1,846 research outputs found
Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems
In this paper, we develop a theory of learning nonlinear input-output maps
with fading memory by dissipative quantum systems, as a quantum counterpart of
the theory of approximating such maps using classical dynamical systems. The
theory identifies the properties required for a class of dissipative quantum
systems to be {\em universal}, in that any input-output map with fading memory
can be approximated arbitrarily closely by an element of this class. We then
introduce an example class of dissipative quantum systems that is provably
universal. Numerical experiments illustrate that with a small number of qubits,
this class can achieve comparable performance to classical learning schemes
with a large number of tunable parameters. Further numerical analysis suggests
that the exponentially increasing Hilbert space presents a potential resource
for dissipative quantum systems to surpass classical learning schemes for
input-output maps.Comment: 33 pages, 12 figures, 2 tables. Close to published version in Quantum
Information Processing (https://rdcu.be/bCBUf
The quest for a Quantum Neural Network
With the overwhelming success in the field of quantum information in the last
decades, the "quest" for a Quantum Neural Network (QNN) model began in order to
combine quantum computing with the striking properties of neural computing.
This article presents a systematic approach to QNN research, which so far
consists of a conglomeration of ideas and proposals. It outlines the challenge
of combining the nonlinear, dissipative dynamics of neural computing and the
linear, unitary dynamics of quantum computing. It establishes requirements for
a meaningful QNN and reviews existing literature against these requirements. It
is found that none of the proposals for a potential QNN model fully exploits
both the advantages of quantum physics and computing in neural networks. An
outlook on possible ways forward is given, emphasizing the idea of Open Quantum
Neural Networks based on dissipative quantum computing.Comment: Review of Quantum Neural Networks research; 21 pages, 5 figs, 71 Ref
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Quantum Memristors with Superconducting Circuits.
Memristors are resistive elements retaining information of their past dynamics. They have garnered substantial interest due to their potential for representing a paradigm change in electronics, information processing and unconventional computing. Given the advent of quantum technologies, a design for a quantum memristor with superconducting circuits may be envisaged. Along these lines, we introduce such a quantum device whose memristive behavior arises from quasiparticle-induced tunneling when supercurrents are cancelled. For realistic parameters, we find that the relevant hysteretic behavior may be observed using current state-of-the-art measurements of the phase-driven tunneling current. Finally, we develop suitable methods to quantify memory retention in the system
Entropic Geometry of Crowd Dynamics
We propose an entropic geometrical model of psycho-physical crowd dynamics
(with dissipative crowd kinematics), using Feynman action-amplitude formalism
that operates on three synergetic levels: macro, meso and micro. The intent is
to explain the dynamics of crowds simultaneously and consistently across these
three levels, in order to characterize their geometrical properties
particularly with respect to behavior regimes and the state changes between
them. Its most natural statistical descriptor is crowd entropy that
satisfies the Prigogine's extended second law of thermodynamics,
(for any nonisolated multi-component system). Qualitative
similarities and superpositions between individual and crowd configuration
manifolds motivate our claim that goal-directed crowd movement operates under
entropy conservation, , while natural crowd dynamics operates
under (monotonically) increasing entropy function, . Between
these two distinct topological phases lies a phase transition with a chaotic
inter-phase. Both inertial crowd dynamics and its dissipative kinematics
represent diffusion processes on the crowd manifold governed by the Ricci flow,
with the associated Perelman entropy-action.
Keywords: Crowd psycho-physical dynamics, action-amplitude formalism, crowd
manifold, Ricci flow, Perelman entropy, topological phase transitionComment: 44 pages, 1 figure, Latex, submitted to Entrop
Neural Graphs and Category of Memory States
The brain as an astonishingly remarkable device has been studied from various
angles. It is now well known that neurons are the seat of all activities of the
brain function. The dynamical properties pertaining to a single neuron and a
collection of neurons may be widely different owing to the clustering
properties of a group of neurons. As it can be clearly understood theory of
complex physical systems has been more and more employed to study the behaviour
of neurons and neuronal circuits. We here mainly discuss neural correlates of
memory and cognitive functions utilizing graph theory and ideas from geometry.
It has been suggested that stochastic processes being at the helm of affairs in
the neuronal level there may exist surfaces to some extent like a hologram for
the existence of memory functions.It is also instructive to mention that
Amari's developments \cite{amari} as regards information geometry has acted as
an important inspiration. Unlike some previous analysis categorization of
memory from neural perspectives have been reconsidered at the neuronal level.
