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Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…
Digital Annealer (DA) is a computer architecture designed for tackling combinatorial optimization problems formulated as quadratic unconstrained binary optimization (QUBO) models. In this paper, we present the results of an extensive…
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.…
With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model…
A quantum annealer heuristically minimizes quadratic unconstrained binary optimization (QUBO) problems, but is limited by the physical hardware in the size and density of the problems it can handle. We have developed a meta-heuristic solver…
In this paper we present a novel strategy to solve optimization problems within a hybrid quantum-classical scheme based on quantum annealing, with a particular focus on QUBO problems. The proposed algorithm is based on an iterative…
In recent years, there is a growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design…
Combinatorial optimization problems play a central role in computer science with many real world applications. A number of relevant problems remain computationally difficult to solve as they lie in the NP-hard complexity class. We present a…
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…
Hypergraph partitioning is a fundamental optimization problem with applications in data management and other domains involving higher-order relations. In this paper, we study balanced hypergraph partitioning from the perspective of quantum…
In this work, we introduce a novel Quadratic Binary Optimization (QBO) framework for training a quantized neural network. The framework enables the use of arbitrary activation and loss functions through spline interpolation, while Forward…
Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard combinatorial optimization problems in the form of binary variables. The Hamiltonian function is often used to formulate QUBO problems where…
For various optimization problems, the classical time to solution is super-polynomial and intractable to solve with classical bit-based computing hardware to date. Digital and quantum annealers have the potential to identify near-optimal…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
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…
Recent hardware advances in quantum and quantum-inspired annealers promise substantial speedup for solving NP-hard combinatorial optimization problems compared to general-purpose computers. These special-purpose hardware are built for…
Quantum annealing technologies aim to solve computational optimization and sampling problems. QPU (Quantum Processing Unit) machines such as the D-Wave system use the QUBO (Quadratic Unconstrained Binary Optimization) formula to define…
In this paper, we present a new method to solve a certain type of Semidefinite Programming (SDP) problems. These types of SDPs naturally arise in the Quadratic Convex Reformulation (QCR) method and can be used to obtain dual bounds of…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…