Related papers: Performance of Variational Algorithms for Local Ha…

We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and…

Variational Quantum Algorithms are a vital part of quantum computing. It is a blend of quantum and classical methods for tackling tough problems in machine learning, chemistry, and combinatorial optimization. Yet as these algorithms scale…

Using Bayesian experimental design techniques, we have shown that for a single two-level quantum mechanical system under strong (projective) measurement, the dynamical parameters of a model Hamiltonian can be estimated with exponentially…

We study the performance of local quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) for the maximum cut problem, and their relationship to that of classical algorithms. (1) We prove that every (quantum or…

Variational quantum eigensolver ans\"atze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis…

We propose a quantum algorithm, inspired by ADAPT-VQE, to variationally prepare the ground state of a quantum Hamiltonian, with the desirable property that if it fails to find the ground state, it still yields a physically meaningful…

The Quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. In a typical QAOA setup, a set of quantum circuit parameters…

We present a new hybrid, local search algorithm for quantum approximate optimization of constrained combinatorial optimization problems. We focus on the Maximum Independent Set problem and demonstrate the ability of quantum local search to…

Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world…

The EPR Hamiltonian is a family of 2-local quantum Hamiltonians introduced by King (arXiv:2209.02589). We introduce a polynomial time $\frac{1+\sqrt{5}}{4}\approx 0.809$-approximation algorithm for the problem of computing the ground energy…

We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from the multi-grid community. Local improvement algorithms are based max-flow min-cut computations and…

Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…

Quantum variational algorithms are one of the most promising applications of near-term quantum computers; however, recent studies have demonstrated that unless the variational quantum circuits are configured in a problem-specific manner,…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…

Quantum Max Cut (QMC) problem for systems of qubits is an example of a 2-local Hamiltonian problem, and a prominent paradigm in computational complexity theory. This paper investigates the algebraic structure of a higher-dimensional analog…

Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This…

We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms. In particular, we certify the maximum energy in terms of the maximum matching of the underlying interaction graph…

Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…