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IEEE Access

A Quantum State Controller Based on the Electromagnetic Potentials

Xiang Chen, Fanming Kong, Kang Li, Meng Liu

Published Jan 1, 2019• 13 citations
Publisher

Abstract

Based on the Maxwell–Schrödinger system, a novel numerical scheme for controlling the quantum states of a single electron is proposed in this paper. The key ingredient of the scheme is to employ the electromagnetic potentials instead of the conventional fields for avoiding extra steps of the simulation. The relevant perfect matched layer is given to simulate seemingly infinite regions. And with the help of precise transfer between the objective and the start state, a control pulse can be designed to accurately excite the particle into the objective state. The proposed scheme can perform an ideal quantum state switching while of a simple numerical process.

DOI
10.1109/access.2019.2907137

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A scheme of designing laser pulses for controlling discrete quantum states has been proposed, relying on the recently developed highly accurate Maxwell-Schr\"odinger hybrid simulation. A single electron confined in a quasi-one-dimensional nanoscale potential well has been used as an illustrative example and a control pulse transferring completely the probability density from the ground state to the first excited state has been designed by the present Maxwell-Schr\"odinger hybrid scheme and by the conventional one that solves the time-dependent Schr\"odinger equation only without accounting for feedback from the electron system to the external electromagnetic field. The resultant pulses obtained by these two methods can be different largely owing to the modification of the laser field by the locally strong radiation from the excited electron. The present study demonstrates that light control pulses designed by the conventional method may need to be rectified for practical implementation in experiments.
Abstract A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stage of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single photon while maintaining the perfect state transfer. The key idea is twofold; (i) the control signal is allowed to vary continuously in time to introduce an additional degree of freedom, and then (ii) an optimal control problem is formulated to design a simple-formed input pulse and the corresponding control signal. Numerical simulations are conducted for Λ-type atomic media and networked atomic ensembles, to show the effectiveness of the proposed method.
The control and readout of a transmon qubit through applied microwave pulses is a key capability in operating many quantum technologies. Currently, the design of microwave pulses for these purposes is done through simple theoretical or numerical models that do not account for how the transmon modifies the applied microwave field. In this work, we present the formulation and discretization of a self-consistent semiclassical model that solves the Schrödinger equation describing qubit dynamics in tandem with a one-dimensional wave equation describing transmission line dynamics. Numerical results are presented using this Maxwell-Schrödinger method to characterize the control and readout of a transmon qubit. We show that our method matches simple theoretical predictions in relevant operating regimes and also look at situations where simplified models break down. In the future, our method can be used to explore these broader operating regimes to search for more effective control and readout protocols.
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We tackle the problem of accurate simulations of switching currents arising from tunnel events in the washboard potentials associated to Josephson junctions. The measurements of the probability distribution of the switching currents is essential to determine the quantum character of the device, and therefore is at the core of technological applications, as Josephson junctions, that have been proposed for quantum computers. In particular, we show how to accurately calibrate the parameters of the boundary conditions to avoid spurious reflections of the wavefunction from the finite border of numerical simulations. The proposed approximate numerical scheme exploits a quantum version of a perfect matched layers for the boundary problems associated with this class of potentials. Thus, we employ the analogous of a well established electromagnetic method to deal with radiation in mesoscopic quantum systems. Numerical simulations demonstrate that the known analytic results are well recovered in the appropriated limits of quantum measurements. We also find that a relaxation time shows up in the dynamics of the quantum evolution in between two consecutive measurements.
We present quantum algorithms for electromagnetic fields governed by Maxwell’s equations. The algorithms are based on the Schrödingerisation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system evolving under unitary dynamics, via a warped phase transformation that maps the equation into one higher dimension. In this paper, our quantum algorithms are based on either a direct approximation of Maxwell’s equations combined with Yee’s algorithm, or a matrix representation in terms of Riemann–Silberstein vectors combined with a spectral approach and an upwind scheme. We implement these algorithms with physical boundary conditions, including perfect conductor and impedance boundaries. We also solve Maxwell’s equations for a linear inhomogeneous medium, specifically the interface problem. Several numerical experiments are performed to demonstrate the validity of this approach. In addition, instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework, which allows the quantum simulation of Maxwell’s equations in analog quantum simulation.