Hybrid Quantum-Classical Approach to Quantum Optimal Control

Abstract

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantumclassical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving messages from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a nine-spin nuclear magnetic resonance system, on which we have succeeded in preparing a seven-correlated quantum state without involving classical computation of the large Hilbert space evolution.PACS numbers: 03.67. Lx,03.65.Yz Quantum computing promises to deliver a new level of computation power [1]. Enormous efforts have been made in exploring the possible ways of using quantum resources to speed up computation. While the fabrication of a full-scale universal quantum computer remains a huge technical challenge [2], special-purpose quantum simulation can be an alternative [3][4][5]. Quantum simulators are designed to imitate specific quantum systems of interest, and are expected to provide significant speed-up over their classical counterparts [6]. Quantum simulation has found important applications for a great variety of computational tasks, such as solving linear equations [7,8], simulating condensed-matter systems [9], calculating molecular properties [10,11] and certificating untrusted quantum devices [12]. However, in view of experimental implementation, most of the proposed algorithms have hardware requirements still far beyond the capability of near-term quantum devices.Recent advances towards building a modest-sized quantum computer have led to emerging interest in a quantum-classical hybrid approach [13][14][15]. The underlying idea is that by letting a quantum simulator work in conjunction with a classical computer, even minimal quantum resources could be made useful. In hybrid quantum-classical computation, the computationally inexpensive calculations, which yet might consume many qubits, are performed on a classical computer, whereas the difficult part of the computation is accomplished on a quantum simulator. The major benefit of this hybrid strategy is that it gives rise to a setup that can have much less stringent hardware requirements.In this Letter, we propose a hybrid quantum-classical method for solving the quantum optimal control problem. Normally, the problem is formulated as follows: given a quantum control system and a fitness function that measures the quality of control, the goal is to find a control that can achieve optimal performance. The importance of the problem lies in its extraordinarily wide range of applications in physics and chemistry [16]. H...

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