Related papers: Quadratic Quantum Speedup for Finding Independent …
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally…
We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary…
We investigate a hybrid quantum-classical algorithm for solving the Maximum Independent Set (MIS) problem on regular graphs, combining the Quantum Approximate Optimization Algorithm (QAOA) with a minimal degree classical greedy algorithm.…
Establishing quantum speedup for computationally hard problems of practical relevance, particularly combinatorial optimization problems, remains a central challenge in quantum computation. In this work, we identify a structurally defined…
With qubits encoded into atomic ground and Rydberg states and situated on the vertexes of a graph, the conditional quantum dynamics of Rydberg blockade, which inhibits simultaneous excitation of nearby atoms, has been employed recently to…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…
Quantum-classical hybrid algorithms offer a promising strategy for tackling computationally challenging problems, such as the maximum independent set (MIS) problem that plays a crucial role in areas like network design and data analysis.…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum…
Rydberg atom arrays are among the leading contenders for the demonstration of quantum speedups. Motivated by recent experiments with up to 289 qubits [Ebadi et al., Science 376, 1209 (2022)] we study the maximum independent set problem on…
Rydberg atom arrays operated by a quantum adiabatic principle are among the most promising quantum simulating platforms due to their scalability and long coherence time. From the perspective of combinatorial optimization, they offer an…
Finding the maximum independent set (MIS) of a large-size graph is a nondeterministic polynomial-time (NP)-complete problem not efficiently solvable with classical computations. Here, we present a set of quantum adiabatic computing data of…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
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…
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
We consider the maximum cut and maximum independent set problems on random regular graphs in the infinite-size limit, and calculate the energy densities achieved by QAOA for high degrees up to $d=100$. Such an analysis is possible because…