Efficient Criteria of Quantumness for a Large System of Qubits

In order to model and evaluate large-scale quantum systems, e.g., quantum computer and quantum annealer, it is necessary to quantify the “quantumness” of such systems. In this paper, we discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems, which could be used to characterize their degree of quantumness. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution, i.e., the accessibility index. Applying it to the case of D-Wave One superconducting quantum annealing device, we find that its operation as described falls well within the quantum domain.

Optimal allocation of relevations in coherent systems

In this paper we study the allocation problem of relevations in coherent systems. The optimal allocation strategies are obtained by implementing stochastic comparisons of different policies according to the usual stochastic order and the hazard rate order. As special cases of relevations, the load-sharing and minimal repair policies are further investigated. Sufficient (and necessary) conditions are established for various stochastic orderings. Numerical examples are also presented as illustrations.

Further Results of the TTT Transform Ordering of Order n

To compare the variability of two random variables, we can use a partial order relation defined on a distribution class, which contains the anti-symmetry. Recently, Nair et al. studied the properties of total time on test (TTT) transforms of order n and examined their applications in reliability analysis. Based on the TTT transform functions of order n, they proposed a new stochastic order, the TTT transform ordering of order n (TTT-n), and discussed the implications of order TTT-n. The aim of the present study is to consider the closure and reversed closure of the TTT-n ordering. We examine some characterizations of the TTT-n ordering, and obtain the closure and reversed closure properties of this new stochastic order under several reliability operations. Preservation results of this order in several stochastic models are investigated. The closure and reversed closure properties of the TTT-n ordering for coherent systems with dependent and identically distributed components are also obtained.