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We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
The Hamiltonian constraint remains the major unsolved problem in Loop Quantum Gravity (LQG). Seven years ago a mathematically consistent candidate Hamiltonian constraint has been proposed but there are still several unsettled questions…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from carefully prepared Ansatz quantum circuits. However, current quantum computers are limited…
This paper studies the Hamiltonian Cycle Problem (HCP) and the Traveling Salesman Problem (TSP) on D-Wave's quantum systems. Initially, motivated by the fact that most libraries present their benchmark instances in terms of adjacency…
Quantum annealers provide an effective framework for solving large-scale combinatorial optimization problems. This work presents a novel methodology for training Variational Quantum Algorithms (VQAs) by reformulating the parameter…
Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem, which potentially can be solved by quantum computing. We propose a method to formulate the Hamiltonian of finding H-matrix…
Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…
Quantum annealers are specialized quantum computers for solving combinatorial optimization problems using special characteristics of quantum computing (QC), such as superposition, entanglement, and quantum tunneling. Theoretically, quantum…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
The Fermi-Hubbard model (FHM) on a two dimensional square lattice has long been an important testbed and target for simulating fermionic Hamiltonians on quantum hardware. We present an alternative for quantum simulation of FHMs based on an…
The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that…
Quantum annealing (QA) that encodes optimization problems into Hamiltonians remains the only near-term quantum computing paradigm that provides sufficient many qubits for real-world applications. To fit larger optimization instances on…
Quantum annealing offers a promising strategy for solving complex optimization problems by encoding the solution into the ground state of a problem Hamiltonian. While most implementations rely on spin-$1/2$ systems, we explore the…
Diagonalizing a Hamiltonian, which is essential for simulating its long-time dynamics, is a key primitive in quantum computing and has been proven to yield a quantum advantage for several specific families of Hamiltonians. Yet, despite its…
In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter…
Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…
Motivated by recent progress in quantum hardware and algorithms researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and…
Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to…