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arXiv:2303.15419

A CQM-based approach to solving a combinatorial problem with applications in drug design

B. Maurice Benson, Victoria M. Ingman, Agarwal, Abhay, Shahar Keinan

Published Mar 27, 2023• 1 citation
arXivHTMLPDF

Abstract

The use of D-Wave's Leap Hybrid solver is demonstrated here in solving a Knapsack optimization problem: finding meal combinations from a fixed menu that fit a diner's constraints. This is done by first formulating the optimization problem as a Constrained Quadratic Model (CQM) and then submitting it to a quantum annealer. We highlight here the steps needed, as well as the implemented code, and provide solutions from a Chicken and Waffle restaurant menu. Additionally, we discuss how this model may be generalized to find optimal drug molecules within a large search space with many complex, and often contradictory, structures and property constraints.

DOI
10.48550/arxiv.2303.15419

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The use of D-Wave's Leap Hybrid solver is demonstrated here in solving a Knapsack optimization problem: finding meal combinations from a fixed menu that fit a diner's constraints. This is done by first formulating the optimization problem as a Constrained Quadratic Model (CQM) and then submitting it to a quantum annealer. We highlight here the steps needed, as well as the implemented code, and provide solutions from a Chicken and Waffle restaurant menu. Additionally, we discuss how this model may be generalized to find optimal drug molecules within a large search space with many complex, and often contradictory, structures and property constraints.
This study compares the performance of D-Wave’s two quantum-classical hybrid optimization solvers, which integrate quantum computing principles with classical optimization techniques to solve complex optimization problems. It focuses on the Binary Quadratic Model (BQM) solver, which encodes optimization problems using a binary quadratic formulation, and the Constrained Quadratic Model (CQM) solver, which can incorporate constraints into the model. The solvers were tested on five combinatorial optimization problems: Traveling Salesman Problem (TSP), Quadratic Knapsack Problem (QKP), Quadratic Assignment Problem (QAP), Weighted Max-Cut Problem (WMP), and Maximum Clique Problem (MCP). The goal is to quantify the accuracy of solutions compared to the optimal ones. Experiments on multiple instances with known optimal solutions examined solver behavior and solution quality. At default execution durations, the CQM solver generally outperforms BQM with lower error and higher consistency. Across all test problem instances in TSP, QKP, QAP, and WMP, the CQM solver achieved lower average absolute errors by 48.38, 27.83, 21.29, and 0.05 percentage points, respectively, compared to the BQM solver. An exception was found in MCP, where the BQM solver outperformed the CQM solver by 0.75 percentage points. These findings provide a guide for end users to understand the characteristics of the solvers and to select the appropriate solver for their specific optimization problems.
We present a quantum-based approach for the optimization of join orders in database applications. Our approach relies on a hybrid framework, where classical heuristics are combined with a quantum processor to accelerate the search over the set of solutions to a constrained problem. By taking advantage of a previously introduced formulation of the join order optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem, we implement it using the Constrained Quadratic Model (CQM), a hybrid classical-quantum solver that interfaces classical heuristics with D-Wave’s quantum annealer. We show that even a generic implementation of this classical-quantum hybrid framework produces competitive results for the join order problem, suggesting that better-tailored hybrid solvers could produce a computational advantage.
Abstract Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the “Optimizing the Production of Test Vehicles” use-case given in the BMW quantum computing challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like coin-or branch and cut and Gurobi solver. We conclude that the performance of the CQM solver is comparable to the classical solvers in optimizing the number of test vehicles, given the noise-prone quantum hardware. However, the CQM solver takes much more time, which prohibits obtaining useful quantum advantages. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.
Quantum computing, leveraging principles such as superposition and entanglement, has shown remarkable potential in solving complex optimization problems. Quantum annealing (QA) is particularly effective for combinatorial optimization and has gained increasing attention in financial applications. However, financial decision-making problems typically involve conflicting objectives, such as the trade-off between minimizing risk and maximizing returns, posing challenges for current QA approaches in efficiently encoding multi-objective problems and constraints. To address this gap, we propose the first quantum annealing framework for bi-objective weighted portfolio optimization based on the trend ratio model, integrating D-Wave's latest constrained quadratic model (CQM) hybrid solver. Our approach offers flexibility to accommodate diverse investor preferences. Experimental evaluations using real-world U.S. stock market data demonstrate the effectiveness of our method, showing higher-quality solutions and faster runtimes compared to classical multi-objective optimization algorithms. These promising results highlight the significant potential of quantum computing in practical financial optimization scenarios.
In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.
Hybrid quantum computing (QC) combines classical and quantum resources to tackle challenging optimization problems, leveraging the strengths of both within the current constraints of quantum computers, which are limited in size and power. Therefore, we explore the efficacy of a hybrid quantum annealing (QA) search algorithm in improving portfolio optimization. This study pioneers the application of the trend ratio (TR) to a quantum annealing computer, converting it into a constrained quadratic model with a flexible presentation. The TR serves as a promising indicator in portfolio evaluation, considering the great balance between expected returns and risks. Utilizing D- Wave's hybrid solver, we present a thorough analysis and discussion of the proposed model realized in the QA structure. The experimental results demonstrate that our model can discover solutions of comparable quality in a significantly shorter amount of time than an exhaustive search. When extending the search space to sizes challenging for exhaustive search, we conducted experiments comparing our approach with state-of-the-art quantum-inspired artificial intelligence (AI) algorithms. The results show that our method not only constructs higher-quality solutions but also requires the least computation time. The hybrid quantum-classical AI represents a forward-looking technology paradigm poised to revolutionize problem-solving methods.