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Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost…
The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure…
An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising…
The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical…
Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems…
We present a framework to deal with a range of large scale compressive sensing problems using a quantum subroutine. We apply a quantum approximate optimization algorithm (QAOA) to support detection in a sparse signal reconstruction…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this…
Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…
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,…
Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum…
Hard combinatorial optimization problems, often mapped to Ising models, promise potential solutions with quantum advantage but are constrained by limited qubit counts in near-term devices. We present an innovative quantum-inspired framework…
Efficient solving of an unseen optimization problem is related to appropriate selection of an optimization algorithm and its hyper-parameters. For this purpose, automated algorithm performance prediction should be performed that in most…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
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…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
We provide some analytical tests of the density of states estimation from the "localization landscape" approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of…