Topological quantum compilation of two-qubit gates

We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-NOT (CNOT) gate up to single-qubit operations. These gates belong to the local eq...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Burke, Phillip C, Aravanis, Christos, Aspman, Johannes, Mareček, Jakub, Vala, Jiří
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.08.2024
Subjects
Braiding
Equivalence
Fibonacci numbers
Gates
Qubits (quantum computing)
Topology
Online AccessGet full text

Cover

More Information
Summary:We investigate the topological quantum compilation of two-qubit operations within a system of Fibonacci anyons. Our primary goal is to generate gates that are approximately leakage-free and equivalent to the controlled-NOT (CNOT) gate up to single-qubit operations. These gates belong to the local equivalence class [CNOT]. Additionally, we explore which local equivalence classes of two-qubit operations can be naturally generated by braiding Fibonacci anyons. We discovered that most of the generated classes are located near the edges of the Weyl chamber representation of two-qubit gates, specifically between the local equivalence classes of the identity [1] and [CNOT], and between those of the double-controlled-NOT [DCNOT] and [SWAP]. Furthermore, we found a numerically exact implementation of a local equivalent of the SWAP gate using a sequence of only nine elements from the Fibonacci braiding gate set.
ISSN:2331-8422