2,546 research outputs found
The Series Product and Its Application to Quantum Feedforward and Feedback Networks
The purpose of this paper is to present simple and general algebraic methods
for describing series connections in quantum networks. These methods build on
and generalize existing methods for series (or cascade) connections by allowing
for more general interfaces, and by introducing an efficient algebraic tool,
the series product. We also introduce another product, which we call the
concatenation product, that is useful for assembling and representing systems
without necessarily having connections. We show how the concatenation and
series products can be used to describe feedforward and feedback networks. A
selection of examples from the quantum control literature are analyzed to
illustrate the utility of our network modeling methodology.Comment: To appear, IEEE Transactions on Automatic Control, 200
Trapped Modes in Linear Quantum Stochastic Networks with Delays
Networks of open quantum systems with feedback have become an active area of
research for applications such as quantum control, quantum communication and
coherent information processing. A canonical formalism for the interconnection
of open quantum systems using quantum stochastic differential equations (QSDEs)
has been developed by Gough, James and co-workers and has been used to develop
practical modeling approaches for complex quantum optical, microwave and
optomechanical circuits/networks. In this paper we fill a significant gap in
existing methodology by showing how trapped modes resulting from feedback via
coupled channels with finite propagation delays can be identified
systematically in a given passive linear network. Our method is based on the
Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued
functions, which has been applied in the past to analog electronic networks.
Our results provide a basis for extending the Quantum Hardware Description
Language (QHDL) framework for automated quantum network model construction
(Tezak \textit{et al.} in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci.
370(1979):5270-5290, to efficiently treat scenarios in which each
interconnection of components has an associated signal propagation time delay
Backpropagation training in adaptive quantum networks
We introduce a robust, error-tolerant adaptive training algorithm for
generalized learning paradigms in high-dimensional superposed quantum networks,
or \emph{adaptive quantum networks}. The formalized procedure applies standard
backpropagation training across a coherent ensemble of discrete topological
configurations of individual neural networks, each of which is formally merged
into appropriate linear superposition within a predefined, decoherence-free
subspace. Quantum parallelism facilitates simultaneous training and revision of
the system within this coherent state space, resulting in accelerated
convergence to a stable network attractor under consequent iteration of the
implemented backpropagation algorithm. Parallel evolution of linear superposed
networks incorporating backpropagation training provides quantitative,
numerical indications for optimization of both single-neuron activation
functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan
Nonlinear quantum input-output analysis using Volterra series
Quantum input-output theory plays a very important role for analyzing the
dynamics of quantum systems, especially large-scale quantum networks. As an
extension of the input-output formalism of Gardiner and Collet, we develop a
new approach based on the quantum version of the Volterra series which can be
used to analyze nonlinear quantum input-output dynamics. By this approach, we
can ignore the internal dynamics of the quantum input-output system and
represent the system dynamics by a series of kernel functions. This approach
has the great advantage of modelling weak-nonlinear quantum networks. In our
approach, the number of parameters, represented by the kernel functions, used
to describe the input-output response of a weak-nonlinear quantum network,
increases linearly with the scale of the quantum network, not exponentially as
usual. Additionally, our approach can be used to formulate the quantum network
with both nonlinear and nonconservative components, e.g., quantum amplifiers,
which cannot be modelled by the existing methods, such as the
Hudson-Parthasarathy model and the quantum transfer function model. We apply
our general method to several examples, including Kerr cavities, optomechanical
transducers, and a particular coherent feedback system with a nonlinear
component and a quantum amplifier in the feedback loop. This approach provides
a powerful way to the modelling and control of nonlinear quantum networks.Comment: 12 pages, 7 figure
Basic protocols in quantum reinforcement learning with superconducting circuits
Superconducting circuit technologies have recently achieved quantum protocols
involving closed feedback loops. Quantum artificial intelligence and quantum
machine learning are emerging fields inside quantum technologies which may
enable quantum devices to acquire information from the outer world and improve
themselves via a learning process. Here we propose the implementation of basic
protocols in quantum reinforcement learning, with superconducting circuits
employing feedback-loop control. We introduce diverse scenarios for
proof-of-principle experiments with state-of-the-art superconducting circuit
technologies and analyze their feasibility in presence of imperfections. The
field of quantum artificial intelligence implemented with superconducting
circuits paves the way for enhanced quantum control and quantum computation
protocols.Comment: Published versio
Quantum Robust Stability of a Small Josephson Junction in a Resonant Cavity
This paper applies recent results on the robust stability of nonlinear
quantum systems to the case of a Josephson junction in a resonant cavity. The
Josephson junction is characterized by a Hamiltonian operator which contains a
non-quadratic term involving a cosine function. This leads to a sector bounded
nonlinearity which enables the previously developed theory to be applied to
this system in order to analyze its stability.Comment: A version of this paper appeared in the proceedings of the 2012 IEEE
Multi-conference on Systems and Contro
A Systems Theory Approach to the Synthesis of Minimum Noise Phase-Insensitive Quantum Amplifiers
We present a systems theory approach to the proof of a result bounding the
required level of added quantum noise in a phase-insensitive quantum amplifier.
We also present a synthesis procedure for constructing a quantum optical
phase-insensitive quantum amplifier which adds the minimum level of quantum
noise and achieves a required gain and bandwidth. This synthesis procedure is
based on a singularly perturbed quantum system and leads to an amplifier
involving two squeezers and two beamsplitters.Comment: To appear in the Proceedings of the 2018 European Control Conferenc
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