Driving at the Quantum Speed Limit: Optimal Control of a Two-Level System

2013/05/31 by Gerhard C. Hegerfeldt · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum limit #Quantum mechanics #Quantum optics and atomic interactions #Speed limit #quant-ph

paper · pdf · doi:10.1103/physrevlett.111.260501

published as Physical Review Letters 111, 260501 (2013) · 4 pages, 1 figure

openalex publication_date 2013/12/27 · arxiv created 2013/12/30 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A remarkably simple result is derived for the minimal time Tmin required to drive a general initial state to a final target state by a Landau-Zener-type Hamiltonian or, equivalently, by time-dependent laser driving. The associated protocol is also derived. A surprise arises for some states when the interaction strength is bounded by a constant c. Then, for large c, the optimal driving is of type bang-off-bang and for increasing c one recovers the unconstrained result. However, for smaller c the optimal driving can suddenly switch to bang-bang type. We discuss the notion of quantum speed limit time.

Citations

• Time-Optimal Quantum Evolution
• Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer

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