# Doubly Nonlinear Superconducting Qubit

**Authors:** Dat Thanh Le, Arne Grimsmo, Clemens Müller, T. M. Stace  
**arXiv:** [1904.01843](https://arxiv.org/abs/1904.01843)  
**Date:** 2019-04-03  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1904.01843v2/

## Key points

- Paper titled "Doubly Nonlinear Superconducting Qubit" by Dat Thanh Le, Arne Grimsmo, Clemens Müller, and T. M. Stace
- Novel superconducting circuit design incorporating Josephson junction and quantum phase slip wire
- Exact diagonalization of Hamiltonian with periodicity in charge and flux domains within double-Bloch band framework
- Eigenstates identified as code states of Gottesman-Kitaev-Preskill quantum error correcting code
- Presence of critical points in eigenspectrum reducing sensitivity to external perturbations
- Unique opportunities for utilizing corresponding states as robust qubits against noise sources
- Promise for advancing quantum information processing technologies by enhancing qubit coherence and fault tolerance
- Enhanced resilience to environmental disturbances in doubly nonlinear superconducting qubits
- Foundation for future advancements in quantum computing and error correction strategies

## Summary

The paper titled "Doubly Nonlinear Superconducting Qubit" by Dat Thanh Le, Arne Grimsmo, Clemens Müller, and T. M. Stace presents a novel superconducting circuit design incorporating a Josephson junction and a quantum phase slip wire. This setup allows for the exact diagonalization of a Hamiltonian with periodicity in both charge and flux domains within a double-Bloch band framework. The resulting eigenstates are identified as code states of the Gottesman-Kitaev-Preskill quantum error correcting code. One significant finding is the presence of critical points in the eigenspectrum where the system's sensitivity to external perturbations diminishes significantly. These critical points offer unique opportunities for utilizing corresponding states as robust qubits against external noise sources. By leveraging these specially engineered states, this proposed superconducting circuit shows promise for advancing quantum information processing technologies by enhancing qubit coherence and fault tolerance. The research provides valuable insights into developing doubly nonlinear superconducting qubits with enhanced resilience to environmental disturbances, laying a foundation for future advancements in quantum computing and error correction strategies. These findings pave the way for further exploration of tailored quantum systems capable of achieving improved performance and reliability in practical applications.