Frontiers of quantum physics

Abstract:

In the Aharonov-Bohm (AB) effect, a superposed charge acquires a detectable phase by enclosing an infinite solenoid, in a region where the solenoid's electric and magnetic fields are zero. Its generation seems therefore explainable only by the local action of gauge-dependent potentials, not of gauge-independent fields. This was recently challenged by Vaidman, who explained the phase by the solenoid's current interacting with the electron's field (at the solenoid). Still, his model has a residual nonlocality: it does not explain how the phase, generated at the solenoid, is detectable on the charge. In this Letter, we solve this nonlocality explicitly by quantizing the field. We show that the AB phase is mediated locally by the entanglement between the charge and the photons, like all electromagnetic phases. We also predict a gauge-invariant value for the phase difference at each point along the charge's path. We propose a realistic experiment to measure this phase difference locally, by partial quantum state tomography on the charge, without closing the interference loop.

Abstract:

Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks—generalized time evolution with a non-Hermitian Hamiltonian, linear algebra problems, and open quantum system dynamics. The algorithm for generalized time evolution provides a unified framework for variational quantum simulation. In particular, we show its application in solving linear systems of equations and matrix-vector multiplications by converting these algebraic problems into generalized time evolution. Meanwhile, assuming a tensor product structure of the matrices, we also propose another variational approach for these two tasks by combining variational real and imaginary time evolution. Finally, we introduce variational quantum simulation for open system dynamics. We variationally implement the stochastic Schrödinger equation, which consists of dissipative evolution and stochastic jump processes. We numerically test the algorithm with a 6-qubit 2D transverse field Ising model under dissipation.