Southwest Quantum Information and Technology

Semiclassical Dynamics, Classical-Quantum Control, and Quantum Computation

Presenting Author: Ilon Joseph, Laurence Livermore National Laboratory
Contributing Author(s): Alessandro R. Castelli, Vasily I. Geyko, Frank R. Graziani, Stephen B. Libby, Roger W. Minich, Max D. Porter, Yuan Shi, Jonathan L. DuBois

Quantum information technology relies on essentially classical hardware to control the underlying quantum hardware. Yet, achieving a fully self-consistent coupling of classical and quantum subsystems that correctly predicts backaction effects is challenging from both the physical and mathematical perspectives. In this work, a self-consistent semiclassical-quantum coupling theory is derived by considering a bipartite quantum system and taking the semiclassical limit for one of the subsystems. This approach yields a self-consistently coupled Hamiltonian that evolves via the configuration space version of the Koopman-van Hove (KvH) Hamiltonian [1,2]. There is a natural mapping from configuration space to the classical phase space where the evolution becomes both linear and unitary. This yields a straightforward proof of the classical-quantum coupling methodology proposed in [1]. Moreover, the semiclassical version has different boundary conditions than the classical version that improve accuracy by generating “quantum” effects such as finite tunneling amplitudes in classically forbidden regions and the Einstein-Brillouin-Keller quantization conditions. Finally, a modified version of the quantum algorithm proposed in [2] can naturally be used to efficiently simulate coupled classical-quantum and semiclassical-quantum dynamics on a quantum computer. [1] D. I. Bondar, F. Gay-Balmaz, C. Tronci, Proc. R. Soc. A 475 20180879 (2019). [2] I. Joseph, Phys. Rev. Research 2, 043102 (2020).

(Session 5 : Thursday from 12:00pm-2:00 pm)