1,152 research outputs found

    A generative modeling approach for benchmarking and training shallow quantum circuits

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    Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as "cat states". We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM's quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.Comment: 16 pages, 9 figures. Minor revisions. As published in npj Quantum Informatio

    Birkhoffian formulation of the dynamics of LC circuits

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    We present a formulation of general nonlinear LC circuits within the framework of Birkhoffian dynamical systems on manifolds. We develop a systematic procedure which allows, under rather mild non-degeneracy conditions, to write the governing equations for the mathematical description of the dynamics of an LC circuit as a Birkhoffian differential system. In order to illustrate the advantages of this approach compared to known Lagrangian or Hamiltonian approaches we discuss a number of specific examples. In particular, the Birkhoffian approach includes networks which contain closed loops formed by capacitors, as well as inductor cutsets. We also extend our approach to the case of networks which contain independent voltage sources as well as independent current sources. Also, we derive a general balance law for an associated "energy function".Comment: 26 pages, 2 figures. Z. Angew. Math. Phys. (ZAMP), accepted for publicatio

    Readout methods and devices for Josephson-junction-based solid-state qubits

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    We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular we focus attention of dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.Comment: 20 pages, 7 figures. To be published in J. Phys.: Condensed Matter, 18 (2006) Special issue: Quantum computin

    What's black and white about the grey matter?

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    In 1873 Camillo Golgi discovered his eponymous stain, which he called la reazione nera. By adding to it the concepts of the Neuron Doctrine and the Law of Dynamic Polarisation, Santiago Ramon y Cajal was able to link the individual Golgi-stained neurons he saw down his microscope into circuits. This was revolutionary and we have all followed Cajal's winning strategy for over a century. We are now on the verge of a new revolution, which offers the prize of a far more comprehensive description of neural circuits and their operation. The hope is that we will exploit the power of computer vision algorithms and modern molecular biological techniques to acquire rapidly reconstructions of single neurons and synaptic circuits, and to control the function of selected types of neurons. Only one item is now conspicuous by its absence: the 21st century equivalent of the concepts of the Neuron Doctrine and the Law of Dynamic Polarisation. Without their equivalent we will inevitably struggle to make sense of our 21st century observations within the 19th and 20th century conceptual framework we have inherite

    The Non-Random Brain: Efficiency, Economy, and Complex Dynamics

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    Modern anatomical tracing and imaging techniques are beginning to reveal the structural anatomy of neural circuits at small and large scales in unprecedented detail. When examined with analytic tools from graph theory and network science, neural connectivity exhibits highly non-random features, including high clustering and short path length, as well as modules and highly central hub nodes. These characteristic topological features of neural connections shape non-random dynamic interactions that occur during spontaneous activity or in response to external stimulation. Disturbances of connectivity and thus of neural dynamics are thought to underlie a number of disease states of the brain, and some evidence suggests that degraded functional performance of brain networks may be the outcome of a process of randomization affecting their nodes and edges. This article provides a survey of the non-random structure of neural connectivity, primarily at the large scale of regions and pathways in the mammalian cerebral cortex. In addition, we will discuss how non-random connections can give rise to differentiated and complex patterns of dynamics and information flow. Finally, we will explore the idea that at least some disorders of the nervous system are associated with increased randomness of neural connections

    Chow's theorem and universal holonomic quantum computation

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    A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented by taking covariant derivatives of the curvature associated to a non-Abelian gauge connection. When applied to the Optical Holonomic Computer, these conditions determine that the holonomy group of the two-qubit interaction model contains SU(2)×SU(2)SU(2) \times SU(2). In particular, a universal two-qubit logic gate is attainable for this model.Comment: 13 page
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