Spin-boson quantum phase transition in multilevel superconducting qubits

TL;DR

This paper investigates how the multilevel nature of superconducting qubits affects the spin-boson model, revealing that multilevel effects significantly alter the quantum phase transition and its critical point.

Contribution

It demonstrates that the multilevel structure of superconducting qubits limits the applicability of the spin-boson model and shifts the quantum critical point, using numerical and variational methods.

Findings

Multilevel effects restrict the spin-boson paradigm.

Quantum critical point shifts out of accessible range.

Charge discreteness influences phase localization.

Abstract

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on non-linear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wavefunction over many charge states. Numerical Renormalization Group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, that are relevant for a large class of devices.