Related papers: Where the Really Hard Quadratic Assignment Problem…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…
Phase diagrams chart material properties with respect to one or more external or internal parameters such as pressure or magnetisation; as such, they play a fundamental role in many theoretical and applied fields of science. In this work,…
Computing diverse solutions for a given problem, in particular evolutionary diversity optimisation (EDO), is a hot research topic in the evolutionary computation community. This paper studies the Boolean satisfiability problem (SAT) in the…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
This perspective outlines promising pathways and critical obstacles on the road to developing useful quantum computing applications, drawing on insights from the Google Quantum AI team. We propose a five-stage framework for this process,…
Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…
We report on the phase transition of finding a complete subgraph, of specified dimensions, in a bipartite graph. Finding a complete subgraph in a bipartite graph is a problem that has growing attention in several domains, including…
We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
We examine the phase transition phenomenon for the Knapsack problem from both a computational and a human perspective. We first provide, via an empirical and a theoretical analysis, a characterization of the phenomenon in terms of two…
Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the…
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…
While accelerated computing has transformed many domains of computing, its impact on logical reasoning, specifically Boolean satisfiability (SAT), remains limited. State-of-the-art SAT solvers rely heavily on inherently sequential…
It has been demonstrated that the critical point of the phase transition in scalar quantum field theory with a quartic interaction in one space dimension can be approximated via a Gaussian Effective Potential (GEP). We discuss how this…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
Research into the development of special-purpose computing architectures designed to solve quadratic unconstrained binary optimization (QUBO) problems has flourished in recent years. It has been demonstrated in the literature that such…