We describe transmon qubit dynamics in the presence of noise introduced by an impedance-matched resistor (50Ω) 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.
The importance of dissipation engineering ranges from universal quantum computation to non-equilibrium quantum thermodynamics. In recent years, more and more theoretical and experimentalstudies have shown the relevance of this topic for circuit quantum electrodynamics, one of the major platforms in the race for a quantum computer. This article discusses how to simulate thermal baths by inserting resistive elements in networks of superconducting qubits. Apart from pedagogically reviewing the phenomenological and microscopic models of a resistor as thermal bath with Johnson-Nyquist noise, the paper introduces some new results in the weak coupling limit, showing that the most common examples of open quantum systems can be simulated through capacitively coupled superconducting qubits and resistors. The aim of the manuscript, written with a broad audience in mind, is to be both an instructive tutorial about how to derive and characterize the Hamiltonian of general dissipative superconducting circuits with capacitive coupling, and a review of the most relevant and topical theoretical and experimental works focused on resistive elements and dissipation engineering.
A common environment acting on two superconducting qubits can give rise to a plethora of phenomena, such as the generation of entanglement between the qubits that, beyond its importancefor quantum computation tasks, also enforces a change of strategy in quantum error correction protocols. Further effects induced by a common bath are quantum synchronization and subradiance. Contrary to entanglement, for which full-state tomography is necessary, the latter can be assessed by detection of local observables only. In this work we explore different regimes to establish when synchronization and subradiance can be employed as reliable signatures of an entangling common bath. Moreover, we address a recently proposed measure of the collectiveness of the dynamics driven by the bath, and find that it almost perfectly witnesses the behavior of entanglement. Finally, we propose an implementation of the model based on two transmon qubits capacitively coupled to a common resistor, which may be employed as a versatile quantum simulation platform of the open system in general regimes.