|Title||Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware|
|Publication Type||Journal Article|
|Year of Publication||2021|
|Authors||S. Singh, H. C. Alderete, R. Balu, C. Monroe, N. M. Linke, and C.. M. Chandrashekar|
|Journal||Phys. Rev. A|
|Date Published||DEC 1|
|Type of Article||Article|
Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.