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Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…

Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited…

Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…

We propose a novel hybrid quantum-classical approach to calculate Graver bases, which have the potential to solve a variety of hard linear and non-linear integer programs, as they form a test set (optimality certificate) with very appealing…

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS…

Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…

Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line…

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. For the weighted case,…

Given a collection of $m$ sets from a universe $\mathcal{U}$, the Maximum Set Coverage problem consists of finding $k$ sets whose union has largest cardinality. This problem is NP-Hard, but the solution can be approximated by a polynomial…

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in…

We present quantum simulation experiments of Ising-like spins on Platonic graphs, which are performed with two-dimensional arrays of Rydberg atoms and quantum-wire couplings. The quantum wires are used to couple otherwise uncoupled…

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…

This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…

Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…

Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum…

We develop a heuristic graph coloring approximation algorithm that uses the D-Wave 2X as an independent set sampler and evaluate its performance against a fully classical implementation. A randomly generated set of small but hard graph…

NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp's 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers…

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…

Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…

Quantum annealers offer an efficient way to compute high quality solutions of NP-hard problems when expressed in a QUBO (quadratic unconstrained binary optimization) or an Ising form. This is done by mapping a problem onto the physical…