Abstract
Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are a leading platform for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the mode energy is stored in each element. The EPRs obey universal constraints and are calculated from one electromagnetic-eigenmode simulation. They lead directly to the system quantum Hamiltonian and dissipative parameters. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. We experimentally tested this method on a variety of Josephson circuits and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five orders of magnitude in energy, across a dozen samples.
Highlights
Quantum information processing based on the control of microwave electromagnetic fields in Josephson circuits is a promising platform for both fundamental physics experiments and emerging quantum technologies[1,2,3]
The heuristic atomic analogy seems seductively accurate, it fails completely in some cases to predict the nonlinear couplings
The qubits were designed to be in the dispersive regime with respect to the cavity, which was detuned by 2–4 GHz
Summary
Quantum information processing based on the control of microwave electromagnetic fields in Josephson circuits is a promising platform for both fundamental physics experiments and emerging quantum technologies[1,2,3]. For all pairs of ports, the complex function Zjj[0] ðωÞ is calculated from a finite-element (FE) driven simulation in the vicinity of the eigenfrequency of every mode Our method replaces these steps with a more economical FE eigenmode simulation, from which one extracts the energy participations pml and pmj, needed to fully characterize both the dissipative and Hamiltonian properties of the circuit. This level of accuracy is sufficient for most current quantum information experiments
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