Related papers: Quasi-exact ground-state algorithm for the random-…
A new Quasiparticle Random Phase Approximation approach is presented. The corresponding ground state is variationally determined and exhibits a minimum energy. New solutions for the ground state, some with spontaneously broken symmetry, of…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
In this paper we look at a class of random optimization problems that arise in the forms typically known as Hopfield models. We view two scenarios which we term as the positive Hopfield form and the negative Hopfield form. For both of these…
Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. For the complete family of parent Hamiltonians with a ground state…
Projected Entangled Pair States (PEPS) are a promising ansatz for the study of strongly correlated quantum many-body systems in two dimensions. But due to their high computational cost, developing and improving PEPS algorithms is necessary…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise…
Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…
We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
The determination of ground state properties of quantum systems is a fundamental problem in physics and chemistry, and is considered a key application of quantum computers. A common approach is to prepare a trial ground state on the quantum…
Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective ground state preparation is also computationally hard for arbitrary Hamiltonians. It is necessary…
Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
The importance of accurate soil moisture data for the development of modern closed-loop irrigation systems cannot be overstated. Due to the diversity of soil, it is difficult to obtain an accurate model for agro-hydrological system. In this…
Calculations of excited states in Green's function formalism often invoke the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. Here, we extend the stochastic approaches applied in the…
We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped…