Multi qubit gates using ZZ interactions in superconducting circuits

In recent years quantum computing has shown great promise and has come on in leaps and bounds. The promise of quantum computers is the speed-up over classical computers in specific areas and hence the ability to tackle even more complex problems. As quantum computers evolve the need for more complex quantum gates requiring more qubits (multi qubit gates) arises. These gates are currently broken down into their one and two qubit gates. Multi qubit gate decomposition’s involve many two qubit gates leading to the fidelity of these gates needing to be much higher in order to produce a usable multi qubit gate. A possible solution to this is to introduce a single shot method for the multi qubit gates. In this thesis we investigate the use of dispersive shifts to create these single shot methods. We examine two scenarios, first being a relatively simple three qubit gate (the iToffoli gate) to demonstrate the procedure. We then move to extend this method to a larger number of qubits examining its uses in quantum error correction and noting the potential pitfalls of this method. This thesis is organised as follows. In Chapter 1 we shall introduce the topic of superconducting circuits discussing some simple circuits such as the LC Oscillator and showing how these circuits can be modified to model superconducting qubits. We shall also introduce the topic of Quantum Computing giving an overview of the topic, discussing some quantum gates which shall be used and finally a short introduction to Quantum Error Correction. In Chapter 2 we shall show how we implemented a single shot multi qubit gate within superconducting circuits. We shall introduce some of the methods and analysis procedures we use within this thesis and show numerical evidence of this gate. In Chapter 3 we shall discuss an extension of the gate mechanism of chapter 1 to larger qubit clusters and show how it can be modified to implement parity check gates and show how they can be used to implement the stabilizer measurements used in the surface code. Finally in chapter 4 we shall discuss the future of this work, looking at some possible future directions for this research and suggesting some other more novel avenues which could be explored