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The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which…
Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…
There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may…
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal…
The syndrome decoding problem is known to be NP-complete. The goal of the decoder is to find an error of low weight that corresponds to a given syndrome obtained from a parity-check matrix. We use the quantum approximate optimization…
Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking…
As power systems expand, solving the Unit Commitment Problem (UCP) becomes increasingly challenging due to the dimensional catastrophe, and traditional methods often struggle to balance computational efficiency and solution quality. To…
The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical…
The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…
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,…
Protein folding -- the problem of predicting the spatial structure of a protein given its sequence of amino-acids -- has attracted considerable research effort in biochemistry in recent decades. In this work, we explore the potential of…
We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At…
We present a detailed study of portfolio optimization using different versions of the quantum approximate optimization algorithm (QAOA). For a given list of assets, the portfolio optimization problem is formulated as quadratic binary…
We present an approach, which we term quantum-enhanced optimization, to accelerate classical optimization algorithms by leveraging quantum sampling. Our method uses quantum-generated samples as warm starts to classical heuristics for…
Driver Hamiltonians and Mixing Operators that satisfy constraints is an important part of ansatz construction for many quantum algorithms. In this manuscript, we give general algebraic expressions for finding Hamiltonian terms and…
Hybrid quantum-classical algorithms, such as variational quantum algorithms (VQA), are suitable for implementation on NISQ computers. In this Letter we expand an implicit step of VQAs: the classical pre-computation subroutine which can…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
Structured variational quantum algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have emerged as leading candidates for exploiting advantages of near-term quantum hardware. They interlace classical computation, in…
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,…