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Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the…
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…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization…
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. Optimal QAOA parameter concentration effects for special…
The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on…
Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm…
Variational Quantum Algorithms, including the Quantum Approximate Optimization Algorithm (QAOA), have shown promise in solving optimization problems but rely on costly variational loops that can themselves be hard optimization problems.…
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 study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of…
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising candidates to achieve the quantum advantage in solving combinatorial optimization problems. The process of finding a good set of variational parameters in the…
Optimization is ubiquitous in quantum information science and technology, however, the corresponding optimization landscape can encounter false traps, i.e., local but not global optima, likely to prevent used optimizers from finding optimal…
Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators,…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
We design two variational algorithms to optimize specific 2-local Hamiltonians defined on graphs. Our algorithms are inspired by the Quantum Approximate Optimization Algorithm. We develop formulae to analyze the energy achieved by these…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…