TY - JOUR
T1 - Efficient quantum circuit implementation of quantum walks
AU - Douglas, Brendan
AU - Wang, Jingbo
PY - 2009
Y1 - 2009
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.
U2 - 10.1103/PhysRevA.79.052335
DO - 10.1103/PhysRevA.79.052335
M3 - Article
VL - 79
SP - Article number 052335, 5pp
JO - Physical Review A (Atomic, Molecular and Optical Physics)
JF - Physical Review A (Atomic, Molecular and Optical Physics)
SN - 1050-2947
IS - 5
ER -