730 research outputs found
Gaussian Optical Ising Machines
It has recently been shown that optical parametric oscillator (OPO) Ising
machines, consisting of coupled optical pulses circulating in a cavity with
parametric gain, can be used to probabilistically find low-energy states of
Ising spin systems. In this work, we study optical Ising machines that operate
under simplified Gaussian dynamics. We show that these dynamics are sufficient
for reaching probabilities of success comparable to previous work. Based on
this result, we propose modified optical Ising machines with simpler designs
that do not use parametric gain yet achieve similar performance, thus
suggesting a route to building much larger systems.Comment: 6 page
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
Gaussian optical Ising machines
It has recently been shown that optical parametric oscillator (OPO) Ising machines, consisting of coupled optical pulses circulating in a cavity with parametric gain, can be used to probabilistically find low-energy states of Ising spin systems. In this work, we study optical Ising machines that operate under simplified Gaussian dynamics. We show that these dynamics are sufficient for reaching probabilities of success comparable to previous work. Based on this result, we propose modified optical Ising machines with simpler designs that do not use parametric gain yet achieve similar performance, thus suggesting a route to building much larger systems
Supporting Energy-Based Learning With An Ising Machine Substrate: A Case Study on RBM
Nature apparently does a lot of computation constantly. If we can harness
some of that computation at an appropriate level, we can potentially perform
certain type of computation (much) faster and more efficiently than we can do
with a von Neumann computer. Indeed, many powerful algorithms are inspired by
nature and are thus prime candidates for nature-based computation. One
particular branch of this effort that has seen some recent rapid advances is
Ising machines. Some Ising machines are already showing better performance and
energy efficiency for optimization problems. Through design iterations and
co-evolution between hardware and algorithm, we expect more benefits from
nature-based computing systems. In this paper, we make a case for an augmented
Ising machine suitable for both training and inference using an energy-based
machine learning algorithm. We show that with a small change, the Ising
substrate accelerate key parts of the algorithm and achieve non-trivial speedup
and efficiency gain. With a more substantial change, we can turn the machine
into a self-sufficient gradient follower to virtually complete training
entirely in hardware. This can bring about 29x speedup and about 1000x
reduction in energy compared to a Tensor Processing Unit (TPU) host
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
On the Challenges of Physical Implementations of RBMs
Restricted Boltzmann machines (RBMs) are powerful machine learning models,
but learning and some kinds of inference in the model require sampling-based
approximations, which, in classical digital computers, are implemented using
expensive MCMC. Physical computation offers the opportunity to reduce the cost
of sampling by building physical systems whose natural dynamics correspond to
drawing samples from the desired RBM distribution. Such a system avoids the
burn-in and mixing cost of a Markov chain. However, hardware implementations of
this variety usually entail limitations such as low-precision and limited range
of the parameters and restrictions on the size and topology of the RBM. We
conduct software simulations to determine how harmful each of these
restrictions is. Our simulations are designed to reproduce aspects of the
D-Wave quantum computer, but the issues we investigate arise in most forms of
physical computation
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