1,141 research outputs found
An Overview of Approaches to Modernize Quantum Annealing Using Local Searches
I describe how real quantum annealers may be used to perform local (in state
space) searches around specified states, rather than the global searches
traditionally implemented in the quantum annealing algorithm. The quantum
annealing algorithm is an analogue of simulated annealing, a classical
numerical technique which is now obsolete. Hence, I explore strategies to use
an annealer in a way which takes advantage of modern classical optimization
algorithms, and additionally should be less sensitive to problem
mis-specification then the traditional quantum annealing algorithm.Comment: In Proceedings PC 2016, arXiv:1606.06513. An extended version of this
contribution will appear on arXiv soon which will describe more detailed
algorithms, comment more on robustness to problem mis-specification, comment
on thermal sampling applications, and discuss applications on real device
A Bayesian Periodogram Finds Evidence for Three Planets in 47 Ursae Majoris
A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data
confirms and refines the properties of two previously reported planets with
periods of 1079 and 2325 days and finds evidence for an additional long period
planet with a period of approximately 10000 days. The three planet model is
found to be 10^5 times more probable than the next most probable model which is
a two planet model. The nonlinear model fitting is accomplished with a new
hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel
tempering, simulated annealing and genetic crossover operations. Each of these
features facilitate the detection of a global minimum in chi-squared. By
combining all three, the HMCMC greatly increases the probability of realizing
this goal. When applied to the Kepler problem it acts as a powerful
multi-planet Kepler periodogram. The measured periods are 1078 \pm 2,
2391{+100}{-87}, and 14002{+4018}{-5095}d, and the corresponding eccentricities
are 0.032 \pm 0.014, 0.098{+.047}{-.096}, and 0.16{+.09}{-.16}. The results
favor low eccentricity orbits for all three. Assuming the three signals (each
one consistent with a Keplerian orbit) are caused by planets, the corresponding
limits on planetary mass (M sin i) and semi-major axis are (2.53{+.07}{-.06}MJ,
2.10\pm0.02au), (0.54\pm0.07MJ, 3.6\pm0.1au), and (1.6{+0.3}{-0.5}MJ,
11.6{+2.1}{-2.9}au), respectively. We have also characterized a noise induced
eccentricity bias and designed a correction filter that can be used as an
alternate prior for eccentricity, to enhance the detection of planetary orbits
of low or moderate eccentricity
Studies of an Off-Lattice Model for Protein Folding: Sequence Dependence and Improved Sampling at Finite Temperature
We study the thermodynamic behavior of a simple off-lattice model for protein
folding. The model is two-dimensional and has two different ``amino acids''.
Using numerical simulations of all chains containing eight or ten monomers, we
examine the sequence dependence at a fixed temperature. It is shown that only a
few of the chains exist in unique folded state at this temperature, and the
energy level spectra of chains with different types of behavior are compared.
Furthermore, we use this model as a testbed for two improved Monte Carlo
algorithms. Both algorithms are based on letting some parameter of the model
become a dynamical variable; one of the algorithms uses a fluctuating
temperature and the other a fluctuating monomer sequence. We find that by these
algorithms one gains large factors in efficiency in comparison with
conventional methods.Comment: 17 pages, 9 Postscript figures. Combined with chem-ph/950500
Integration of Simulated Quantum Annealing in Parallel Tempering and Population Annealing for Heterogeneous-Profile QUBO Exploration
Simulated Quantum Annealing (SQA) is a heuristic algorithm which can solve Quadratic Unconstrained Binary Optimization (QUBO) problems by emulating the exploration of the solution space done by a quantum annealer. It mimics the quantum superposition and tunnelling effects through a set of correlated replicas of the spins system representing the problem to be solved and performing Monte Carlo steps. However, the effectiveness of SQA over a classical algorithm strictly depends on the cost/energy profile of the target problem. In fact, quantum annealing only performs well in exploring functions with high and narrow peaks, while classical annealing is better in overcoming flat and wide energy-profile barriers. Unfortunately, real-world problems have a heterogeneous solution space and the probability of success of each solver depends on the size of the energy profile region compatible with its exploration mechanism. Therefore, significant advantages could be obtained by exploiting hybrid solvers, which combine SQA and classical algorithms. This work proposes four new quantum-classical algorithms: Simulated Quantum Parallel Tempering (SQPT), Simulated Quantum Population Annealing (SQPA), Simulated Quantum Parallel Tempering - Population Annealing v1 (SQPTPA1) and Simulated Quantum Parallel Tempering - Population Annealing v2 (SQPTPA2). They are obtained by combining SQA, Parallel Tempering (PT), and Population Annealing (PA). Their results are compared with those provided by SQA, considering benchmark QUBO problems, characterized by different profiles. Even though this work is preliminary, the obtained results are encouraging and prove hybrid solvers’ potential in solving a generic optimization problem
Importance Tempering
Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC)
method for sampling from a multimodal density . Typically, ST
involves introducing an auxiliary variable taking values in a finite subset
of and indexing a set of tempered distributions, say . In this case, small values of encourage better
mixing, but samples from are only obtained when the joint chain for
reaches . However, the entire chain can be used to estimate
expectations under of functions of interest, provided that importance
sampling (IS) weights are calculated. Unfortunately this method, which we call
importance tempering (IT), can disappoint. This is partly because the most
immediately obvious implementation is na\"ive and can lead to high variance
estimators. We derive a new optimal method for combining multiple IS estimators
and prove that the resulting estimator has a highly desirable property related
to the notion of effective sample size. We briefly report on the success of the
optimal combination in two modelling scenarios requiring reversible-jump MCMC,
where the na\"ive approach fails.Comment: 16 pages, 2 tables, significantly shortened from version 4 in
response to referee comments, to appear in Statistics and Computin
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