scholarly journals Perfect sampling with unitary tensor networks

2012 ◽  
Vol 85 (16) ◽  
Author(s):  
Andrew J. Ferris ◽  
Guifre Vidal
Keyword(s):  
Perfect Sampling ◽  
Tensor Networks ◽  
Unitary Tensor

Anyon Networks from Geometric Models of Matter

2021 ◽  
Author(s):  
Michael Atiyah ◽  
Matilde Marcolli
Keyword(s):  
Normal Bundle ◽  
Present Form ◽  
Joint Work ◽  
Geometric Models ◽  
Tensor Networks

Abstract This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.

Variational quantum tensor networks classifiers

2021 ◽  
Author(s):  
Rui Huang ◽  
Xiaoqing Tan ◽  
Qingshan Xu
Keyword(s):  
Tensor Networks

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

Platonic entanglement

2021 ◽  
Vol 21 (13&14) ◽  
pp. 1081-1090
Author(s):  
Jose I. Latorre ◽  
German Sierra
Keyword(s):  
Prime Number ◽  
Quantum State ◽  
Entangled States ◽  
Platonic Solid ◽  
Platonic Solids ◽  
Reed Solomon Codes ◽  
Tensor Networks

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.

scholarly journals Ryu-Takayanagi formula for symmetric random tensor networks

2018 ◽  
Vol 97 (12) ◽  
Author(s):  
Goffredo Chirco ◽  
Daniele Oriti ◽  
Mingyi Zhang
Keyword(s):  
Tensor Networks ◽  
Random Tensor
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