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Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near term and beyond. At the same time, as quantum computing hardware not only continues to improve but also begins to incorporate new features…
The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the…
We comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial…
The Quantum Alternating Operator Ansatz (QAOA) and its predecessor, the Quantum Approximate Optimization Algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems. However, as there is yet…
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…
Variational Quantum Algorithms (VQAs) have emerged as a powerful class of algorithms that is highly suitable for noisy quantum devices. Therefore, investigating their design has become key in quantum computing research. Previous works have…
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…
We develop a framework for analyzing layered quantum algorithms such as quantum alternating operator ans\"atze. Our framework relates quantum cost gradient operators, derived from the cost and mixing Hamiltonians, to classical cost…
The quantum approximate optimization algorithm (QAOA) promises to solve classically intractable computational problems in the area of combinatorial optimization. A growing amount of evidence suggests that the originally proposed form of the…
The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and…
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…
A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. This circuit is most commonly designed to respect the symmetries of the problem Hamiltonian and, in this…
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…
Realizing the potential of near-term quantum computers to solve industry-relevant constrained-optimization problems is a promising path to quantum advantage. In this work, we consider the extractive summarization constrained-optimization…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
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 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…
Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate…
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…
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),…