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The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems, derived from an approximation to the Quantum Adiabatic Algorithm (QAA). In solving…
Noise on near-term quantum devices will inevitably limit the performance of Quantum Approximate Optimization Algorithm (QAOA). One significant consequence is that the performance of QAOA may fail to monotonically improve with depth. In…
Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit,…
The Quantum Alternating Operator Ansatz (QAOA) represents a branch of quantum algorithms for solving combinatorial optimization problems. A specific variant, the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA), ensures uniform…
The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial problems with shallow circuits. We present a scheme to parallelize this…
Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…
The quantum approximate optimization algorithm (QAOA) is a variational method for noisy, intermediate-scale quantum computers to solve combinatorial optimization problems. Quantifying performance bounds with respect to specific problem…
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. Here we show that the \emph{density} of problem constraints versus problem variables acts as a performance…
The quantum approximate optimization algorithm (QAOA) is a leading iterative variational quantum algorithm for heuristically solving combinatorial optimization problems. A large portion of the computational effort in QAOA is spent by the…
Quantum computers are increasing in size and quality, but are still very noisy. Error mitigation extends the size of the quantum circuits that noisy devices can meaningfully execute. However, state-of-the-art error mitigation methods are…
The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid quantum-classical algorithm for solving combinatorial optimisation problems. QAOA encodes solutions into the ground state of a Hamiltonian, approximated by a $p$-level…
Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling combinatorial optimization challenges. However, their practical realization confronts a dilemma: the requisite circuit depth for…
Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary near intermediate-scale quantum (NISQ) era. The quantum approximate optimisation algorithm (QAOA)…
The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to…
An enhanced framework of quantum approximate optimization algorithm (QAOA) is introduced and the parameter setting strategies are analyzed. The enhanced QAOA is as effective as the QAOA but exhibits greater computing power and flexibility,…
The present tutorial aims to provide a comprehensible and easily accessible introduction into the theory and implementation of the famous Quantum Approximate Optimization Algorithm (QAOA). We lay our focus on practical aspects and…
Developing quantum algorithms adaptive to specific constraints of near-term devices is an essential step towards practical quantum advantage. In a recent work [Phys. Rev. Lett. 131, 103601(2023)], we show cold atoms in an optical cavity can…
Quantum Approximate Optimisation (QAOA) is the most studied gate based variational quantum algorithm today. We train QAOA one layer at a time to maximize overlap with an $n$ qubit target state. Doing so we discovered that such training…
Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit…
Considerable effort has been made recently in the development of heuristic quantum algorithms for solving combinatorial optimization problems. Meanwhile, these problems have been studied extensively in classical computing for decades. In…