75 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
Probabilistic Label Relation Graphs with Ising Models
We consider classification problems in which the label space has structure. A
common example is hierarchical label spaces, corresponding to the case where
one label subsumes another (e.g., animal subsumes dog). But labels can also be
mutually exclusive (e.g., dog vs cat) or unrelated (e.g., furry, carnivore). To
jointly model hierarchy and exclusion relations, the notion of a HEX (hierarchy
and exclusion) graph was introduced in [7]. This combined a conditional random
field (CRF) with a deep neural network (DNN), resulting in state of the art
results when applied to visual object classification problems where the
training labels were drawn from different levels of the ImageNet hierarchy
(e.g., an image might be labeled with the basic level category "dog", rather
than the more specific label "husky"). In this paper, we extend the HEX model
to allow for soft or probabilistic relations between labels, which is useful
when there is uncertainty about the relationship between two labels (e.g., an
antelope is "sort of" furry, but not to the same degree as a grizzly bear). We
call our new model pHEX, for probabilistic HEX. We show that the pHEX graph can
be converted to an Ising model, which allows us to use existing off-the-shelf
inference methods (in contrast to the HEX method, which needed specialized
inference algorithms). Experimental results show significant improvements in a
number of large-scale visual object classification tasks, outperforming the
previous HEX model.Comment: International Conference on Computer Vision (2015
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
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