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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…
Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose…
Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to…
Single atoms in dipole microtraps or optical tweezers have recently become a promising platform for quantum computing and simulation. Here we report a detailed theoretical analysis of the physics underlying an implementation of a Rydberg…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
New computational strategies, such as molecular docking, are emerging to speed up the drug discovery process. This method predicts the activity of molecules at the binding site of proteins, helping to select the ones that exhibit desirable…
Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.…
The maximum independent set (MIS) problem of graph theory using the quantum alternating operator ansatz is studied. We perform simulations on the Rigetti Forest simulator for the square ring, $K_{2,3}$, and $K_{3,3}$ graphs and analyze the…
With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable…
Quantum annealing is a heuristic algorithm for solving combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware for implementing this algorithm. The current version of the D-Wave quantum annealer can solve…
Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more…
We perform exact diagonalization and time evolution of the Lechner-Hauke-Zoller (LHZ) annealing architecture [Science Advances 1(9), e1500838 (2015)] for ten physical qubits. Thereby, on a training set consisting of $2400$ problem…
Many-body entangled states are key elements in quantum information science and quantum metrology. One important problem in establishing a high degree of many-body entanglement using optical techniques is the leakage of the system…
Quantum annealing and quantum approximate optimization algorithms hold a great potential to speed-up optimization problems. This could be game-changing for a plethora of applications. Yet, in order to hope to beat classical solvers, quantum…
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…
Among the limitations of current quantum machines, the qubits count represents one of the most critical challenges for porting reasonably large computational problems, such as those coming from real-world applications, to the scale of the…
Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that play an important role in networking, computational biology, and biochemistry. We show an explicit construction…
We present a general error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. Given any Ising model optimization problem, the encoding replaces each…