TY - JOUR

T1 - Quantum walks on embedded hypercubes

AU - Makmal, Adi

AU - Zhu, Manran

AU - Manzano, Daniel

AU - Tiersch, Markus

AU - Briegel, Hans J.

PY - 2014/8/14

Y1 - 2014/8/14

N2 - It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the expected hitting time. Yet, to what extent this striking result survives in more general graphs is to date an open question. Here, we tackle this question by studying the expected hitting time for quantum walks on HCs that are embedded into larger symmetric structures. By performing numerical simulations of the discrete quantum walk and deriving a general expression for the classical hitting time, we observe an exponentially increasing gap between the expected classical and quantum hitting times, not only for walks on the bare HC, but also for a large family of embedded HCs. This suggests that the quantum speedup is stable with respect to such embeddings.

AB - It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the expected hitting time. Yet, to what extent this striking result survives in more general graphs is to date an open question. Here, we tackle this question by studying the expected hitting time for quantum walks on HCs that are embedded into larger symmetric structures. By performing numerical simulations of the discrete quantum walk and deriving a general expression for the classical hitting time, we observe an exponentially increasing gap between the expected classical and quantum hitting times, not only for walks on the bare HC, but also for a large family of embedded HCs. This suggests that the quantum speedup is stable with respect to such embeddings.

UR - http://www.scopus.com/inward/record.url?scp=84936978070&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.90.022314

DO - 10.1103/PhysRevA.90.022314

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AN - SCOPUS:84936978070

SN - 1050-2947

VL - 90

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 2

M1 - 022314

ER -