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جستجو

Quantum Walks on Finite Graphs and Bounded Infinite Graphs

Mohammadesmail Nikfar¹

Abstract :
Consider a weighted graph (G) whose vertex set is countable. We call (G) bounded when there exists a uniform constant that bounds, for every vertex, the sum of the absolute values of the weights of all edges incident with that vertex. In this work, we establish a basic theorem concerning equitable partitions of bounded weighted graphs containing twin subgraphs. This result provides a framework for constructing both finite graphs and bounded infinite graphs that exhibit pair state transfer and plus state transfer, with the adjacency matrix serving as the Hamiltonian governing the associated continuous-time quantum walk. For every integer (kgeq 3), we demonstrate that there exist infinitely many connected, unweighted graphs whose maximum degree is (k) and which possess pair state transfer at specified times. We also construct infinitely many signed graphs containing precisely one negatively weighted edge, while their corresponding underlying unweighted graphs have maximum degree (k); these graphs exhibit plus state transfer at the same designated times. Related constructions are obtained for perfect state transfer occurring between a plus state and a pair state. We additionally establish families of graphs that contain sedentary pair states and sedentary plus states. Our results extend to broad classes of planar graphs. In particular, we prove that, in the asymptotic sense, almost every connected finite unweighted planar graph possesses pair state transfer at the relevant transfer times. Moreover, for almost every connected finite unweighted planar graph, it is possible to assign a negative weight to exactly one edge so that the resulting signed graph admits plus state transfer. The same single-edge modification can also produce perfect state transfer between a plus state and a pair state. These phenomena occur at the same specified transfer times. Corresponding statements are established for finite unweighted trees. We further develop several construction techniques—including graph blow-ups, Cayley graphs, and graphs obtained by attaching tails—to generate new infinite families of both finite and infinite unweighted graphs, as well as signed graphs, exhibiting pair state transfer or plus state transfer. Overall, the paper develops structural methods for producing quantum-walk systems with prescribed state-transfer behavior across finite and bounded infinite graph families. The results connect equitable graph partitions, signed graph structures, graph transformations, and quantum state-transfer phenomena within a unified framework.

Keywords : continuous time quantum walks equitable partitions signed graphs infinite graphs perfect state transfer pair states

زبان مقاله : انگلیسی
محور مقاله : مدیریت
محل انتشار : پنجمین کنفرانس بین المللی پژوهش در حسابداری، مدیریت، اقتصاد و علوم انسانی
آدرس وب سایت کنفرانس : meaconf.com
کد IOI مقاله : ACEE-ACZHZE
لینک مستقیم مقاله : https://isnac.ir/ACEE-ACZHZE
نمایش چکیده فارسی : https://isnac.ir/SA/ACEE-ACZHZE

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جستجو

Quantum Walks on Finite Graphs and Bounded Infinite Graphs

Mohammadesmail Nikfar¹

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جستجو

Quantum Walks on Finite Graphs and Bounded Infinite Graphs

Mohammadesmail Nikfar1

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سایر مقالات محل انتشار

Mohammadesmail Nikfar¹