Related papers: A Quantum Approximate Optimization Algorithm
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…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state…
The Quantum Approximate Optimization Algorithm (QAOA) is widely studied for combinatorial optimization and has achieved significant advances both in theoretical guarantees and practical performance, yet for general combinatorial…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this…
We study polynomial-time approximation algorithms for the Quantum Max-Cut (QMC) problem. Given an edge-weighted graph $G$ on n vertices, the QMC problem is to determine the largest eigenvalue of a particular $2^n \times 2^n$ matrix that…
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…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential…
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…
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…
One of the central goals of the DARPA Optimization with Noisy Intermediate-Scale Quantum (ONISQ) program is to implement a hybrid quantum/classical optimization algorithm with high $N\cdot p$, where $N$ is the number of qubits and $p$ is…
Quantum approximate optimization algorithm (QAOA) aims to solve discrete optimization problems by sampling bitstrings using a parameterized quantum circuit. The circuit parameters (angles) are optimized in the way that minimizes the cost…