Fundamental Limits to Cat-Code Qubits from Chaos-Assisted Tunneling

Abstract

We show that chaos-assisted tunneling (CAT) imposes an intrinsic limit to the protection of Kerr-cat qubits. In the static effective description, tunneling between the quasidegenerate cat states can be exponentially suppressed, ensuring long lifetimes. However, our Floquet analysis reveals that when the nonlinearities increase, chaotic states mediate tunneling between the cat states, producing large quasienergy splittings. We compute tunneling rates using both full quantum simulations and semiclassical WKB theory, finding quantitative agreement and confirming that the splittings are directly linked to chaos. These results provide the first evidence of CAT in the Kerr-cat qubit and demonstrate that chaos sets a fundamental bound on the coherence of dynamically protected superconducting qubits.

5 pages, 2 figures + Supp. Mat. 4 figures. Closest to published version

References in corpus (23)

• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network: Toward quantum soft computing
• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Optimizing the nonlinearity and dissipation of a SNAIL Parametric Amplifier for dynamic range
• First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
• Chaos-assisted directional light emission from microcavity lasers
• Excited-state quantum phase transitions
• Transmon platform for quantum computing challenged by chaotic fluctuations
• One hundred second bit-flip time in a two-photon dissipative oscillator
• Regular-to-chaotic tunneling rates using a fictitious integrable system
• On the static effective Hamiltonian of a rapidly driven nonlinear system
• Dynamical tunneling in molecules: Quantum routes to energy flow
• The squeezed Kerr oscillator: spectral kissing and phase-flip robustness
• Chaos-assisted tunneling resonances in a synthetic Floquet superlattice
• Effective versus Floquet theory for the Kerr parametric oscillator
• Classical Chaos in Quantum Computers
• Driving superconducting qubits into chaos
• Symmetrically Threaded Superconducting Quantum Interference Devices As Next Generation Kerr-cat Qubits
• Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator