White Papers

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

Long-Short Minimum Risk Parity Optimization Using a Quantum or Digital Annealer

By Gili Rosenberg & Maxwell Rounds

In portfolio optimization, many weight allocation strategies result in long-only positions. We show how it is possible to formulate and solve an optimization problem that assigns a direction (long or short) to each weight allocation, such that the variance is minimized or maximized. This optimization problem can then be solved by many solvers, including D-Wave Systems’ quantum annealer, the Fujitsu Digital Annealer, and others. We present backtested results for three datasets solved using a tabu solver run on a CPU. Our results suggest that by utilizing intelligent shorting, this method is able to reduce the volatility of long-only strategies, leading to shorter maximum drawdowns and higher Sharpe ratios, albeit with a higher turnover. We also discuss possible extensions of this model such that it attempts to achieve market neutrality, sector neutrality, or takes into account a shorting aversion.


Optimal Feature Selection in Credit Scoring and Classification Using a Quantum Annealer

By Andrew Milne, Maxwell Rounds, & Phil Goddard

In credit scoring and classification, feature selection is used to reduce the number of variables input to a classifier. This can be done with a quadratic unconstrained binary optimization (QUBO) model, which attempts to select features that are both independent and influential. Quadratic optimization scales exponentially with the number of features, but a QUBO implementation on a quantum annealer has the potential to be faster than classical solvers. Tests were done using the German Credit Data from UC Irvine, and the results compared with those reported in the literature. In comparison with recursive feature elimination (RFE), a technique found in many software packages, QUBO Feature Selection yielded a smaller feature subset with no loss of accuracy. This opens up the possibility of using quantum annealers to programatically reduce the size of very large feature sets, especially as the size and availability of these devices increases.

An expanded version of this white paper has been published in: High-Performance Computing in Finance: Problems, Methods, and Solutions (2018)


Quantum-Inspired Hierarchical Risk Parity

By Elham Alipour, Clemens Adolphs, Arman Zaribafiyan, & Maxwell Rounds

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.


Swap Netting Using a Quantum Annealer

By Gili Rosenberg, Clemens Adolphs, Andrew Milne, & Andrew Lee

Swap trades that are cleared through a clearing house may be netted against each other. By doing this, the clearing house reduces its risk exposure, and the counterparties regain the use of capital that was previously tied up in margin accounts. The simplest form of netting is to cancel trades that offset each other exactly. However, it is also possible to net trades, or chains of trades, that sum to a very small residual. The ability to find new nettable combinations can lead to new capital efficiencies. The 1QBit swap netting solution makes use of a quantum annealer to identify such combinations and presents them as a netting proposal. The candidate swaps are chosen based on an incompatibility function, which incorporates differences in economic terms in a flexible way.


Finding Optimal Arbitrage Opportunities Using a Quantum Annealer

By Gili Rosenberg

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.


Cognitive Radio Optimization

By Arman Zaribafiyan & Jaspreet Oberoi

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.


Quantum Approaches to Graph Similarity

By Maritza Hernandez, Arman Zaribafiyan, & Mohammad Naghibi

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.

White paper

Simulated Annealing via Quantum Annealing

By Pooya Ronagh

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.

White paper

Integer Optimization Toolbox

By Pooya Ronagh

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.

White paper