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A promising approach to the practical application of the Quantum Approximate Optimization Algorithm (QAOA) is finding QAOA parameters classically in simulation and sampling the solutions from QAOA with optimized parameters on a quantum…
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization…
We investigate the Maximum Cut (MaxCut) problem on different graph classes with the Quantum Approximate Optimization Algorithm (QAOA) using symmetries. In particular, heuristics on the relationship between graph symmetries and the…
Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. While they have demonstrated considerable promise in solving problems of practical interest, efficiently determining the minimal…
The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA…
We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion…
Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading…
We study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of…
The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high…
We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX-$k$-CUT, the problem of finding an approximate $k$-vertex coloring of a graph. We compare this proposal to the best known classical and hybrid…
In low-depth implementations of the Quantum Approximate Optimization Algorithm (QAOA), the dominant cost is often the number of objective evaluations rather than circuit depth. We introduce a graph-conditioned trust-region method for…
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…
The Quantum Approximate Optimization Algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ans\"atze for…
Learning the problem structure at multiple levels of coarseness to inform the decomposition-based hybrid quantum-classical combinatorial optimization solvers is a promising approach to scaling up variational approaches. We introduce a…
The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of…
We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…
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…
The prospect of using quantum computers to solve combinatorial optimization problems via the quantum approximate optimization algorithm (QAOA) has attracted considerable interest in recent years. However, a key limitation associated with…
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We…
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…