Dynamics of a dispersively coupled transmon qubit in the presence of a noise source embedded in the control line

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.

arXiv comment20 pages, 10 figures

References in corpus (46)

• Charge insensitive qubit design derived from the Cooper pair box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Quantifying Coherence
• Circuit Quantum Electrodynamics
• A Quantum Engineer's Guide to Superconducting Qubits
• Resolving photon number states in a superconducting circuit
• Coherent Josephson qubit suitable for scalable quantum integrated circuits
• Decoherence in a superconducting quantum bit circuit
• Controlling the spontaneous emission of a superconducting transmon qubit
• Symmetries and conserved quantities in Lindblad master equations
• Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting
• Spectral theory of Liouvillians for dissipative phase transitions
• Engineering cryogenic setups for 100-qubit scale superconducting circuit systems
• Coplanar Waveguide Resonators for Circuit Quantum Electrodynamics
• Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits
• Decoherence benchmarking of superconducting qubits
• Introduction to Quantum Electromagnetic Circuits
• Dispersive regime of circuit QED: photon-dependent qubit dephasing and relaxation rates
• Markovian master equations for quantum thermal machines: local vs global approach
• Impact of ionizing radiation on superconducting qubit coherence
• Qubit-oscillator dynamics in the dispersive regime: analytical theory beyond rotating-wave approximation
• Protecting superconducting qubits from external sources of loss and heat
• Thermal and Residual Excited-State Population in a 3D Transmon Qubit
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• Photon Shot Noise Dephasing in the Strong-Dispersive Limit of Circuit QED
• Perturbative treatment of inter-site couplings in the local description of open quantum networks
• Using a qubit to measure photon number statistics of a driven, thermal oscillator
• Cavity Attenuators for Superconducting Qubits
• Microwave attenuators for use with quantum devices below 100 mK
• Multi-mode ultra-strong coupling in circuit quantum electrodynamics
• Decoherence of superconducting qubits caused by quasiparticle tunneling
• Quantum synchronization as a local signature of super- and subradiance
• Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics
• Environmental Radiation Impact on Lifetimes and Quasiparticle Tunneling Rates of Fixed-Frequency Transmon Qubits
• Cutoff-free Circuit Quantum Electrodynamics
• Fundamentals of Quantum Mechanics in Liouville Space
• Quantum Networks in Divergence-free Circuit QED
• The upside of noise: engineered dissipation as a resource in superconducting circuits
• Symmetry and block structure of the Liouvillian superoperator in partial secular approximation
• Origin and Implications of $A^2$-like Contribution in the Quantization of Circuit-QED Systems
• Local master equations bypass the secular approximation
• Engineering dissipation with resistive elements in circuit quantum electrodynamics
• Bath-induced collective phenomena on superconducting qubits: synchronization, subradiance, and entanglement generation
• Quantum Microwave Radiometry with a Superconducting Qubit
• Non-Markovian dynamics of a superconducting qubit in an open multimode resonator
• Josephson nanocircuit in the presence of linear quantum noise