For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus, propagates at a rate which is linear in time, as compared to the square root rate for a classical random walk. Indeed, it has been suggested that there are graphs that can be traversed by a quantum walker exponentially faster than by the classical random analogue. In this note we adopt the approach of exploring the conditions to impose on a Markov process in order to emulate its quantum counterpart: the central issue that emerges is the problem of taking into account, in the numerical generation of each sample path, the causative effect of the ensemble of trajectories to which it belongs. How to deal numerically with this problem is shown in a paradigmatic example.
Quantum walks : a Markovian perspective / D. de Falco, D. Tamascelli - In: SOFSEM 2008 : Theory and Practice of Computer Science, Nový Smokovec, Slovakia, January 19 - 25, 2008 : proceedings / [a cura di] V. Geffert, J. Karhumäki, A. Bertoni, B. Preenel, P. Návrat, M. Bieliková. - Berlino : Springer, 2008. - ISBN 3-540-77565-X. - pp. 519-530 (( Intervento presentato al 34. convegno SOFSEM 2008 : Theory and Practice of Computer Science tenutosi a Nový Smokovec, Slovakia nel 2008.
Quantum walks : a Markovian perspective
D. de FalcoPrimo
;D. TamascelliUltimo
2008
Abstract
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus, propagates at a rate which is linear in time, as compared to the square root rate for a classical random walk. Indeed, it has been suggested that there are graphs that can be traversed by a quantum walker exponentially faster than by the classical random analogue. In this note we adopt the approach of exploring the conditions to impose on a Markov process in order to emulate its quantum counterpart: the central issue that emerges is the problem of taking into account, in the numerical generation of each sample path, the causative effect of the ensemble of trajectories to which it belongs. How to deal numerically with this problem is shown in a paradigmatic example.File | Dimensione | Formato | |
---|---|---|---|
sofsem08.pdf
accesso aperto
Tipologia:
Post-print, accepted manuscript ecc. (versione accettata dall'editore)
Dimensione
1.46 MB
Formato
Adobe PDF
|
1.46 MB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.