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In this article we report on the application of the Quantum Approximate Optimization Algorithm (QAOA) to solve the unweighted MaxCut problem on tree-structured graphs. Specifically, we utilize the Nauty (No Automorphisms, Yes?) package to…
We propose a framework to solve non-linear and history-dependent mechanical problems based on a hybrid classical computer -- quantum annealer approach. Quantum Computers are anticipated to solve particular operations exponentially faster.…
Simulating molecular systems on quantum processors has the potential to surpass classical methods in computational resource efficiency. The limited qubit connectivity, small processor size, and short coherence times of near-term quantum…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has…
The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
In recent years, neutral atom quantum computers (NAQCs) have attracted a lot of attention, primarily due to their long coherence times and good scalability. One of their main drawbacks is their comparatively time-consuming control overhead,…
Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of the practical quantum advantage remains elusive. Recent studies have reported that both…
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…
Sampling a diverse set of high-quality solutions for hard optimization problems is of great practical relevance in many scientific disciplines and applications, such as artificial intelligence and operations research. One of the main open…
The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit…
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
The randomized linear combination of unitaries (LCU) method with many applications to early fault-tolerant quantum computing algorithms has been proposed. This quantum algorithm computes the same expectation values as the original, fully…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
Quantum computing holds the potential for quantum advantage in optimization problems, which requires advances in quantum algorithms and hardware specifications. Adiabatic quantum optimization is conceptually a valid solution that suffers…
We investigate the classical reducibility of random unit-disk graph (UDG) instances of the maximum independent set (MIS) and maximum weighted independent set (MWIS) problems, which can be natively realised in Rydberg atom quantum…