Related papers: Transforming optimization problems into a QUBO for…
A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO, which in itself is a potentially difficult and expensive task. State-of-the-art transformations from MAX-3SAT to…
We present PyQUBO, an open-source, Python library for constructing quadratic unconstrained binary optimizations (QUBOs) from the objective functions and the constraints of optimization problems. PyQUBO enables users to prepare QUBOs or…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables…
In this article, we introduce and study the Quadratic Bin Packing Problem (QBPP), which generalizes the classical bin packing problem by introducing a fixed cost for each used bin and a pairwise cost (or profit) incurred whenever two items…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
We present QUBO.jl, an end-to-end Julia package for working with QUBO (Quadratic Unconstrained Binary Optimization) instances. This tool aims to convert a broad range of JuMP problems for straightforward application in many physics and…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz (QAOA). Real-world optimization problems typically consist of multiple types of constraints. To solve these optimization…
Convex quadratic objective functions are an important base case in state-of-the-art benchmark collections for single-objective optimization on continuous domains. Although often considered rather simple, they represent the highly relevant…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…
The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer.…
We analyze the transformation of QUBO from its conventional Boolean presentation into an equivalent spin glass problem with coupled $\pm1$ spin variables exposed to a site-dependent external field. We find that in a widely used testbed for…
Quadratic Unconstrained Binary Optimization (QUBO or UBQP) is concerned with maximizing/minimizing the quadratic form $H(J, \eta) = W \sum_{i,j} J_{i,j} \eta_{i} \eta_{j}$ with $J$ a matrix of coefficients, $\eta \in \{0, 1\}^N$ and $W$ a…
Many organizations that vitally depend on computation for their competitive advantage are keen to exploit the expected performance of quantum computers (QCs) as soon as quantum advantage is achieved. The best approach to deliver hardware…
An increasingly popular method for solving a constrained combinatorial optimisation problem is to first convert it into a quadratic unconstrained binary optimisation (QUBO) problem, and solve it using a standard QUBO solver. However, this…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
Despite the abundance of benchmark problems for optimization algorithms, there is a notable scarcity of such problems in multidisciplinary design optimization (MDO). To address this gap, we introduce a novel methodology that enables the…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…