accelerate, decelerate, stop and reverse the dynamics of quantum systems. This paper describes the basic concept of FFST and review the recent developments and its applications such as fast state-preparations, state protection and ion sorting.
arXiv Detail & Related papers (2022-07-26T08:43:54Z)
Speed Limits for Macroscopic Transitions [0.0]
We show for the first time that the speed of the expectation value of an observable defined on an arbitrary graph is bounded by the "gradient" of the observable. Unlike previous bounds, the speed limit decreases when the expectation value of the transition Hamiltonian increases.
arXiv Detail & Related papers (2021-10-19T03:39:51Z)
From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
arXiv Detail & Related papers (2021-07-29T18:27:38Z)
Bridging the Gap Between the Transient and the Steady State of a Nonequilibrium Quantum System [58.720142291102135]
Many-body quantum systems in nonequilibrium remain one of the frontiers of many-body physics. Recent work on strongly correlated electrons in DC electric fields illustrated that the system may evolve through successive quasi-thermal states. We demonstrate an extrapolation scheme that uses the short-time transient calculation to obtain the retarded quantities.
arXiv Detail & Related papers (2021-01-04T06:23:01Z)
Fast and differentiable simulation of driven quantum systems [58.720142291102135]
We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
arXiv Detail & Related papers (2020-12-16T21:43:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.