The expressive power of quantum walks in terms of language acceptance

Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language acceptance, and present two ways in which discrete time quantum walks can accept some languages with certainty. These walks can take quantum as well as classical inputs, and we show that when the input is quantum, the walks can also be interpreted as performing the task of quantum state discrimination.

[1]  Anthony Chefles.  Quantum state discrimination , 2000 .

[2]  Viv Kendon,et al.  Quantum walks on general graphs , 2003, quant-ph/0306140.

[3]  Neil B. Lovett,et al.  Universal quantum computation using the discrete-time quantum walk , 2009, 0910.1024.

[4]  Aharonov,et al.  Quantum random walks. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[5]  I. Chuang,et al.  Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance , 2001, Nature.

[6]  Andrew M. Childs,et al.  Universal computation by quantum walk. , 2008, Physical review letters.

[7]  Christino Tamon,et al.  Perfect State Transfer in Quantum Walks on Graphs , 2011 .

[8]  Andris Ambainis,et al.  Quantum walks on graphs , 2000, STOC '01.

[9]  Vivien M. Kendon,et al.  Simulation methods for quantum walks on graphs applied to formal language recognition , 2014, Natural Computing.

[10]  Andrew M. Childs,et al.  Universal Computation by Multiparticle Quantum Walk , 2012, Science.

[11]  Andris Ambainis,et al.  Algebraic Results on Quantum Automata , 2005, Theory of Computing Systems.

[12]  Andris Ambainis,et al.  One-dimensional quantum walks , 2001, STOC '01.

[13]  Matthias Christandl,et al.  Perfect Transfer of Arbitrary States in Quantum Spin Networks , 2005 .

[14]  Paweł Kurzyński,et al.  Quantum walk as a generalized measuring device. , 2012, Physical review letters.

[15]  S. Bose.  Quantum communication through an unmodulated spin chain. , 2002, Physical review letters.