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QI: Fachverband Quanteninformation

QI 18: Poster II

QI 18.32: Poster

Wednesday, March 20, 2024, 11:00–14:30, Poster A

Analytical approximations to single fluxonium circuits — •Longxiang Huang, Johannes Schirk, Florian Wallner, Ivan Tsitsilin, Christian Schneider, Klaus Liegener, and Stefan Filipp — Walther-Meißner-Institut, Garching, Germany

In the ongoing effort of realizing quantum computers based on superconducting circuits, fluxonium qubits have recently emerged as a promising architecture, which show high coherence times and high anharmonicity compared to transmon qubits[1]. However, the eigensystem of fluxonium still deserves further investigation due to the difficulties of solving the double well potential. Previous efforts focused on numerical diagonalizations of the fluxonium Hamiltonian on harmonic oscillator basis[2]. Here, we present an alternative way to solve the double well potentials analytically with the help of a hyperbolic quasi-exactly solvable Generalized Manning potential. An analytical exact solution to certain eigenfunctions has been shown to terminate as confluent Heun's polynomials and associated eigenenergies could be determined by Wronskians[3]. We develop an analytical method to determine an approximation to the wavefunctions with above 99.9% fidelity and energies with 1% error rates in the light fluxonium regime.

[1] Nguyen, L. B. et al. Blueprint for a High-Performance Fluxonium Quantum Processor. PRX Quantum 3, 037001 (2022).

[2] Zhu, G. et al. Circuit QED with fluxonium qubits: Theory of the dispersive regime. Phys. Rev. B 87, 024510 (2013).

[3] Xie, Q.-T. New quasi-exactly solvable double-well potentials. J. Phys. A: Math. Theor. 45, 175302 (2012).

Keywords: fluxonium qubits; double well potential; confluent Heun's functions