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- Title
On the quantum entanglement of random walks and queueing systems.
- Authors
Squillante, Mark S.
- Abstract
There is a long history of research on such classical computational methods for obtaining HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold">R</mi></math> ht as well as a related matrix HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold">G</mi></math> ht , the minimal nonnegative solution of the nonlinear matrix equation HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="bold">G</mi><mo>=</mo><msub><mi mathvariant="bold">A</mi><mn>0</mn></msub><msup><mrow><mi mathvariant="bold">G</mi></mrow><mn>2</mn></msup><mo>+</mo><msub><mi mathvariant="bold">A</mi><mn>1</mn></msub><mi mathvariant="bold">G</mi><mo>+</mo><msub><mi mathvariant="bold">A</mi><mn>2</mn></msub></mrow></math> ht . Recently, various algorithms for estimating the stationary distribution HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="bold-italic"> </mi></mrow></math> ht of a RW on quantum computers have been proposed and extensively studied. In short, the quantum walk (QW) is defined on a composite Hilbert space HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi mathvariant="script">H</mi><mi>p</mi></msub><mo> </mo><msub><mi mathvariant="script">H</mi><mi>c</mi></msub></mrow></math> ht in terms of a discrete position space HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="script">H</mi><mi>p</mi></msub></math> ht and a coin flip space HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="script">H</mi><mi>c</mi></msub></math> ht representing transition actions.
- Subjects
QUANTUM entanglement; RANDOM walks; MATHEMATICAL forms; MATHEMATICAL analysis; DISTRIBUTION (Probability theory); STOCHASTIC analysis; COMPUTATIONAL complexity
- Publication
Queueing Systems, 2022, Vol 100, Issue 3/4, p253
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-022-09843-x