2,183 research outputs found
Supervised Quantum Learning without Measurements
We propose a quantum machine learning algorithm for efficiently solving a
class of problems encoded in quantum controlled unitary operations. The central
physical mechanism of the protocol is the iteration of a quantum time-delayed
equation that introduces feedback in the dynamics and eliminates the necessity
of intermediate measurements. The performance of the quantum algorithm is
analyzed by comparing the results obtained in numerical simulations with the
outcome of classical machine learning methods for the same problem. The use of
time-delayed equations enhances the toolbox of the field of quantum machine
learning, which may enable unprecedented applications in quantum technologies
Adiabatic evolution on a spatial-photonic Ising machine
Combinatorial optimization problems are crucial for widespread applications
but remain difficult to solve on a large scale with conventional hardware.
Novel optical platforms, known as coherent or photonic Ising machines, are
attracting considerable attention as accelerators on optimization tasks
formulable as Ising models. Annealing is a well-known technique based on
adiabatic evolution for finding optimal solutions in classical and quantum
systems made by atoms, electrons, or photons. Although various Ising machines
employ annealing in some form, adiabatic computing on optical settings has been
only partially investigated. Here, we realize the adiabatic evolution of
frustrated Ising models with 100 spins programmed by spatial light modulation.
We use holographic and optical control to change the spin couplings
adiabatically, and exploit experimental noise to explore the energy landscape.
Annealing enhances the convergence to the Ising ground state and allows to find
the problem solution with probability close to unity. Our results demonstrate a
photonic scheme for combinatorial optimization in analogy with adiabatic
quantum algorithms and enforced by optical vector-matrix multiplications and
scalable photonic technology.Comment: 9 pages, 4 figure
Asymptotic behavior of memristive circuits
The interest in memristors has risen due to their possible application both
as memory units and as computational devices in combination with CMOS. This is
in part due to their nonlinear dynamics, and a strong dependence on the circuit
topology. We provide evidence that also purely memristive circuits can be
employed for computational purposes. In the present paper we show that a
polynomial Lyapunov function in the memory parameters exists for the case of DC
controlled memristors. Such Lyapunov function can be asymptotically
approximated with binary variables, and mapped to quadratic combinatorial
optimization problems. This also shows a direct parallel between memristive
circuits and the Hopfield-Little model. In the case of Erdos-Renyi random
circuits, we show numerically that the distribution of the matrix elements of
the projectors can be roughly approximated with a Gaussian distribution, and
that it scales with the inverse square root of the number of elements. This
provides an approximated but direct connection with the physics of disordered
system and, in particular, of mean field spin glasses. Using this and the fact
that the interaction is controlled by a projector operator on the loop space of
the circuit. We estimate the number of stationary points of the approximate
Lyapunov function and provide a scaling formula as an upper bound in terms of
the circuit topology only.Comment: 20 pages, 8 figures; proofs corrected, figures changed; results
substantially unchanged; to appear in Entrop
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