Quantum Simulation of Continuous-Time Random Walks
Jiangfeng Du, Hui Li, Xiaodong Xu, Jihui Wu, Xianyi Zhou, Rongdian Han · arXiv (Cornell University) · 2002
We investigate the quantization of continuous-time random walks (CTRW) on a circle. It is demonstrated that, for quantum CTRW on a circle with four nodes, the probability distribution can be exactly uniform at certain finite time, while in classical CTRW the uniform distribution can only be approximated at infinite-time limit. The procedure of this quantum CTRW is periodic and reversible, which is in sharp contrast to the dissipativeness of classical CTRW. Furthermore, this quantum CTRW is successfully simulated in a two-qubit system on our NMR quantum computer. We find that the quantum probability distribution is closely tied with the entanglement between the two qubits. The uniform distribution can be obtained only when the two qubits are maximally entangled.