# RESEARCH PAPERS

Selected research papers published by 1QBit’s team and collaborators.

## A Subgradient Approach for Constrained Binary Optimization via Quantum Adiabatic Evolution

By Sahar Karimi & Pooya Ronagh

Posted on January 25, 2017

## Enhancing Quantum Annealing Performance for the Molecular Similarity Problem

By Maritza Hernandez & Maliheh Aramon

Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to enhance the efficiency of such a solver. In this work, we present a quantum annealing approach to measure similarity among molecular structures. Implementing real-world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity, intrinsic control error, and limited precision. In order to overcome the limited connectivity, a problem must be reformulated using minor-embedding techniques. Using a real data set, we investigate the performance of a quantum annealer in solving the molecular similarity problem. We provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance. Common practices for embedding include minimizing either the number of qubits or the chain length, and determining the strength of ferromagnetic couplers empirically. We show that current criteria for selecting an embedding do not improve the hardware’s performance for the molecular similarity problem. Furthermore, we use a theoretical approach to determine the strength of ferromagnetic couplers. Such an approach removes the computational burden of the current empirical approaches, and also results in hardware solutions that can benefit from simple local classical improvement. Although our results are limited to the problems considered here, they can be generalized to guide future benchmarking studies.

## Boosting Quantum Annealer Performance via Quantum Persistence

By Hamed Karimi & Gili Rosenberg

Posted on June 24, 2016

## Prime Factorization Using Quantum Annealing and Algebraic Geometry

By Raouf Dridi & Hedayat Alghassi

Posted on April 20, 2016

## Systematic and Deterministic Graph-Minor Embedding for Cartesian Products of Graphs

By Arman Zaribafiyan, Dominic Marchand, & S. Saeed C. Rezaei

Posted on February 15, 2016

## A Novel Graph-based Approach for Determining Molecular Similarity

By Maritza Hernandez, Arman Zaribafiyan, Maliheh Aramon, & Mohammad Naghibi

Posted on January 26, 2016

*k*-plex relaxation method, which allows dissimilarities among graphs up to a predetermined level. We then formulate the problem as a novel quadratic unconstrained binary optimization problem that can be solved by a quantum annealer. The context of our study is molecular similarity where the presence of noise might be due to regular errors in measuring molecular features. We develop a similarity measure and use it to predict the mutagenicity of a molecule. Our results indicate that the relaxed similarity measure, designed to accommodate the regular errors, yields a higher prediction accuracy than the measure that ignores the noise.

## Homology Computation of Large Point Clouds Using Quantum Annealing

By Raouf Dridi & Hedayat Alghassi

Posted on December 23, 2015

*K*approximating the given point cloud. It uses quantum annealing to compute a clique cover of the 1-skeleton of

*K*and then uses this cover to blow up

*K*into a Mayer-Vietoris complex. Finally, it computes the homology of the Mayer-Vietoris complex in parallel. The novelty here is the use of clique covering which, compared to graph partitioning, substantially reduces the computational load assigned to each slave machine in the computing cluster. We describe two different clique covers and their quantum annealing formulation in the form of quadratic unconstrained binary optimization (QUBO).

## Solving Constrained Quadratic Binary Problems via Quantum Adiabatic Evolution

By Pooya Ronagh, Brad Woods, & Ehsan Iranmanesh

Posted on September 16, 2015

## Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

By Gili Rosenberg, Poya Haghnegahdar, Phil Goddard, Peter Carr, Kesheng Wu, & Marcos López de Prado

Posted on August 22, 2015

## Building an Iterative Heuristic Solver for a Quantum Annealer

By Gili Rosenberg, Mohammad Vazifeh, Brad Woods, & Eldad Haber

Posted on July 27, 2015