LIMIT DISTRIBUTIONS FOR DIFFERENT FORMS OF FOUR-STATE QUANTUM WALKS ON A TWO-DIMENSIONAL LATTICE

作者：Machida Takuya^*; Chandrashekar C M; Konno Norio; Busch Thomas

来源：Quantum Information & Computation, 2015, 15(13-14): 1248-1258.

• discrete-time quantum walk
• 2-dimensional lattice
• limit distribution

Long-time limit distributions are key quantities for understanding the asymptotic dynamics of quantum walks, and they are known for most forms of one-dimensional quantum walks using two-state coin systems. For two-dimensional quantum walks using a four-state coin system, however, the only known limit distribution is for a walk using a parameterized Grover coin operation and analytical complexities have been a major obstacle for obtaining long-time limit distributions for other coins. In this work however, we present two new types of long-time limit distributions for walks using different forms of coin-flip operations in a four-state coin system. This opens the road towards understanding the dynamics and asymptotic behaviour for higher state coin system from a mathematical view point.

• 出版日期2015-10