Quantum amplifier such as the Josephson Traveling Wave Parametric Amplifier (JTWPA) have grown in importance with the advent of superconducting quantum processors. However, these amplifiers rely on fine tuning of the Hamiltonian of the circuit such as through resonant phase matching. Using these fundamental circuit elements removes some of the intuition behind the workings of the Amplifier.

In this paper, I instead design and simulate a novel superconducting quantum amplifier circuit using only resonators and qubits. Through restricting the design of the amplifier to these circuit elements, I allow for an easy and intuitive explanation for the operation of the amplifier circuit. This project therefore proposes a useful tool for beginners to start exploring engineering in Circuit-QED through limiting themselves to only designing circuits with resonators and qubits. This approach allows excitations to be traced throughout the circuit, and classical intuition is still somewhat useful in this domain. Once beginners have explored many of the interesting properties of quantum circuits, they can then begin engineering more complex Hamiltonians using the more fundamental circuit elements of capacitors, inductors, and Josephson Junctions.

The code to simulate this quantum amplifier circuit was written in python using QuTiP and can be found here.