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The quantum approximate optimization algorithm/quantum alternating operator ansatz (QAOA) is a heuristic to find approximate solutions of combinatorial optimization problems. Most literature is limited to quadratic problems without…

Combinatorial optimization problems on graphs have broad applications in science and engineering. The Quantum Approximate Optimization Algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of…

Constructing an optimal mixer for Quantum Approximate Optimization Algorithm (QAOA) Hamiltonian is crucial for enhancing the performance of QAOA in solving combinatorial optimization problems. We present a systematic methodology for…

One of the most promising attempts towards solving optimization problems with quantum computers in the noisy intermediate scale era of quantum computing are variational quantum algorithms. The Quantum Alternating Operator Ansatz provides an…

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm that offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization…

The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid heuristic for combinatorial optimization, but efficiently handling hard constraints remains a significant challenge. XY-mixers successfully confine quantum state…

We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which it is possible to efficiently prepare an…

Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as…

The Quantum Alternating Operator Ansatz is a generalization of the Quantum Approximate Optimization Algorithm (QAOA) designed for finding approximate solutions to combinatorial optimization problems with hard constraints. In this paper, we…

The XY-mixer has widespread utilization in modern quantum computing, including in variational quantum algorithms, such as Quantum Alternating Operator Ansatz (QAOA). The XY ansatz is particularly useful for solving Cardinality Constrained…

The quantum approximate optimization algorithm (QAOA) is a near-term quantum algorithm aimed at solving combinatorial optimization problems. Since its introduction, various generalizations have emerged, spanning modifications to the initial…

Quantum optimization algorithms, such as the Quantum Approximate Optimization Algorithm, are emerging as promising heuristics for solving complex combinatorial problems. To improve performance, several extensions to the standard QAOA…

The Quantum Approximate Optimization Algorithm (QAOA) has been one of the leading candidates for near-term quantum advantage in gate-model quantum computers. From its inception, this algorithm has sparked the desire for comparison between…

Recently, Hadfield et al. proposed the quantum alternating operator ansatz algorithm (QAOA+), an extension of the quantum approximate optimization algorithm (QAOA), to solve constrained combinatorial optimization problems (CCOPs). Compared…

The quantum approximate optimization algorithm (QAOA) is a promising quantum algorithm that can be used to approximately solve combinatorial optimization problems. The usual QAOA ansatz consists of an alternating application of the cost and…

This paper concerns quantum heuristics based on Mixer Hamiltonians that allow to restrict investigation on a specific subspace. Mixer Hamiltonian based approaches can be included in QAOA algorithm and we can state that Mixer Hamiltonians…

We present a novel formalism to both understand and construct mixers that preserve a given subspace. The method connects and utilizes the stabilizer formalism that is used in error correcting codes. This can be useful in the setting when…

The Quantum Approximate Optimization Algorithm (QAOA) is among leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant…

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit…

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…