Date:

Wednesday, May 9, 2018 - 4:00pm

Series:

Condensed Matter Physics Seminar

We will discuss the computational role of coherent multiqubit tunneling that gives rise to bands of delocalized quantum states providing a coherent pathway for population transfer (PT) between computational states with similar energies. We study PT resulting from quantum evolution under a constant transverse field B of an n-spin system that encodes a classical energy landscape. We focus on several random spin modes without a structure, including random energy model. In the absence of any fine-tuning of the transfer field B >1, we find that scaling of a typical runtime for PT with n and the number of “solution” states is the same as that in multi-target Grover's algorithm, except for a factor of Exp(n a), where a=1/(4B^2) can be made small for B>>1. Unlike a Hamiltonian in analog Grover search, the models we consider are non integrable, and the transverse field delocalizes the initial state. As a result, our PT protocol is not sensitive to the value of B, and may be initialized with a computational basis state. We will describe microscopic theory of PT by applying cavity method to an effective tunneling Hamiltonian H acting in the space of computational states within a narrow energy belt that belongs to the class of preferred basis Levy matrices. In a certain range of energies and transverse fields, the eigenspectrum of H forms minibands of nonergodic delocalized states, because the steep decay of the off-diagonal matrix elements of H with the Hamming distance is compensated by a dramatic increase in the number of neighbors. We calculate the fractal dimension of the eigenstates as a function of energy and transverse field. We discuss how our approach can be applied to study PT protocol in other transverse field spin glass models, with the potential quantum advantage over classical algorithms.

Location:

PAB 4-330

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