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Register a new userHybrid quantum-classical models as constrained quantum systems
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Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions for classical behavior are imposed on one of its subsystems and the corresponding hybrid dynamical equations are derived. The presented formalism suggests that the hybrid systems have properties that are not exhausted by those of quantum and classical systems.
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We present a protocol for the fully automated construction of quantum mechanical-(QM)-classical hybrid models by extending our previously reported approach on self-parametrizing system-focused atomistic models (SFAM) J. Chem. Theory Comput. 2020, 16, 1646]. In this QM/SFAM approach, the size and composition of the QM region is evaluated in an automated manner based on first principles so that the hybrid model describes the atomic forces in the center of the QM region accurately. This entails the automated construction and evaluation of differently sized QM regions with a bearable computational overhead that needs to be paid for automated validation procedures. Applying SFAM for the classical part of the model eliminates any dependence on pre-existing parameters due to its system-focused quantum mechanically derived parametrization. Hence, QM/SFAM is capable of delivering a high fidelity and complete automation. Furthermore, since SFAM parameters are generated for the whole system, our ansatz allows for a convenient re-definition of the QM region during a molecular exploration. For this purpose, a local re-parametrization scheme is introduced, which efficiently generates additional classical parameters on the fly when new covalent bonds are formed (or broken) and moved to the classical region.
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible physically distinguishable statistical ensembles of hybrid systems. Nevertheless, statistical operators associated with the hybrid system and with the quantum subsystem can be consistently defined. Dynamical equations for the statistical operators representing the mixed states of the hybrid system and its quantum subsystem are derived and analyzed. In particular, these equations irreducibly depend on the total probability density on the hybrid phase space.
Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, and are expected to be the first useful applications for quantum computing. Meanwhile, mitigation of errors on quantum processors is also crucial to obtain reliable results. In this article, we review the basic results for hybrid quantum-classical algorithms and quantum error mitigation techniques. Since quantum computing with NISQ devices is an actively developing field, we expect this review to be a useful basis for future studies.
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated parameter with given resources. Here, we address this problem by introducing adjustable controls into the encoding process and then utilizing a hybrid quantum-classical approach to automatically optimize the controls online. Our scheme does not require any complex or intractable off-line design, and it can inherently correct certain unitary errors during the learning procedure. We also report the first experimental demonstration of this promising scheme for the task of finding optimal probes for frequency estimation on a nuclear magnetic resonance (NMR) processor. The proposed scheme paves the way to experimentally auto-search optimal protocol for improving the metrology precision.
Deep learning has been shown to be able to recognize data patterns better than humans in specific circumstances or contexts. In parallel, quantum computing has demonstrated to be able to output complex wave functions with a few number of gate operations, which could generate distributions that are hard for a classical computer to produce. Here we propose a hybrid quantum-classical convolutional neural network (QCCNN), inspired by convolutional neural networks (CNNs) but adapted to quantum computing to enhance the feature mapping process. QCCNN is friendly to currently noisy intermediate-scale quantum computers, in terms of both number of qubits as well as circuits depths, while retaining important features of classical CNN, such as nonlinearity and scalability. We also present a framework to automatically compute the gradients of hybrid quantum-classical loss functions which could be directly applied to other hybrid quantum-classical algorithms. We demonstrate the potential of this architecture by applying it to a Tetris dataset, and show that QCCNN can accomplish classification tasks with learning accuracy surpassing that of classical CNN.
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