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We propose a platform for braiding Majorana non-Abelian anyons basedon a heterostructure between a d d -wavehigh- T_c T c superconductor and a quantum spin-Hall insulator. It has been recentlyshown that such a setup for a quantum spin-Hall insulator leads to apair of Majorana zero modes at each corner of the sample, and thus canbe regarded as a higher-order topological superconductor. We show thatupon applying a Zeeman field in the region, these Majorana modes splitin space and can be manipulated for braiding processes by tuning thefield and pairing phase. We show that such a setup can achieve fullbraiding, exchanging, and arbitrary phase gates (including the \pi/8 π / 8 magic gates) of the Majorana zero modes, all of which are robust andprotected by symmetries. As many of the ingredients of our proposedplatform have been realized in recent experiments, our results provide anew route toward universal topological quantum computation.
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This content will become publicly available on December 1, 2026
Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
Abstract The remarkable complexity of a topologically ordered many-body quantum system is encoded in the characteristics of its anyons. Quintessential predictions emanating from this complexity employ the Fibonacci string net condensate (Fib SNC) and its anyons: sampling Fib-SNC would estimate chromatic polynomials while exchanging its anyons would implement universal quantum computation. However, physical realizations remained elusive. We introduce a scalable dynamical string net preparation (DSNP) that constructs Fib SNC and its anyons on reconfigurable graphs suitable for near-term superconducting processors. Coupling the DSNP approach with composite error-mitigation on deep circuits, we create, measure, and braids Fibonacci anyons; charge measurements show 94% accuracy, and exchanging the anyons yields the expected golden ratioϕwith 98% average accuracy. We then sample the Fib SNC to estimate chromatic polynomial atϕ + 2 for several graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and aim at a classically hard problem.
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- Award ID(s):
- 2118310
- PAR ID:
- 10615340
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 16
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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