Related papers: Constant Factor Analysis of Optimal Quantum Linear…
This paper investigates the performance of quantum, classical, and hybrid solvers on the NP-hard Max-Cut and QUBO problems, examining their solution quality relative to the global optima and their computational efficiency. We benchmark the…
The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for demonstrating quantum advantage on near-term devices, yet the physical origins of its efficacy remain poorly understood. In this work, we study QAOA for random…
We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will…
Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this work, we introduce a new benchmark for variational quantum algorithm (VQA), recently proposed as…
We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
The quantum adiabatic unstructured search algorithm is one of only a handful of quantum adiabatic optimization algorithms to exhibit provable speedups over their classical counterparts. With no fault tolerance theorems to guarantee the…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…
This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…
This paper describes how to make the problem of binary classification amenable to quantum computing. A formulation is employed in which the binary classifier is constructed as a thresholded linear superposition of a set of weak classifiers.…
Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different…
In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs.…
Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…