# Two-Step Single Qubit Gates for Superconducting Qubits

#### Abstract

Why quantum information processing? Contemporary manipulation and transmission of information is executed through physical machines (computers, routers, scanners, etc.) in which Classical Mechanics is used to describe the embodiment and transformation of information. However, the physical theory of the world is not Classical Mechanics. And so, there is no reason to suppose that machines following the laws of Classical Mechanics would have the same computational power like quantum machines. Quantum computers would break the rules of classical computers and they would be able solve problems that are intractable on conventional supercomputers. In order to fabricate quantum computers and make significant strides in the field of quantum data, we need quantum objects that can function as qubits. A qubit is the quantum mechanical analogue of a classical bit. To implement qubits, numerous techniques have been put forth, most of which rely on microscopic quantum systems like nuclear or electronicspins, photon polarizations, or electronic levels in trapped ions or crystal defects. However, one method uses the macroscale quantum phenomenon known as superconductivity. This has two significant benefits. Firstly, these systems can be constructed to meet desired criteria, unlike an atom, which is fixed by nature. Secondly, their size makes it possible to construct them using the scalable, well-known micro-fabrication techniques used in the traditional semiconductor industry, which is crucial if these qubits are to be produced into arbitrarily large computers. Currently, superconducting qubits are the leading candidates for qubit architecture due to their relative ease of fabrication and long coherence times. From the mathematical viewpoint, every single-qubit gate (up to a global phase) is a rotation in the Bloch sphere representation. In practice, we cannot directly implement rotations around all possible axes. However, it is practically possible to implement rotations around fixed axes from coordinate planes, i.e., xy-, xz-, and yz-planes. At present, single qubit gates are implemented as a composition of three sequential rotations around fixed axes from coordinate planes. In this thesis, we demonstrate that for any coordinate plane, any single-qubit gate (up to a global phase) can be implemented as a composition of only two sequential rotations around arbitrary axes that have been constrained to lie in that single plane. This reduction from three to two implementable rotations makes qubit processing faster and more reliable. Our technique is readily applicable to many qubit systems especially, superconducting qubit systems.

#### Subject Area

Quantum physics

#### Recommended Citation

Takyi, Edward, "Two-Step Single Qubit Gates for Superconducting Qubits" (2022). *ETD Collection for University of Texas, El Paso*. AAI30246320.

https://scholarworks.utep.edu/dissertations/AAI30246320