Ilia Zintchenko

Optimised simulated annealing for Ising spin glasses

Abstract We present several efficient implementations of the simulated annealing algorithm for Ising spin glasses on sparse graphs. In particular, we provide a generic code for any choice of couplings, an optimised code for bipartite graphs, and highly optimised implementations using multi-spin coding for graphs with small maximum degree and discrete couplings with a finite range. The latter codes achieve up to 50 spin flips per nanosecond on modern Intel CPUs. We also compare the performance of the codes to that of the special purpose D-Wave devices built for solving such Ising spin glass problems. Program summary Program title: SimAn v1.0 Catalogue identifier: AEVZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVZ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 14999 No. of bytes in distributed program, including test data, etc.: 26594 Distribution format: tar.gz Programming language: C++, OpenMP for parallelization. Computer: Any PC. Operating system: Linux/OS X/UNIX. Has the code been vectorised or parallelized?: Parallelized using OpenMP. RAM: Variable, from a few megabytes. Classification: 4.13, 6.5, 23. Nature of problem: Ising spin glass ground states on sparse graphs. Solution method: Simulated annealing. Running time: From milliseconds to seconds.

From local to global ground states in Ising spin glasses

We consider whether it is possible to find ground states of frustrated spin systems by solving them locally. Using spin glass physics and Imry-Ma arguments in addition to numerical benchmarks we quantify the power of such local solution methods and show that for the average low-dimensional spin glass problem outside the spin- glass phase the exact ground state can be found in polynomial time. In the second part we present a heuristic, general-purpose hierarchical approach which for spin glasses on chimera graphs and lattices in two and three dimensions outperforms, to our knowledge, any other solver currently around, with significantly better scaling performance than simulated annealing.

Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena

Abstract We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) computed via density functional theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional OLs, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks–Girardeau limit and in very deep OLs. We also consider a three-dimensional OL at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries.

Randomized gap and amplitude estimation

We provide a new method for estimating spectral gaps in low-dimensional systems. Unlike traditional phase estimation, our approach does not require ancillary qubits nor does it require well characterised gates. Instead, it only requires the ability to perform approximate Haar–random unitary operations, applying the unitary whose eigenspectrum is sought out and performing measurements in the computational basis. We discuss application of these ideas to in-place amplitude estimation and quantum device calibration.