Design of an inductively shunted transmon qubit with tunable transverse and longitudinal coupling

  1. Susanne Richer
This thesis is set in the framework of superconducting transmon-type qubit architectures with special focus on two important types of coupling between qubits and harmonic resonators:
transverse and longitudinal coupling. We will see that longitudinal coupling offers some remarkable advantages with respect to scalability and readout. This thesis will focus on a design, which combines both these coupling types in a single circuit and provides the possibility to choose between pure transverse and pure longitudinal or have both at the same time. We will start with an introduction to circuit quantization, where we will explain how to describe and analyze superconducting electrical circuits in a systematic way and discuss which characteristic circuit elements make up qubits and resonators. We will then introduce the two types of coupling between qubit and resonator which are provided in our design. Translating this discussion from the Hamiltonian level to the language of circuit quantization, we will show how to design circuits with specifically tailored couplings. We will focus on our circuit design that consists of an inductively shunted transmon qubit with tunable coupling to an embedded harmonic mode. The distinctive feature of the tunable design is that the transverse coupling disappears when the longitudinal is maximal and vice versa. Subsequently, we will turn to the implementation of our circuit design, discuss how to choose the parameters, and present an adapted alternative circuit, where coupling strength and anharmonicity scale better than in the original circuit. In addition, we present a proposal for an experimental device that will serve as a prototype for a first experiment. We will conclude the thesis discussing different possibilities to do readout with our circuit design, including a short discussion of the influence of dissipation.

Inductively shunted transmon qubit with tunable transverse and longitudinal coupling

  1. Susanne Richer,
  2. Nataliya Maleeva,
  3. Sebastian T. Skacel,
  4. Ioan M. Pop,
  5. and David DiVincenzo
We present the design of an inductively shunted transmon qubit with flux-tunable coupling to an embedded harmonic mode. This circuit construction offers the possibility to flux-choose
between pure transverse and pure longitudinal coupling, that is coupling to the σx or σz degree of freedom of the qubit. While transverse coupling is the coupling type that is most commonly used for superconducting qubits, the inherently different longitudinal coupling has some remarkable advantages both for readout and for the scalability of a circuit. Being able to choose between both kinds of coupling in the same circuit provides the flexibility to use one for coupling to the next qubit and one for readout, or vice versa. We provide a detailed analysis of the system’s behavior using realistic parameters, along with a proposal for the physical implementation of a prototype device.

Circuit design implementing longitudinal coupling: a scalable scheme for superconducting qubits

  1. Susanne Richer,
  2. and David DiVincenzo
We present a circuit construction for a new fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization
we propose implements σz-type coupling between a superconducting qubit and any number of LC resonators. The resulting \textit{longitudinal coupling} is inherently different from the usual σx-type \textit{transverse coupling}, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators; there is never any direct qubit-qubit coupling. We note that just four distinct resonator frequencies, and only a single unique qubit frequency, suffice for the scalability of this scheme. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a supreme advantage for the scalability of this scheme.