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Periodicity and absolute zeta functions of multi-state Grover walks on cycles [0.0]
Quantum walks are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions of Grover walks on cycle graphs.
arXiv Detail & Related papers (2025-01-16T12:50:01Z)
Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
arXiv Detail & Related papers (2024-08-19T09:15:54Z)
Absolute zeta functions and periodicity of quantum walks on cycles [0.0]
The study presents a connection between quantum walks and absolute zeta functions. The Hadamard walks and $3$-state Grover walks are typical models of the quantum walks. It is shown that our zeta functions of quantum walks are absolute automorphic forms.
arXiv Detail & Related papers (2024-05-09T06:30:00Z)
Look into the Mirror: Evolving Self-Dual Bent Boolean Functions [35.305121158674964]
This paper experiments with evolutionary algorithms with the goal of evolving (anti-)self-dual bent Boolean functions. We successfully construct self-dual bent functions for each dimension. We also tried evolving secondary constructions for self-dual bent functions, but this direction provided no successful results.
arXiv Detail & Related papers (2023-11-20T16:20:16Z)
On the relation between quantum walks and absolute zeta functions [0.0]
We deal with a zeta function determined by a time evolution matrix of the Grover walk on a graph. We prove that the zeta function given by the quantum walk is an absolute automorphic form of weight depending on the number of edges of the graph. We consider an absolute zeta function for the zeta function based on a quantum walk.
arXiv Detail & Related papers (2023-06-26T11:58:07Z)
Special functions in quantum phase estimation [61.12008553173672]
We focus on two special functions. One is prolate spheroidal wave function, which approximately gives the maximum probability that the difference between the true parameter and the estimate is smaller than a certain threshold. The other is Mathieu function, which exactly gives the optimum estimation under the energy constraint.
arXiv Detail & Related papers (2023-02-14T08:33:24Z)
A Complete Equational Theory for Quantum Circuits [58.720142291102135]
We introduce the first complete equational theory for quantum circuits. Two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations.
arXiv Detail & Related papers (2022-06-21T17:56:31Z)
Walk/Zeta Correspondence for quantum and correlated random walks [0.0]
We compute the zeta function for the three- and four-state quantum walk and correlated random walk. We also deal with the four-state quantum walk and correlated random walk on the two-dimensional torus.
arXiv Detail & Related papers (2021-09-16T01:49:23Z)
Walk/Zeta Correspondence [0.0]
This paper extends these walks to a class of walks including random walks, correlated random walks, quantum walks, and open quantum random walks on the torus by the Fourier analysis.
arXiv Detail & Related papers (2021-04-21T00:17:54Z)
Riemann zeros from a periodically-driven trapped ion [36.992645836923394]
Non-trivial zeros of the Riemann zeta function are central objects in number theory. We present an experimental observation of the lowest non-trivial zeros by using a trapped ion qubit in a Paul trap. The waveform of the driving is engineered such that the dynamics of the ion is frozen when the driving parameters coincide with a zero of the real component of the zeta function.
arXiv Detail & Related papers (2021-02-13T14:33:10Z)
Random Walks: A Review of Algorithms and Applications [37.226218097358284]
In computer science, classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding.
arXiv Detail & Related papers (2020-08-09T03:41:56Z)

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