arXiv subjects

Alicia B. Magann

Publications and source records attributed to Alicia B. Magann.

22 records · Page 2Linked to original sources

arXiv2021

Progress toward favorable landscapes in quantum combinatorial optimization

The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on algorithms for solving the combinatorial optimization problem MaxCut, and study how the structure of the classical optimization landscape relates to the quantum circuit used to evaluate the MaxCut objective function. In order to analytically characterize the impact of quantum features on the critical points of the landscape, we consider a family of quantum circuit ansätze composed of mutually commuting elements. We identify multiqubit operations as a key resource and show that overparameterization allows for obtaining favorable landscapes. Namely, we prove that an ansatz from this family containing exponentially many variational parameters yields a landscape free of local optima for generic graphs. However, we further prove that these ansätze do not offer superpolynomial advantages over purely classical MaxCut algorithms. We then present a series of numerical experiments illustrating that noncommutativity and entanglement are important features for improving algorithm performance.

quant-ph↗

arXiv2021

Digital quantum simulation of molecular dynamics and control

Optimally-shaped electromagnetic fields have the capacity to coherently control the dynamics of quantum systems and thus offer a promising means for controlling molecular transformations relevant to chemical, biological, and materials applications. Currently, advances in this area are hindered by the prohibitive cost of the quantum dynamics simulations needed to explore the principles and possibilities of molecular control. However, the emergence of nascent quantum-computing devices suggests that efficient simulations of quantum dynamics may be on the horizon. In this article, we study how quantum computers could be employed to design optimally-shaped fields to control molecular systems. We introduce a hybrid algorithm that utilizes a quantum computer for simulating the field-induced quantum dynamics of a molecular system in polynomial time, in combination with a classical optimization approach for updating the field. Qubit encoding methods relevant for molecular control problems are described, and procedures for simulating the quantum dynamics and obtaining the simulation results are discussed. Numerical illustrations are then presented that explicitly treat paradigmatic vibrational and rotational control problems, and also consider how optimally-shaped fields could be used to elucidate the mechanisms of energy transfer in light-harvesting complexes. Resource estimates, as well as a numerical assessment of the impact of hardware noise and the prospects of near-term hardware implementations, are provided for the latter task.

quant-ph↗

arXiv2021

From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms

The last decade has witnessed remarkable progress in the development of quantum technologies. Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes. Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities. In this Perspective, we propose a variety of ways that the performance of VQAs could be informed by quantum optimal control theory. To set the stage, we identify VQAs and quantum optimal control as formulations of variational optimization at the circuit level and pulse level, respectively, where these represent just two levels in a broader hierarchy of abstractions that we consider. In this unified picture, we suggest several ways that the different levels of abstraction may be connected, in order to facilitate the application of quantum optimal control theory to VQA challenges associated with ansatz selection, optimization landscapes, noise, and robustness. A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and conclude with a look to the future.

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arXiv2018

Optimal control of interacting quantum systems based on the first-order Magnus approximation: Application to multiple dipole-dipole coupled molecular rotors

We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction picture, where the interactions between different degrees of freedom are treated as the perturbation. We present a numerical procedure for implementing this approximation, which leverages the separability of the zeroth-order time evolution operator and the pairwise nature of common interactions for a reduced computational cost. This formulation of the first-order Magnus approximation is suitable to be combined with gradient-free methods for control field optimization; to this end, we adopt a Stochastic Hill Climbing algorithm. The associated computational costs are analyzed and compared with those of the exact simulation in the large N limit. For numerical illustrations, we perform approximate optimal control simulations for systems of two and three dipole-dipole coupled molecular rotors under the influence of a global control field. For the two rotor system, we optimize fields for both orientation and entanglement control objectives. For the three rotor system, we optimize fields for orienting rotors in the same direction as well as in opposite directions.

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