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Paper 1
On the Necessity of Entanglement for the Explanation of Quantum Speedup
Michael E. Cuffaro
- Year
- 2011
- Journal
- arXiv preprint
- DOI
- arXiv:1112.1347
- arXiv
- 1112.1347
In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play.
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A Quantum-Classical Liouville Formalism in a Preconditioned Basis and Its Connection with Phase-Space Surface Hopping
Yanze Wu, Joseph Subotnik
- Year
- 2022
- Journal
- arXiv preprint
- DOI
- arXiv:2209.03912
- arXiv
- 2209.03912
We revisit a recent proposal to model nonadiabatic problems with a complex-valued Hamiltonian through a phase-space surface hopping (PSSH) algorithm employing a pseudo-diabatic basis. Here, we show that such a pseudo-diabatic PSSH (PD-PSSH) ansatz is consistent with a quantum-classical Liouville equation (QCLE) that can be derived following a preconditioning process, and we demonstrate that a proper PD-PSSH algorithm is able to capture some geometric magnetic effects (whereas the standard FSSH approach cannot). We also find that a preconditioned QCLE can outperform the standard QCLE in certain cases, highlighting the fact that there is no unique QCLE. Lastly, we also point out that one can construct a mean-field Ehrenfest algorithm using a phase-space representation similar to what is done for PSSH. These findings would appear extremely helpful as far understanding and simulating nonadiabatic dynamics with complex-valued Hamiltonians and/or spin degeneracy.
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