Quantum dynamics with an ensemble of Hamiltonians

Abstract

We review recent progress in the nonequilibrium dynamics of thermally isolated many-body quantum systems, evolving with an ensemble of Hamiltonians as opposed to deterministic evolution with a single time-dependent Hamiltonian. Such questions arise in (i) quantum dynamics of disordered systems, where different realizations of disorder give rise to an ensemble of real-time quantum evolutions. (ii) quantum evolution with noisy Hamiltonians (temporal disorder), which leads to stochastic Schrodinger equations, and, (iii) in the broader context of quantum optimal control, where one needs to analyze an ensemble of permissible protocols in order to find one that optimizes a given figure of merit. The theme of ensemble quantum evolution appears in several emerging new directions in noneqilibrium quantum dynamics of thermally isolated many-body systems, which include many-body localization, noise-driven systems, and shortcuts to adiabaticity.

brief review, 22 pages, 4 figures

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Cited by in corpus (9)

• Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
• Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field
• Optimal Control of Majorana Zero Modes
• Optimal control of superconducting gmon qubits using Pontryagin's minimum principle: preparing a maximally entangled state with singular bang-bang protocols
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Optimal diabatic dynamics of Majorana-based quantum gates
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Interplay of Anderson localization and quench dynamics
• Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: application to the $XXZ$ model on the square lattice