Mimicking the Hadamard discrete-time quantum walk with a time-independent Hamiltonian

Khatibi Moqadam, J ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1007/s11128-019-2262-1
  3. Publisher: Springer New York LLC , 2019
  4. Abstract:
  5. The discrete-time quantum walk dynamics can be generated by a time-dependent Hamiltonian, repeatedly switching between the coin and the shift generators. We change the model and consider the case where the Hamiltonian is time-independent, including both the coin and the shift terms in all times. The eigenvalues and the related Bloch vectors for the time-independent Hamiltonian are then compared with the corresponding quantities for the effective Hamiltonian generating the quantum walk dynamics. Restricted to the non-localized initial quantum walk states, we optimize the parameters in the time-independent Hamiltonian such that it generates a dynamics similar to the Hadamard quantum walk. We find that the dynamics of the walker probability distribution and the corresponding standard deviation, the coin-walker entanglement, and the quantum-to-classical transition of the discrete-time quantum walk model can be approximately generated by the optimized time-independent Hamiltonian. We, further, show both dynamics are equivalent in the classical regime, as expected
  6. Keywords:
  7. Quantum control ; Quantum simulation ; Quantum walk ; Dynamics ; Eigenvalues and eigenfunctions ; Electron energy levels ; Hamiltonians ; Probability distributions ; Quantum chemistry ; Effective Hamiltonian ; Quantum simulations ; Quantum to classical transition ; Standard deviation ; Time-dependent Hamiltonians ; Time-independent Hamiltonian ; Quantum entanglement
  8. Source: Quantum Information Processing ; Volume 18, Issue 5 , 2019 ; 15700755 (ISSN)
  9. URL: https://www.springerprofessional.de/en/mimicking-the-hadamard-discrete-time-quantum-walk-with-a-time-in/16583196