and analysis of the circuits.'
author:
- 'Firat Solgun^1^, David P. DiVincenzo^2,3^ and Jay M. Gambetta^1^'
date: 'December 21st, 2017'
title: Simple Impedance Response Formulas for the Dispersive Interaction Rates in the Effective Hamiltonians of Low Anharmonicity Superconducting Qubits
---

Introduction
============

Superconducting circuits are a promising platform for the realization of quantum computers. Operated at microwave frequencies they include Josephson junctions for the non-linearity needed to obtain qubit modes without introducing significant loss. Coherence times of the superconducting qubits have been improved by several orders of magnitude in the last two decades and the Transmon qubit [@Koch-Transmon; @Zombie-paper-Gambetta] (and its several variations [@Xmon; @Dicarlo]) has now become the superconducting qubit of choice in many groups around the world due to its simplicity of design and its superior coherence. Fidelities of the single qubit gates are now routinely below [@Martinis-Nature; @Sarah-Single-Qubit] and those of the two-qubit gates are at the fault-tolerance threshold levels required by the surface code [@Martinis-Nature; @Sarah-CR; @Maika-Parity]. The challenge now is to scale the circuits up while maintaining and improving further the qubit coherence times and gate fidelities [@Nick]. Many important engineering problems however arise in the design of larger multi-qubit devices such as signal crosstalk 