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The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization. In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model,…
Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for…
We present a thorough investigation of problems that can be solved exactly with the level-1 Quantum Approximate Optimization Algorithm (QAOA). To this end we implicitly define a class of problem Hamiltonians that employed as phase separator…
Quantum approximate optimization algorithm (QAOA) have promising applications in combinatorial optimization problems (COPs). We investigated the MaxCut problem in three different families of graphs using QAOA ansats with parameter transfer…
We present new advances towards achieving exponential quantum speedups for solving optimization problems by low-depth quantum algorithms. Specifically, we focus on families of combinatorial optimization problems that exhibit symmetry and…
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA),…
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is…
Hadfield et al. proposed a novel Quantum Alternating Operator Ansatz algorithm (QAOA+), and this algorithm has wide applications in solving constrained combinatorial optimization problems (CCOPs) because of the advantages of QAOA+ ansatz in…
The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical…
The Quantum Approximate Optimization Algorithm (QAOA) represents a significant opportunity for practical quantum computing applications, particularly in the era before error correction is fully realized. This algorithm is especially…
As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of…
Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass…
Across diverse synthetic and real-world interaction graphs, the variational landscapes of reduced Quantum Approximate Optimization Algorithm (QAOA) instances obtained via variable freezing exhibit a robust universality. Leveraging this…
We report on the energy-expectation-value landscapes produced by the single-layer ($p=1$) Quantum Approximate Optimization Algorithm (QAOA) when being used to solve Ising problems. The landscapes are obtained using an analytical formula…
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…
While a Quantum Approximate Optimization Algorithm (QAOA) is intended to provide a quantum advantage in finding approximate solutions to combinatorial optimization problems, noise in the system is a hurdle in exploiting its full potential.…
The Quantum Approximate Optimization Algorithm (QAOA) constitutes one of the often mentioned candidates expected to yield a quantum boost in the era of near-term quantum computing. In practice, quantum optimization will have to compete with…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained -- by repeatedly adjusting circuit parameters -- to solve a problem.…