arXiv subjects

Ethan W. Brown

Publications and source records attributed to Ethan W. Brown.

5 recordsLinked to original sources

arXiv2017

Designing Adiabatic Quantum Optimization: A Case Study for the Traveling Salesman Problem

With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal design of adiabatic algorithms plays an important role in their assessment, we illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP). We demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dynamics are not carefully tailored to the problem. Furthermore we show that inequality constraints, in particular, present a major hurdle for the implementation on analog quantum annealers. We finally argue that programmable digital quantum annealers can overcome many of these obstacles and can - once large enough quantum computers exist - provide an interesting route to using quantum annealing on a large class of problems.

quant-ph↗

arXiv2016

Accurate exchange-correlation energies for the warm dense electron gas

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the $k$-space configuration path-integral formalism disagree by up to $\sim$$10$\% at certain reduced temperatures $T/T_F \le 0.5$ and densities $r_s \le 1$. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that DMQMC can calculate free energies directly and present exact free energies for $T/T_F \ge 1$ and $r_s \le 2$.

cond-mat.str-el↗

arXiv2014

Overcoming the fermion sign problem in homogeneous systems

Explicit treatment of many-body Fermi statistics in path integral Monte Carlo (PIMC) results in exponentially scaling computational cost due to the near cancellation of contributions to observables from even and odd permutations. Through direct analysis of exchange statistics we find that individual exchange probabilities in homogeneous systems are, except for finite size effects, independent of the configuration of other permutations present. For two representative systems, 3-He and the homogeneous electron gas, we show that this allows the entire antisymmetrized density matrix to be generated from a simple model depending on only a few parameters obtainable directly from a standard PIMC simulation. The result is a polynomial scaling algorithm and up to a 10 order of magnitude increase in efficiency in measuring fermionic observables for the systems considered.

cond-mat.str-el↗

arXiv2013

Exchange-correlation energy for the 3D homogeneous electron gas at arbitrary temperature

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r_{s} = (3/4πn)^{1/3} a_{B}^{-1} < 40 and Θ= T/T_{F} > 0.0625). In doing so, we construct a Padé approximant which collapses to Debye-Hückel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.

cond-mat.str-el↗

arXiv2012

Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas

We perform calculations of the {3D} finite-temperature homogeneous electron gas (HEG) in the warm-dense regime ({r_{s} \equiv (3/4πn)^{1/3}a_{B}^{- 1} = 1.0- 40.0} and {Θ\equiv T/T_{F} = 0.0625- 8.0}) using restricted path integral Monte Carlo (RPIMC). Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parameterized local density approximation (LDA) and our results around {T_{F}} . These results can be used as a benchmark for improved functionals, as well as input for orbital-free DFT formulations.

cond-mat.str-el↗