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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) uses a quantum computer to implement a variational method with $2p$ layers of alternating unitary operators, optimized by a classical computer to minimize a cost function. While rigorous…
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…
The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the $p\to\infty$ limit the…
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…
We study fundamental limitations of the generic Quantum Approximate Optimization Algorithm (QAOA) on constrained problems where valid solutions form a low dimensional manifold inside the Boolean hypercube, and we present a provable route to…
Quantum amplitude estimation (QAE) is a pivotal quantum algorithm to estimate the squared amplitude $a$ of the target basis state in a quantum state $|\Phi\rangle$. Various improvements on the original quantum phase estimation-based QAE…
We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the…
We introduce a generalized \textit{Probabilistic Approximate Optimization Algorithm (PAOA)}, a classical variational Monte Carlo framework that extends and formalizes prior work by Weitz \textit{et al.}~\cite{Combes_2023}, enabling…
There exist numerous problems in nature inherently described by finite $D$-dimensional states. Formulating these problems for execution on qubit-based quantum hardware requires mapping the qudit Hilbert space to that of multiqubit which may…
The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth $p$. We apply the QAOA to MaxCut on large-girth $D$-regular…
The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling…
Inspired by a class of algorithms proposed by Farhi et al. (arXiv:1411.4028), namely the quantum approximate optimization algorithm (QAOA), we present a circuit-based quantum algorithm to search for a needle in a haystack, obtaining the…
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…
In the search for quantum advantage in real--world problems, one promising avenue is to use a quantum algorithm to improve on the solution found using an efficient classical algorithm. The quantum approximate optimization algorithm (QAOA)…
The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into…
The Quantum Approximate Optimization Algorithm (QAOA) is a quantum algorithm designed for Combinatorial Optimization Problem (COP). We show that if a local algorithm is limited in performance at logarithmic depth for a spin glass type COP…
Combinatorial optimization problems are central to science and engineering and specialized hardware from quantum annealers to classical Ising machines are being actively developed to address them. These systems typically sample from a fixed…
The Quantum Approximate Optimization Algorithm (QAOA) -- one of the leading algorithms for applications on intermediate-scale quantum processors -- is designed to provide approximate solutions to combinatorial optimization problems with…
The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also heavily used as a vehicle to study the…