What is Quantum Random Walk?
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چکیده
• Classical: random walk in one dimension describes a particle that moves in the positive or negative direction according to the random outcome of some unbiased binary variable (e.g., a fair coin). • Quantum: The particle with two degree of freedom (for example spin) can move left or right according to its spin and one unitary operator can play coin roles (for example Hadamard operator).In quantum random walk (QRW) we have 2 operator, coin operator (C) and translation operator (S).C act on Hilbert space of particle’s spin (coin space) HC and S act on Hilbert space of particle’s position HP. C makes superposition of particle’s spin and S moves particle left or right according to particle’s spin. The QRW of n step defined as the transformation Un, where U, acting on H= HC ⊗ HP . ( ) I C S U ⊗ = . ,
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