40 research outputs found
Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines
Recently, a programmable quantum annealing machine has been built that
minimizes the cost function of hard optimization problems by adiabatically
quenching quantum fluctuations. Tests performed by different research teams
have shown that, indeed, the machine seems to exploit quantum effects. However
experiments on a class of random-bond instances have not yet demonstrated an
advantage over classical optimization algorithms on traditional computer
hardware. Here we present evidence as to why this might be the case. These
engineered quantum annealing machines effectively operate coupled to a
decohering thermal bath. Therefore, we study the finite-temperature critical
behavior of the standard benchmark problem used to assess the computational
capabilities of these complex machines. We simulate both random-bond Ising
models and spin glasses with bimodal and Gaussian disorder on the D-Wave
Chimera topology. Our results show that while the worst-case complexity of
finding a ground state of an Ising spin glass on the Chimera graph is not
polynomial, the finite-temperature phase space is likely rather simple: Spin
glasses on Chimera have only a zero-temperature transition. This means that
benchmarking optimization methods using spin glasses on the Chimera graph might
not be the best benchmark problems to test quantum speedup. We propose
alternative benchmarks by embedding potentially harder problems on the Chimera
topology. Finally, we also study the (reentrant) disorder-temperature phase
diagram of the random-bond Ising model on the Chimera graph and show that a
finite-temperature ferromagnetic phase is stable up to 19.85(15)%
antiferromagnetic bonds. Beyond this threshold the system only displays a
zero-temperature spin-glass phase. Our results therefore show that a careful
design of the hardware architecture and benchmark problems is key when building
quantum annealing machines.Comment: 8 pages, 5 figures, 1 tabl
Robust Parameter Selection for Parallel Tempering
This paper describes an algorithm for selecting parameter values (e.g.
temperature values) at which to measure equilibrium properties with Parallel
Tempering Monte Carlo simulation. Simple approaches to choosing parameter
values can lead to poor equilibration of the simulation, especially for Ising
spin systems that undergo -order phase transitions. However, starting
from an initial set of parameter values, the careful, iterative respacing of
these values based on results with the previous set of values greatly improves
equilibration. Example spin systems presented here appear in the context of
Quantum Monte Carlo.Comment: Accepted in International Journal of Modern Physics C 2010,
http://www.worldscinet.com/ijmp
Bayesian Optimization for Adaptive MCMC
This paper proposes a new randomized strategy for adaptive MCMC using
Bayesian optimization. This approach applies to non-differentiable objective
functions and trades off exploration and exploitation to reduce the number of
potentially costly objective function evaluations. We demonstrate the strategy
in the complex setting of sampling from constrained, discrete and densely
connected probabilistic graphical models where, for each variation of the
problem, one needs to adjust the parameters of the proposal mechanism
automatically to ensure efficient mixing of the Markov chains.Comment: This paper contains 12 pages and 6 figures. A similar version of this
paper has been submitted to AISTATS 2012 and is currently under revie
Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities
Recent tests performed on the D-Wave Two quantum annealer have revealed no
clear evidence of speedup over conventional silicon-based technologies. Here,
we present results from classical parallel-tempering Monte Carlo simulations
combined with isoenergetic cluster moves of the archetypal benchmark problem-an
Ising spin glass-on the native chip topology. Using realistic uncorrelated
noise models for the D-Wave Two quantum annealer, we study the best-case
resilience, i.e., the probability that the ground-state configuration is not
affected by random fields and random-bond fluctuations found on the chip. We
thus compute classical upper-bound success probabilities for different types of
disorder used in the benchmarks and predict that an increase in the number of
qubits will require either error correction schemes or a drastic reduction of
the intrinsic noise found in these devices. We outline strategies to develop
robust, as well as hard benchmarks for quantum annealing devices, as well as
any other computing paradigm affected by noise.Comment: 8 pages, 5 figure