TY - JOUR

T1 - Efficient quantum circuit implementation of quantum walks

AU - Douglas, B. L.

AU - Wang, J. B.

N1 - Erratum can be found in Physical Review A - Atomic, Molecular, and Optical Physics, Volume 80(5), 059901, http://dx.doi.org/10.1103/PhysRevA.80.059901

PY - 2009/5/1

Y1 - 2009/5/1

N2 - Quantum walks, being the quantum analog of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the "glued trees" algorithm, which provides an exponential speedup over classical methods, relative to a particular quantum oracle. Here, we discuss the possibility of a quantum walk algorithm yielding such an exponential speedup over possible classical algorithms, without the use of an oracle. We provide examples of some highly symmetric graphs on which efficient quantum circuits implementing quantum walks can be constructed and discuss potential applications to quantum search for marked vertices along these graphs.

AB - Quantum walks, being the quantum analog of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the "glued trees" algorithm, which provides an exponential speedup over classical methods, relative to a particular quantum oracle. Here, we discuss the possibility of a quantum walk algorithm yielding such an exponential speedup over possible classical algorithms, without the use of an oracle. We provide examples of some highly symmetric graphs on which efficient quantum circuits implementing quantum walks can be constructed and discuss potential applications to quantum search for marked vertices along these graphs.

UR - http://www.scopus.com/inward/record.url?scp=66349135590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/record.url?scp=84921001504&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.79.052335

DO - 10.1103/PhysRevA.79.052335

M3 - Article

VL - 79

SP - 1

EP - 5

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

SN - 2469-9926

IS - 5

M1 - 052335

ER -