The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, but also diagnoses the chaotic behavior of many-body quantum systems and characterizes the information scrambling. Based on the OTOCs, three different concepts -quantum chaos, holographic duality, and information scrambling -are found to be intimately related to each other. Despite of its theoretical importance, the experimental measurement of the OTOC is quite challenging and so far there is no experimental measurement of the OTOC for local operators. Here we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator. We observe that the OTOC behaves differently in the integrable and non-integrable cases. Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for non-intgrable models. With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation. Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.Recent studies also reveal that the OTOC can be applied to study physical properties beyond chaotic systems. The decay of the OTOC is closely related to the delocalization of information and implies the informationtheoretic definition of scrambling. In the high tem-arXiv:1609.01246v3 [cond-mat.str-el]

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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Majorana fermions (MFs) are exotic particles that are their own anti-particles. Recently, the search for the MFs occurring as quasi-particle excitations in solid-state systems has attracted widespread interest, because of their fundamental importance in fundamental physics and potential applications in topological quantum computation based on solid-state devices. Here we study the quantum correlations between two spatially separate quantum dots induced by a pair of MFs emerging at the two ends of a semiconductor nanowire, in order to develop a new method for probing the MFs. We find that without the tunnel coupling between these paired MFs, quantum entanglement cannot be induced from an unentangled (i.e., product) state, but quantum discord is observed due to the intrinsic nonlocal correlations of the paired MFs. This finding reveals that quantum discord can indeed demonstrate the intrinsic non-locality of the MFs formed in the nanowire. Also, quantum discord can be employed to discriminate the MFs from the regular fermions. Furthermore, we propose an experimental setup to measure the onset of quantum discord due to the nonlocal correlations. Our approach provides a new, and experimentally accessible, method to study the Majorana bound states by probing their intrinsic non-locality signature.

We present an efficient approach, based on a number-conditioned master equation, for large-deviation analysis in mesoscopic transports. Beyond the conventional full-counting-statistics study, the large-deviation approach encodes complete information of both the typical trajectories and the rare ones, in terms of revealing a continuous change of the dynamical phase in trajectory space. The approach is illustrated with two examples: (i) transport through a single quantum dot, where we reveal the inhomogeneous distribution of trajectories in a general case and find a particular scale invariance point in trajectory statistics; and (ii) transport through double dots, where we find a dynamical phase transition between two distinct phases induced by the Coulomb correlation and quantum interference.

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.