White Papers

Our white papers outline how our research can be applied to address industry challenges.

Quantum-Inspired Hierarchical Risk Parity

By Elham Alipour, Clemens Adolphs, Arman Zaribafiyan, & Maxwell Rounds
Posted on November 14, 2016

We present a quantum-inspired approach to portfolio optimization that is based on an optimization problem that can be solved using a quantum annealer. The proposed algorithm utilizes a hierarchical clustering tree that is based on the covariance matrix of the asset returns. We use real market data to benchmark our approach against other common portfolio optimization methods and demonstrate its strong performance in terms of a variety of risk measures and lower susceptibility to inaccuracies in the input data.

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Finding Optimal Arbitrage Opportunities Using a Quantum Annealer

By Gili Rosenberg
Posted on October 20, 2016

We present two formulations for finding optimal arbitrage opportunities as a quadratic unconstrained binary optimization problem, which can be solved using a quantum annealer. The formulations are based on finding the most profitable cycle in a graph in which the nodes are the assets and the edge weights are the conversion rates. The edge-based formulation is simpler, whereas the node-based formulation allows for the identification of specific optimal arbitrage strategies, while possibly requiring fewer variables. In addition, an alternative form is presented which allows the arbitrage opportunities that best balance profit and risk to be found, based on the trader’s risk aversion. We discuss considerations for usage in practice. In particular, we suggest an application to illiquid assets and present an illustrative example.

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Cognitive Radio Optimization

By Arman Zaribafiyan & Jaspreet Oberoi
Posted on March 3, 2015

This research proposes a new approach for tackling cognitive radio asset allocation optimization problems. The cognitive radio optimization problem is generally an NP-hard mixed-integer programming problem due to its convoluted constraints. In contrast to conventional methods of using meta-heuristics and evolutionary algorithms, we implement non-linear constraints as polynomial penalty functions of binary variables and build a new objective function in a quadratic unconstrained binary optimization (QUBO) format.

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Quantum Approaches to Graph Similarity

By Maritza Hernandez, Arman Zaribafiyan, & Mohammad Naghibi
Posted on January 22, 2015

At 1QBit we have developed a method of measuring similarity between graphs with the aid of a quantum annealer. In contrast to conventional methods, our method is capable of identifying the reasons for determining that two arbitrary graphs are similar, and can illustrate how much each component of each graph contributes to the decision. Moreover, the method can be used to mine similar patterns in a group of graphs by solving subset matching problems. To validate our approach we apply our method in a biochemical scenario, classifying the toxicity properties of a library of molecules based on their similarity to labelled molecules. Benchmarking results show that this general-purpose similarity determination method can perform as accurately as the best-known classical solution while providing higher sensitivity or higher specificity, and maintaining the same predictive accuracy.

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Simulated Annealing via Quantum Annealing

By Pooya Ronagh

Posted on July 23, 2014

This paper describes a general method developed by 1QBit for solving continuous optimization problems inspired by different types of simulated annealing and genetic algorithms. This method works under the assumption of the existence of a computation model with a Turing reduction of problems to either quadratic unconstrained binary optimization (QUBO) problems or to an Ising spin problem. The paper presents an application of this method to a mixed-integer optimization problem. This will demonstrate an interesting method of representing a cardinality-constrained optimization problem using analytic expressions, and the ability of the method to solve such mixed-integer optimization problems.

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Integer Optimization Toolbox

By Pooya Ronagh
Posted on August 13, 2013

We describe how the Integer Optimization Toolbox approaches the problem of minimization of a (low-degree) polynomial over an integer lattice. In theory, the method illustrated here can be used for arbitrarily large polynomials with a large enough quantum annealing oracle.

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