# DWave Rapid Response Second Round April 2017

**Leveraging LANL’s D-WAVE 2X for Random Number Generation (pdf)**

Sarah Michalak**Abstract: **This project investigated use of LANL’s DWAVE 2X to generate random bit strings. As anticipated, raw bit strings are not random: a characterization study demonstrates deviations from randomness including qubit-specific probabilities of a 1 unequal to 0.5 and spatial and temporal association (correlation) in bit values. Further characterization will be completed to enable production of random bit strings.

LA-UR:17-23343

**Beyond Pairwise Ising Models in D-Wave: Searching for Hidden Multi-Body Interactions (pdf) ** Andrey Lokhov

**Abstract:**The input to the D-Wave quantum computer is specified in the form of a classical Ising model with pairwise interactions. However, it is likely that the spin statistics is best described by a model more general than a pairwise Ising model, in particular containing higher-order interactions. For example, these effective multi-body terms can be the signature of the noise created by malfunctioning qubits that are not used for computations, but are inevitably present in every D-Wave chip. In this work, we developed a reconstruction method that allows one to to capture the multi-body effects from the samples produced by D-Wave. We found that the 3-body interactions are indeed present in the chip, however their amplitude is at least order of magnitude smaller than residual couplings and magnetic fields for the zero Hamiltonian problem. Hence, these higher-order interactions can be safely ignored in all practical applications.

LA-UR: 17-23748

**Using the D‐Wave 2X to Explore the Formation of Global Terrorist Networks (pdf)** John Ambrosiano

**Abstract:**Social networks with signed edges (+/-) play an important role in an area of social network theory called structural balance. In these networks, edges represent relationships labeled as either friendly (+) or hostile (-). Given the edges, the problem of estimating the imbalance in the network, by trying to assign each node in one of two cohorts (+/-) so that like nodes are friends an unlike nodes are enemies, is NP-hard. The system is also equivalent to an Ising model, so solving the problem on the D-Wave computer is a natural fit. This project explores the application of this idea to signed social networks derived from the rivalries and alliances of terrorist groups.

LA-UR: 17-23946

**Connecting D-Wave 2X to Bayesian Inference Image Analysis (pdf)**

John Perry**Abstract:** The image processing capabilities afforded by the novel DWave 2X quantum computer were explored. By utilizing the DWave 2X’s optimization model and chimera graph based topology, we developed a simple approach for computing cyclic shifts of small binary vectors (up to a length of 9). Additionally, compressed sensing as it pertains to radiography was studied. Finally, a Smalltalk to C interface was developed in order to execute quantum computing jobs from an image analysis software known as the Bayesian Inference Engine (BIE).

LA-UR: 17-23376

**Quantum interaction of a few particle system mediated by photons (pdf)**

Petr Anisimov**Abstract:** We have focused on the physics of quantum x-ray free electron lasers yet there are many systems where particles interact with photon efficiently. This interaction depends on number of photons present as well as quantum states of particles. In an x-ray free electron laser, emission or absorption of a single photon results in a momentum recoil experienced by an electron. This changes the quantum state of an electron in the momentum space so that consecutive interactions will be affected. Furthermore, it changes the number of photons available to other electrons so that their evolution is now changed as well. One is interested in a steady state where exchange is balanced so that mean photon number and its variation could be found. We have attempted to use the D-Wave 2X in order to find momentum states of electrons and corresponding photon numbers at a steady state where photon emission and absorption is balanced by momentum recoils. Ising Hamiltonian has been used with some spins tracking photon states while other spins tracking momentum recoils. We have considered three approaches to analyze quantum interaction of a few particle system mediated by photons on the D-Wave 2X and have found that, although some information could be obtained, it is a difficult problem for D-Wave to solve.

LA-UR: 17-23498

**Simulations of non-local spin interaction in atomic magnetometers using LANL’s DWave 2X (pdf) ** Igor Savukov

**Abstract:**NV-diamond magnetometers are based on atomic spins with a Hamiltonian that contains Zeeman and magnetic dipole-dipole interactions, resembling the Izing model Hamiltonian used in the DWave computer. At some conditions and for some applications, only the z component needs to be considered, so the DWave computer can be applied directly. One problem important for a NV-diamond magnetometer is the understanding of behavior of spin ensembles, which affects the sensitivity of the magnetometer and applications in quantum computing. We simulated small, where intuitively the answer can be immediately obtained, and large systems of spins, where DWave can over perform classical computers. For example, we found ground-state energies and spin configurations for the system of 3 spins positioned along z direction, x direction, or in the x and y plane, and found that the DWave computer has some bias, which can be removed by applying a magnetic field. In addition, in a large system of spins, limited by embedding, which also caused some systematic effects, we studied the appearance of the ground state for different annealing times, and found that at a too short annealing time, the ground state does not appear. Various solutions of the DWave computing problems were proposed and investigated.

LA-UR: 17-23758

**Problem Reformulation and Matrix Sparsification (pdf)**Hristo Djidjev

**Abstract:**This research explores the suitability of preprocessing methods capable of reducing the number of variables in a quadratic unconstrained binary optimization (QUBO) program. Such methods allow one to determine the value of certain variables that hold in either every optimal solution (called strong persistencies) or in at least one optimal solution (weak persistencies). We investigate preprocessing methods for two important NP-hard graph problems, finding a maximum clique in a graph and the computation of a maximum cut. We show that the computation of strong and weak persistencies for those two graph instances is very instance-specific, but can lead to substantial reductions in problem size.

LA-UR: 17-23726

**Quantum Annealing Approaches to Graph Partitioning for Electronic Structure Problems (pdf) ** Sue Mniszewski

**Abstract:**Our previous work has shown that graph partitioning approaches using quantum annealing on the D-Wave 2X equal or out-perform current state-of-the-art methods. We have further extended this work by focusing on the k-concurrent all at once approaches using the super-node concept and a classical-quantum multi-level partitioning approach using the quantum annealer for refinement. Results based on the new k-concurrent formulations for graph partitioning and community detection are demonstrated with benchmark graphs, random graphs, social networks, bio-systems, and molecule electron structure graphs. Software tools used include

*sapi*Python for graphs that fit directly on the QPU and the hybrid classical-quantum

*qbsolv*for larger graphs.

LA-UR: 17-23580

**Nonnegative/Binary Matrix Factorization with a D-Wave Quantum Annealer (pdf)**

Dan O’Malley**Abstract:** We show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method can be used to analyze large datasets. The D-Wave only limits the number of features that can be extracted from the dataset. We apply this method to learn the features from a set of facial images.

LA-UR: 17:23437

**A Rigorous Comparison of the D-Wave 2X to Established B-QP Solution Methods (pdf)**

Carleton Coffrin **Abstract:** Binary Quadratic Programs (BQP) are a challenging class of NP-Hard discrete optimization problems with a wide variety of real-world applications and established solution methods. This work compares the performance of an industrial-strength Integer Programming solver (gurobi), a state-of-the-art Large Neighborhood Search heuristic (HFS), and a D-Wave 2X QPU on five BQP problem classes from the literature. The computational results suggest that the 2X QPU consistently produces high-quality solutions with runtimes that are comparable, but not strictly better than, the established methods. A key conclusion of this work is that further efforts are required to identify challenging problems classes for benchmarking QPUs.

LA-UR: 17:23540

**Solving Sparse Representation as for Object Classification Using the D-Wave 2X (pdf)**

Nga Nguyen

LA-UR: 16:27927