Skippy algorithm disk graph12/31/2023 Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum-weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including maximum-weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry. Programmable quantum systems offer unique possibilities to test the performance of various quantum optimization algorithms. Some of the main practical limitations in this context are often set by specific hardware restrictions. In particular, the native connectivity of the qubits for a given platform typically restricts the class of problems that can addressed. For instance, Rydberg atom arrays naturally allow encoding maximum independent set problems, but native encodings are restricted to so-called unit disk graphs. In this work we significantly expand the class of problems that can be addressed with Rydberg atom arrays, overcoming the limitations to geometric graphs. We develop a specific encoding scheme to map a variety of problems into arrangements of Rydberg atoms, including maximum weighted independent sets on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Our work thus provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems, using technology already available in experiments. MWIS representation of some example constraints. Recall that for unit disk graphs, we can branch to reduce the maximum clique size, and hence also the ply. Each bit is represented by a corresponding vertex in the MWIS problem graph. The weight of the vertices is indicated by its interior color on a gray scale. For each example, the degenerate MWIS configurations are shown by identifying vertices in a MWIS with a red boundary. We prove that the TDS problem is NP-hard in unit disk graphs. For example, the Skippy 2 algorithm (a fast algorithm to measure the number of surfaces, cylinder switch times, and head switch times) no longer works on modern drives because the algorithm assumes one particular ordering of tracks onto multiple platters that is no longer used on modern disks (that several head switches occur before a seek to. Here we consider the TDS problem in unit disk graphs, where the objective is to find a minimum cardinality total dominating set for an input graph. The MWISs correspond to the satisfying assignments to the corresponding constraint-satisfaction problem. We call as a total dominating set (TDS) of if each vertex has a dominator in other than itself. The algorithm is given in Section 2.1 and the analysis of the approximation ratio is given in. Here, we are given a disk graph with a set D of n disks in the Euclidean plane, and we are interested in computing a minimum cardinality dominating set of the disk graph. We give algorithms with running time \(2^\).(b) MWIS representation of n 1 n 2 = 0, with the third, unlabeled vertex being an ancillary vertex. In this section, we give our PTAS for minimum dominating set for disk graphs.
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