SciPost Phys. Core 6, 005 (2023) ·
published 1 February 2023
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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.
Andrew J. Groszek, Matthew J. Davis, Tapio P. Simula
SciPost Phys. 8, 039 (2020) ·
published 12 March 2020
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We numerically model decaying quantum turbulence in two-dimensional
disk-shaped Bose-Einstein condensates, and investigate the effects of finite
temperature on the turbulent dynamics. We prepare initial states with a range
of condensate temperatures, and imprint equal numbers of vortices and
antivortices at randomly chosen positions throughout the fluid. The initial
states are then subjected to unitary time-evolution within the c-field
methodology. For the lowest condensate temperatures, the results of the zero
temperature Gross-Pitaevskii theory are reproduced, whereby vortex evaporative
heating leads to the formation of Onsager vortex clusters characterised by a
negative absolute vortex temperature. At higher condensate temperatures the
dissipative effects due to vortex-phonon interactions tend to drive the vortex
gas towards positive vortex temperatures dominated by the presence of vortex
dipoles. We associate these two behaviours with the system evolving toward an
anomalous non-thermal fixed point, or a Gaussian thermal fixed point,
respectively.
