![]() Description Ī skip graph is a distributed data structure based on skip lists designed to resemble a balanced search tree. ![]() In addition, constructing, inserting, searching, and repairing a skip graph that was disturbed by failing nodes can be done by straightforward algorithms. In contrast to skip lists and other tree data structures, they are very resilient and can tolerate a large fraction of node failures. As they provide the ability to query by key ordering, they improve over search tools based on the hash table functionality only. Skip graphs are mostly used in searching peer-to-peer networks. Skip graphs have the full functionality of a balanced tree in a distributed system. They were invented in 2003 by James Aspnes and Gauri Shah.Ī nearly identical data structure called SkipNet was independently invented by Nicholas Harvey, Michael Jones, Stefan Saroiu, Marvin Theimer and Alec Wolman, also in 2003. Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms with hundreds of qubits.Skip graphs are a kind of distributed data structure based on skip lists. 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. 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. The MWISs correspond to the satisfying assignments to the corresponding constraint-satisfaction problem. (b) MWIS representation of n 1 n 2 = 0, with the third, unlabeled vertex being an ancillary vertex.
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