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Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
Combinatorial optimization problems have a broad range of applications and map to physical systems with complex dynamics. Among them, the 3-SAT problem is prominent due to its NP-complete nature. In physics terms, its solution corresponds…
The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…
Most data based state and parameter estimation methods require suitable initial values or guesses to achieve convergence to the desired solution, which typically is a global minimum of some cost function. Unfortunately, however, other…
The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert-space with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced…
We proposed the method that translates the 2-D CSP for minimizing the number of cuts to the Ising model. After that, we conducted computer experiments of the proposed model using the benchmark problem. From the above, the following results…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
In this paper, we consider the problem of minimizing quantum free energies under the constraint that the density of particles is fixed at each point of Rd, for any d $\ge$ 1. We are more particularly interested in the characterization of…
We demonstrate that it is possible to construct operators that stabilize the constraint-satisfying subspaces of computational problems in their Ising representations. We provide an explicit recipe to construct unitaries and associated…
We investigate the complexity of three optimization problems in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a…
Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…
We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…
The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
Quantum computing offers a promising route for tackling hard optimization problems by encoding them as Ising models. However, sparse qubit connectivity requires the use of minor-embedding, mapping logical qubits onto chains of physical…
A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…