Affiliation:
1. Swinburne University of Technology
Abstract
Non-universal topological quantum computation models, such as the
Majorana fermion-based Ising anyon model, have to be supplemented with
an additional non-topological noisy gate in order to achieve
universality. Here we endeavour to remedy this using an Einstein—Cartan
analog gravity picture of scalar fields. Specifically, we show that the
analog gravity picture enables unitary transformations to be realized in
two distinct ways: (i) via space-time holonomy and (ii) as gravitational
time dilation. The non-abelian geometric phases are enabled by
gravitational interactions, which are mediated by the spin-connection.
We analytically compute its matrix elements as a function of the scalar
field density distribution. This density can be regarded as the
gravitating distribution of matter in an analog universe. We show via
explicit calculations that there exists an infinite set of
asymptotically flat analog gravitational fields, each of which
implements a unique unitary transformation, that render the interactions
topological. We emphasise the generality of this result by asserting
that such gravitational gates could potentially be implemented in a
broad range of real systems modeled by scalar field with an acoustic
metric.
Funder
Australian Research Council
Subject
Statistical and Nonlinear Physics,Atomic and Molecular Physics, and Optics,Nuclear and High Energy Physics,Condensed Matter Physics
Cited by
1 articles.
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