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Understanding the benefits of quantum computing for solving combinatorial optimization problems (COPs) remains an open research question. In this work, we extend and analyze algorithms that solve COPs by recursively shrinking them. The…
This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy…
Combinatorial optimization plays a crucial role in many industrial applications. While classical computing often struggles with complex instances, quantum optimization emerges as a promising alternative. Here, we present an enhanced…
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…
We present a hybrid classical-quantum framework for portfolio construction and rebalancing. Asset selection is performed using Ledoit-Wolf shrinkage covariance estimation combined with hierarchical correlation clustering to extract n = 10…
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…
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal…
Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate…
Quantum optimization, both for classical and quantum functions, is one of the most well-studied applications of quantum computing, but recent trends have relied on hybrid methods that push much of the fine-tuning off onto costly classical…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
Quantum optimization solvers typically rely on one-variable-to-one-qubit mapping. However, the low qubit count on current quantum computers is a major obstacle in competing against classical methods. Here, we develop a qubit-efficient…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently…
The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…
Quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate optimization algorithm (QAOA). However, many combinatorial optimization…
We consider some classical and quantum approximate optimization algorithms with bounded depth. First, we define a class of "local" classical optimization algorithms and show that a single step version of these algorithms can achieve the…
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently…
In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…