Computing Minimum-Weight Perfect Matchings

Cook, William J.; Rohe, André

doi:10.1287/ijoc.11.2.138

Cited by 205 publications

(184 citation statements)

References 51 publications

(69 reference statements)

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“…Next, a matching of all the syndrome changes collected up to this point (an example is shown in Fig 5a) is used to guess where errors occurred. Since shorter error chains are more likely than longer ones, we use a minimum weight matching algorithm to do this [14]. Before the matching algorithm can find a minimum weight solution, we convert all the syndrome change results into a graph, with locations of the syndrome changes representing the nodes, and edges between these nodes having a weight which depends on the distance between them.…”

Section: Threshold Error Ratementioning

confidence: 99%

High-threshold universal quantum computation on the surface code

2009

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We present a comprehensive and self-contained simplified review of the quantum computing scheme of [1,2], which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction and low overhead, arbitrarily long-range logical gates. These features make it by far the best and most practical quantum computing scheme devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.

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Section: Threshold Error Ratementioning

confidence: 99%

High-threshold universal quantum computation on the surface code

2009

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“…Then, to study 2D samples with pfbc, we have used one implementation of the Blossom algorithm [32] which has allowed us to obtain the RS of larger systems sizes. Table III shows the corresponding parameters.…”

Section: Numerical Resultsmentioning

confidence: 99%

Backbone structure of the Edwards-Anderson spin-glass model

Romá

Risau-Gusmán

2013

Phys. Rev. E

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We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.

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“…Viewing individual players as vertices in a graph, with incident edges corresponding to the game-wise contributions of (4), the maximum-weight perfect matching problem involves ÿnding a subset of edges in the graph such that each vertex is met by only one edge (resulting in a "perfect matching"), and that the sum of the weights of the edges in the perfect matching is maximal. An e cient algorithm for determining the maximum-weight perfect matching was originally developed by Edmonds (1965), and improvements have more recently been worked out by Gabow and Tarjan (1991) and Cook and Rohe (1999) as well as others. An additional feature of the weighted perfect matching algorithms that makes it useful for optimal tournament pairing is that constraints on the inclusion of edges can be easily incorporated.…”

Section: Determination Of the Optimal Designmentioning

confidence: 99%

Adaptive paired comparison design

Glickman

Jensen

2005

Journal of Statistical Planning and Inference

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An important aspect of paired comparison experiments is the decision of how to form pairs in advance of collecting data. A weakness of typical paired comparison experimental designs is the di culty in incorporating prior information, which can be particularly relevant for the design of tournament schedules for players of games and sports. Pairing methods that make use of prior information are often ad hoc algorithms with little or no formal basis. The problem of pairing objects can be formalized as a Bayesian optimal design. Assuming a linear paired comparison model for outcomes, we develop a pairing method that maximizes the expected gain in Kullback-Leibler information from the prior to the posterior distribution. The optimal pairing is determined using a combinatorial optimization method commonly used in graph-theoretic contexts. We discuss the properties of our optimal pairing criterion, and demonstrate our method as an adaptive procedure for pairing objects multiple times. We compare the performance of our method on simulated data against random pairings, and against a system that is currently in use in tournament chess.

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Computing Minimum-Weight Perfect Matchings

Cited by 205 publications

References 51 publications

High-threshold universal quantum computation on the surface code

High-threshold universal quantum computation on the surface code

Backbone structure of the Edwards-Anderson spin-glass model

Adaptive paired comparison design

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