[Paper Review] Dynamics of a dispersively coupled transmon qubit in the presence of a noise source embedded in the control line

Antti Vaaranta, Marco Cattaneo+1 more|arXiv (Cornell University)|Jun 17, 2022

Quantum Information and Cryptography60 references18 citations

TL;DR

This paper develops a rigorous quantum master equation for a transmon qubit dispersively coupled to a readout resonator, with noise introduced via a 50Ω resistor embedded in the control line. Using the Caldeira-Leggett model and symmetry-based block diagonalization of the Liouvillian, it shows that decoherence rates exceed standard approximations in the dispersive weak regime, especially at high resonator dissipation, offering a quantitative framework to reduce control-line-induced noise in superconducting qubits.

ABSTRACT

We describe transmon qubit dynamics in the presence of noise introduced by an impedance-matched resistor ($50\,\mathrm{\Omega}$) that is embedded in the qubit control line. To obtain the time evolution, we rigorously derive the circuit Hamiltonian of the qubit, readout resonator and resistor by describing the latter as an infinite collection of bosonic modes through the Caldeira-Leggett model. Starting from this Jaynes-Cummings Hamiltonian with inductive coupling to the remote bath comprised of the resistor, we consistently obtain the Lindblad master equation for the qubit and resonator in the dispersive regime. We exploit the underlying symmetries of the master equation to transform the Liouvillian superoperator into a block diagonal matrix. The block diagonalization method reveals that the rate of exponential decoherence of the qubit is well-captured by the slowest decaying eigenmode of a single block of the Liouvillian superoperator, which can be easily computed. The model captures the often used dispersive strong limit approximation of the qubit decoherence rate being linearly proportional to the number of thermal photons in the readout resonator but predicts remarkably better decoherence rates when the dissipation rate of the resonator is increased beyond the dispersive strong regime. Our work provides a full quantitative description of the contribution to the qubit decoherence rate coming from the control line in chips that are currently employed in circuit QED laboratories, and suggests different possible ways to reduce this source of noise.

Motivation & Objective

• To model the dynamics of a transmon qubit coupled to a readout resonator when noise is introduced via a 50Ω resistor in the control line.
• To derive a Lindblad master equation for the system using circuit quantum electrodynamics and open quantum systems theory.
• To identify and quantify the contribution of control-line noise to qubit decoherence in experimentally relevant regimes.
• To explore how resonator dissipation and coupling strength affect decoherence rates beyond the standard dispersive strong limit.

Proposed method

• Derives the full circuit Hamiltonian for a transmon qubit, resonator, and control-line resistor using lumped-element modeling.
• Models the resistor as an infinite bath of bosonic modes via the Caldeira-Leggett formalism.
• Constructs a Jaynes-Cummings-type Hamiltonian with inductive coupling to the remote bath.
• Applies symmetry analysis to transform the Liouvillian superoperator into block-diagonal form.
• Solves the master equation by focusing on the slowest-decaying eigenmode of the dominant block to extract decoherence rates.
• Validates results against the standard dispersive strong limit and extends analysis to the dispersive weak regime.

Experimental results

Research questions

• RQ1 How does the presence of a 50Ω resistor in the control line affect the decoherence rate of a transmon qubit in the dispersive regime?
• RQ2 Does the standard approximation of qubit decoherence being linearly proportional to thermal photon number in the resonator hold when resonator dissipation increases?
• RQ3 Can the block-diagonalization of the Liouvillian superoperator accurately capture the dominant decoherence channel in the presence of remote bath coupling?
• RQ4 What is the quantitative impact of increasing resonator dissipation on qubit decoherence beyond the dispersive strong limit?
• RQ5 How does the model compare to existing approximations in the weak and strong coupling regimes?

Key findings

• The model confirms the standard approximation of qubit decoherence rate being linearly proportional to the number of thermal photons in the resonator in the dispersive strong regime.
• In the dispersive weak regime, the model predicts significantly higher decoherence rates than the standard approximation when resonator dissipation increases.
• The slowest-decaying eigenmode of a single block of the Liouvillian superoperator accurately captures the dominant qubit decoherence rate.
• The block-diagonalization method simplifies the full Liouvillian, enabling efficient computation of decoherence dynamics.
• The results suggest that operating in the dispersive weak regime may improve qubit coherence times by reducing sensitivity to control-line noise.
• The framework provides a quantitative tool to assess and mitigate noise contributions from attenuators in control lines of current circuit QED platforms.