4,414 research outputs found
Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization
Many artificial intelligence (AI) problems naturally map to NP-hard
optimization problems. This has the interesting consequence that enabling
human-level capability in machines often requires systems that can handle
formally intractable problems. This issue can sometimes (but possibly not
always) be resolved by building special-purpose heuristic algorithms, tailored
to the problem in question. Because of the continued difficulties in automating
certain tasks that are natural for humans, there remains a strong motivation
for AI researchers to investigate and apply new algorithms and techniques to
hard AI problems. Recently a novel class of relevant algorithms that require
quantum mechanical hardware have been proposed. These algorithms, referred to
as quantum adiabatic algorithms, represent a new approach to designing both
complete and heuristic solvers for NP-hard optimization problems. In this work
we describe how to formulate image recognition, which is a canonical NP-hard AI
problem, as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The
QUBO format corresponds to the input format required for D-Wave superconducting
adiabatic quantum computing (AQC) processors.Comment: 7 pages, 3 figure
Binary crystals in two-dimensional two-component Yukawa mixtures
The zero-temperature phase diagram of binary mixtures of particles
interacting via a screened Coulomb pair potential is calculated as a function
of composition and charge ratio. The potential energy obtained by a Lekner
summation is minimized among a variety of candidate two-dimensional crystals. A
wealth of different stable crystal structures is identified including
structures [ particles correspond to large
(small) charge.] Their elementary cells consist of triangular, square or
rhombic lattices of the particles with a basis comprising various
structures of and particles. For small charge asymmetry there are no
intermediate crystals besides the pure and triangular crystals.Comment: RevTeX 4 - 17 pages - 6 main figure
For Fixed Control Parameters the Quantum Approximate Optimization Algorithm's Objective Function Value Concentrates for Typical Instances
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth
quantum circuit to produce a parameter dependent state. For a given
combinatorial optimization problem instance, the quantum expectation of the
associated cost function is the parameter dependent objective function of the
QAOA. We demonstrate that if the parameters are fixed and the instance comes
from a reasonable distribution then the objective function value is
concentrated in the sense that typical instances have (nearly) the same value
of the objective function. This applies not just for optimal parameters as the
whole landscape is instance independent. We can prove this is true for low
depth quantum circuits for instances of MaxCut on large 3-regular graphs. Our
results generalize beyond this example. We support the arguments with numerical
examples that show remarkable concentration. For higher depth circuits the
numerics also show concentration and we argue for this using the Law of Large
Numbers. We also observe by simulation that if we find parameters which result
in good performance at say 10 bits these same parameters result in good
performance at say 24 bits. These findings suggest ways to run the QAOA that
reduce or eliminate the use of the outer loop optimization and may allow us to
find good solutions with fewer calls to the quantum computer.Comment: 16 pages, 1 figur
Bayesian Optimization Using Domain Knowledge on the ATRIAS Biped
Controllers in robotics often consist of expert-designed heuristics, which
can be hard to tune in higher dimensions. It is typical to use simulation to
learn these parameters, but controllers learned in simulation often don't
transfer to hardware. This necessitates optimization directly on hardware.
However, collecting data on hardware can be expensive. This has led to a recent
interest in adapting data-efficient learning techniques to robotics. One
popular method is Bayesian Optimization (BO), a sample-efficient black-box
optimization scheme, but its performance typically degrades in higher
dimensions. We aim to overcome this problem by incorporating domain knowledge
to reduce dimensionality in a meaningful way, with a focus on bipedal
locomotion. In previous work, we proposed a transformation based on knowledge
of human walking that projected a 16-dimensional controller to a 1-dimensional
space. In simulation, this showed enhanced sample efficiency when optimizing
human-inspired neuromuscular walking controllers on a humanoid model. In this
paper, we present a generalized feature transform applicable to non-humanoid
robot morphologies and evaluate it on the ATRIAS bipedal robot -- in simulation
and on hardware. We present three different walking controllers; two are
evaluated on the real robot. Our results show that this feature transform
captures important aspects of walking and accelerates learning on hardware and
simulation, as compared to traditional BO.Comment: 8 pages, submitted to IEEE International Conference on Robotics and
Automation 201
Ultrafast dynamic conductivity and scattering rate saturation of photoexcited charge carriers in silicon investigated with a midinfrared continuum probe
We employ ultra-broadband terahertz-midinfrared probe pulses to characterize
the optical response of photoinduced charge-carrier plasmas in high-resistivity
silicon in a reflection geometry, over a wide range of excitation densities
(10^{15}-10^{19} cm^{-3}) at room temperature. In contrast to conventional
terahertz spectroscopy studies, this enables one to directly cover the
frequency range encompassing the resultant plasma frequencies. The intensity
reflection spectra of the thermalized plasma, measured using sum-frequency
(up-conversion) detection of the probe pulses, can be modeled well by a
standard Drude model with a density-dependent momentum scattering time of
approx. 200 fs at low densities, reaching approx. 20 fs for densities of
approx. 10^{19} cm^{-3}, where the increase of the scattering rate saturates.
This behavior can be reproduced well with theoretical results based on the
generalized Drude approach for the electron-hole scattering rate, where the
saturation occurs due to phase-space restrictions as the plasma becomes
degenerate. We also study the initial sub-picosecond temporal development of
the Drude response, and discuss the observed rise in the scattering time in
terms of initial charge-carrier relaxation, as well as the optical response of
the photoexcited sample as predicted by finite-difference time-domain
simulations.Comment: 9 pages, 4 figure
Thermodynamic consistency of the charge response in dynamical mean-field based approaches
We consider the thermodynamic consistency of the charge response function in
the (extended) Hubbard model. In DMFT, thermodynamic consistency is preserved.
We prove that the static, homogeneous DMFT susceptibility is consistent as long
as vertex corrections obtained from the two-particle impurity correlation
function are included. In presence of a nonlocal interaction, the problem may
be treated within extended DMFT (EDMFT), or its diagrammatic extension, the
dual boson approach. We show that here, maintaining thermodynamic consistency
requires knowledge of three- and four-particle impurity correlation functions,
which are typically neglected. Nevertheless, the dual boson approximation to
the response is remarkably close to consistency. This holds even when
two-particle vertex corrections are neglected. EDMFT is consistent only in the
strongly correlated regime and near half-filling, where the physics is
predominantly local.Comment: 11 pages (incl. appendix), 4 figure
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