“Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape” Vadim Smelyanskiy (Quantum AI Laboratory, Google)

Wednesday, May 9, 2018 - 4:00pm
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.

PAB 4-330