Quantum acceleration limit

Synergy Quantum, Research and Innovation Park, IIT Delhi Campus - New Delhi, India

Received: 2 April 2025
Accepted: 18 August 2025

Abstract

The speed limit provides an upper bound for the dynamical evolution time of a quantum system. Here, we introduce the notion of quantum acceleration limit for unitary time evolution of quantum systems under time-dependent Hamiltonian. We prove that the quantum acceleration is upper bounded by the fluctuation in the derivative of the Hamiltonian. This leads to a universal quantum acceleration limit (QAL) which answers the question: What is the minimum time required for a quantum system to be accelerated from arbitrary initial speed to final speed? We illustrate the quantum acceleration limit for a two-level quantum system and show that the bound is indeed tight. This notion can have important applications in adiabatic quantum computing, quantum control and quantum thermodynamics.