1,152 research outputs found
A generative modeling approach for benchmarking and training shallow quantum circuits
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
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
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?
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
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
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 . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
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