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Topological quantum computation using analog gravitational holonomy and time dilation
by Emil Genetay Johansen, Tapio Simula
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Emil Génetay Johansen |
| Submission information | |
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| Preprint Link: | scipost_202206_00002v1 (pdf) |
| Date submitted: | June 3, 2022, 3:29 a.m. |
| Submitted by: | Emil Génetay Johansen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2022-8-1 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202206_00002v1, delivered 2022-08-01, doi: 10.21468/SciPost.Report.5471
Strengths
Weaknesses
Report
Requested changes
I would like to invite the authors to address and clarify a number of points.
1. It would be helpful to this reader to give a bit more detail on how the quasiparticles (arising as spinors in a BdG formalism) transform under gravitational transformations, backing up expressions such as eq. (21), (22).
2. The ``pertinent remarks” on the Unruh effect (end of section 4) seem unrelated to the gravitational holonomy gates. Is there a connection, or a physical effect that’s relevant in this context?
3. In section 4.2, it is unclear to this reader in what sense the mechanism for the Pauli-iX boost is topological, as the effect seems to depend on a time $\Delta t$ which is not a discrete quantity.
4. I find it confusing that section 5 uses the term ``universality” in the sense of being dense on the 1-qubit Bloch sphere, leaving aside the 2-qubit gates.
5. In section 6 it is suggested that gravitational holonomy gates supplement a quantum computational scheme based on MZM or quantum doubles. Can this be made more concrete – for example could the analog gravity scenario be realized in a $p_x+ip_y$ superfluid that supports MZM?
6. In section 6 it is suggested that a gravity-only platform for TQC can be developed, for example by employing the kelvon quasi-particles. It is unclear to me how 2-qubit gates can be realized in such a scenario?
Author: Emil Génetay Johansen on 2022-09-22 [id 2842]
(in reply to Report 1 on 2022-08-01)Dear referee,
Please see the file attached containing our detailed response to the report.
Best regards,
Emil Génetay Johansen and Tapio Simula
Attachment:
Response_letter.pdf