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Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems---the main reason for this being the rigid layout of their…
The Quantum Alternating Operator Ansatz (QAOA) is a promising gate-model meta-heuristic for combinatorial optimization. Applying the algorithm to problems with constraints presents an implementation challenge for near-term quantum…
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…
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…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
Constrained binary optimization aims to find an optimal assignment to minimize or maximize the objective meanwhile satisfying the constraints, which is a representative NP problem in various domains, including transportation, scheduling,…
The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware…
This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz (QAOA). Real-world optimization problems typically consist of multiple types of constraints. To solve these optimization…
In this paper, the Quantum Approximate Optimization Algorithm (QAOA) is analyzed by leveraging symmetries inherent in problem Hamiltonians. We focus on the generalized formulation of optimization problems defined on the sets of $n$-element…
We present a quantum alternating operator ansatz (QAOA$^+$) that solves a class of linearly constrained optimization problems by evolving a quantum state within a Hilbert subspace of feasible problem solutions. Our main focus is on a class…
Quantum approximate optimization algorithm (QAOA) has attracted much attention as an algorithm that has the potential to efficiently solve combinatorial optimization problems. Among them, a fermionic QAOA (FQAOA) for solving constrained…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to…
We introduce multiple parametrized circuit ans\"atze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ans\"atze are inspired by mixing and phase…
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…
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 approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz comprising a problem…
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…
The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it…