This paper proposes a novel architecture for adaptive quantum circuits leveraging the protective effects of topological defects in superconducting quantum circuits. The core concept involves constructing superconducting circuits incorporating multiple topological defects, wherein the circuit's quantum states can be dynamically reconfigured upon encountering noise, preserving quantum computation accuracy. This approach addresses the critical challenge of noise resilience in quantum computing by exploiting the inherent robustness of topological protection. The design emphasizes adaptability, allowing the circuit to self-correct and maintain fidelity under fluctuating environmental conditions. Mathematical formulations describe the circuit dynamics and the topological protection mechanism. The proposed architecture offers a promising pathway toward robust and scalable quantum computation. ---This paper proposes a novel architecture for adaptive quantum circuits leveraging the protective effects of topological defects in superconducting quantum circuits. The core concept involves constructing superconducting circuits incorporating multiple topological defects, wherein the circuit's quantum states can be dynamically reconfigured upon encountering noise, preserving quantum computation accuracy. This approach addresses the critical challenge of noise resilience in quantum computing by exploiting the inherent robustness of topological protection. The design emphasizes adaptability, allowing the circuit to self-correct and maintain fidelity under fluctuating environmental conditions. Mathematical formulations describe the circuit dynamics and the topological protection mechanism. The proposed architecture offers a promising pathway toward robust and scalable quantum computation. ---

Aug 29, 20260 citations

Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

Lachezar S. Georgiev

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the $\ensuremath{\pi}∕8$ gate, are also explicitly implemented by quasihole braidings. Instead of the $\ensuremath{\pi}∕8$ gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled- $Z$ precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate ${g}_{3}$ .We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma et al., in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the $\ensuremath{\pi}∕8$ gate, are also explicitly implemented by quasihole braidings. Instead of the $\ensuremath{\pi}∕8$ gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled-$Z$ precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate ${g}_{3}$.

arXiv:cond-mat/0607125Physical Review BDec 21, 200654 citations

Topological Quantum Computation

R. W. Ogburn, John P. Preskill

Lecture notes in computer scienceJan 1, 199980 citations

Topological quantum computation

Giuseppe Mussardo

Springer eBooksJan 1, 20250 citations

基于拓扑量子计算的容错编码设计

Jincheng Zhang

This paper explores the design of a fault-tolerant encoding scheme specifically tailored for topological quantum computing. The central premise is to leverage the inherent robustness of topological protection against decoherence, a primary challenge in realizing practical quantum computers. We propose a scheme utilizing non-Abelian anyons, exotic quasiparticles found in topological superconductors, to construct a robust quantum code. The core concept involves encoding quantum information within the braiding operations of these anyons, where the resulting topological transformations inherently protect against local errors. The scheme's efficacy relies on the topological protection mechanism, effectively mitigating errors arising from environmental noise and imperfections in qubit control. This work provides a theoretical foundation for utilizing topological quantum computing to achieve high-fidelity quantum computation. The key mathematical elements explored include qubit states, braiding operations, and the mathematical description of the topological protection effect.This paper explores the design of a fault-tolerant encoding scheme specifically tailored for topological quantum computing. The central premise is to leverage the inherent robustness of topological protection against decoherence, a primary challenge in realizing practical quantum computers. We propose a scheme utilizing non-Abelian anyons, exotic quasiparticles found in topological superconductors, to construct a robust quantum code. The core concept involves encoding quantum information within the braiding operations of these anyons, where the resulting topological transformations inherently protect against local errors. The scheme's efficacy relies on the topological protection mechanism, effectively mitigating errors arising from environmental noise and imperfections in qubit control. This work provides a theoretical foundation for utilizing topological quantum computing to achieve high-fidelity quantum computation. The key mathematical elements explored include qubit states, braiding operations, and the mathematical description of the topological protection effect.

Sep 7, 20260 citations

Z

precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate

{g}_{3}