TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.1.005
TI  - Topological quantum computation using analog gravitational holonomy and time dilation
PY  - 2023/02/01
UR  - https://scipost.org/SciPostPhysCore.6.1.005
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 1
SP  - 005
A1  - Génetay Johansen, Emil
AU  - Simula, Tapio
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.1.005,
	title={{Topological quantum computation using analog gravitational holonomy and time dilation}},
	author={Emil Génetay Johansen and Tapio Simula},
	journal={SciPost Phys. Core},
	volume={6},
	pages={005},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.1.005},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.1.005},
}