In essence the main point of discussion here has been to give an alternative
model of memory where stochastic geometry and algebraic surfaces is an
important ingredient.Comment: 24 pages, 8 figure
Quantum Neuron: an elementary building block for machine learning on quantum computers
Even the most sophisticated artificial neural networks are built by
aggregating substantially identical units called neurons. A neuron receives
multiple signals, internally combines them, and applies a non-linear function
to the resulting weighted sum. Several attempts to generalize neurons to the
quantum regime have been proposed, but all proposals collided with the
difficulty of implementing non-linear activation functions, which is essential
for classical neurons, due to the linear nature of quantum mechanics. Here we
propose a solution to this roadblock in the form of a small quantum circuit
that naturally simulates neurons with threshold activation. Our quantum circuit
defines a building block, the "quantum neuron", that can reproduce a variety of
classical neural network constructions while maintaining the ability to process
superpositions of inputs and preserve quantum coherence and entanglement. In
the construction of feedforward networks of quantum neurons, we provide
numerical evidence that the network not only can learn a function when trained
with superposition of inputs and the corresponding output, but that this
training suffices to learn the function on all individual inputs separately.
When arranged to mimic Hopfield networks, quantum neural networks exhibit
properties of associative memory. Patterns are encoded using the simple Hebbian
rule for the weights and we demonstrate attractor dynamics from corrupted
inputs. Finally, the fact that our quantum model closely captures (traditional)
neural network dynamics implies that the vast body of literature and results on
neural networks becomes directly relevant in the context of quantum machine
learning.Comment: 27 pages, 11 figure
Topographic Representation for Quantum Machine Learning
This paper proposes a brain-inspired approach to quantum machine learning
with the goal of circumventing many of the complications of other approaches.
The fact that quantum processes are unitary presents both opportunities and
challenges. A principal opportunity is that a large number of computations can
be carried out in parallel in linear superposition, that is, quantum
parallelism. The challenge is that the process is linear, and most approaches
to machine learning depend significantly on nonlinear processes. Fortunately,
the situation is not hopeless, for we know that nonlinear processes can be
embedded in unitary processes, as is familiar from the circuit model of quantum
computation. This paper explores an approach to the quantum implementation of
machine learning involving nonlinear functions operating on information
represented topographically (by computational maps), as common in neural
cortex.Comment: 29 page
A steady state quantum classifier
We report that under some specific conditions a single qubit model weakly
interacting with information environments can be referred to as a quantum
classifier. We exploit the additivity and the divisibility properties of the
completely positive (CP) quantum dynamical maps in order to obtain an open
quantum classifier. The steady state response of the system with respect to the
input parameters was numerically investigated and it's found that the response
of the open quantum dynamics at steady state acts non-linearly with respect to
the input data parameters. We also demonstrate the linear separation of the
quantum data instances that reflects the success of the functionality of the
proposed model both for ideal and experimental conditions. Superconducting
circuits were pointed out as the physical model to implement the theoretical
model with possible imperfections.Comment: 11 pages, 7 figure
Passivity Analysis of Replicator Dynamics and its Variations
In this paper, we focus on studying the passivity properties of different
versions of replicator dynamics (RD). RD is an important class of evolutionary
dynamics in evolutionary game theory. Evolutionary dynamics describe how the
population composition changes in response to the fitness levels, resulting in
a closed-loop feedback system. RD is a deterministic monotone non-linear
dynamic that allows incorporation of the distribution of population types
through a fitness function. Here, in this paper, we use a tools for control
theory, in particular, the passivity theory, to study the stability of the RD
when it is in action with evolutionary games. The passivity theory allows us to
identify class of evolutionary games in which stability with RD is guaranteed.
We show that several variations of the first order RD satisfy the standard
loseless passivity property. In contrary, the second order RD do not satisfy
the standard passivity property, however, it satisfies a similar dissipativity
property known as negative imaginary property. The negative imaginary property
of the second order RD allows us to identify the class of games that converge
to a stable equilibrium with the second order RD
Temporal Information Processing on Noisy Quantum Computers
The combination of machine learning and quantum computing has emerged as a
promising approach for addressing previously untenable problems. Reservoir
computing is an efficient learning paradigm that utilizes nonlinear dynamical
systems for temporal information processing, i.e., processing of input
sequences to produce output sequences. Here we propose quantum reservoir
computing that harnesses complex dissipative quantum dynamics. Our class of
quantum reservoirs is universal, in that any nonlinear fading memory map can be
approximated arbitrarily closely and uniformly over all inputs by a quantum
reservoir from this class. We describe a subclass of the universal class that
is readily implementable using quantum gates native to current noisy gate-model
quantum computers. Proof-of-principle experiments on remotely accessed
cloud-based superconducting quantum computers demonstrate that small and noisy
quantum reservoirs can tackle high-order nonlinear temporal tasks. Our
theoretical and experimental results pave the path for attractive temporal
processing applications of near-term gate-model quantum computers of increasing
fidelity but without quantum error correction, signifying the potential of
these devices for wider applications including neural modeling, speech
recognition and natural language processing, going beyond static classification
and regression tasks.Comment: 9 pages main text, 14 pages appendices, 13 figures. Added
implementation scheme using QND measurements and proposal of more efficient
implementation schemes without and with QND measurements. To appear in
Physical Review Applie
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