Study of producing resourceful quantum states via modular combinations of two-qubit circuits

Abstract

Quantum computers are a technology that has garnered much attention throughout the last decades. This interest can partially be attributed to the realization that quantum computers seemingly can accomplish some computational tasks more efficiently than classical computers. The computational components that a quantum computer requires for these speed-ups are called resources. In this thesis, we implement and study an algorithm that aims to obtain a set of resourceful states that could mediate computational speed-up, even exponential speed-up, which are called T- and H-type magic states. This algorithm is named modular magic synthesis (MMS) and is inspired by a method proposed by Sergey Bravyi and Alexei Kitaev in Ref. [1], which can obtain magic states that are arbitrarily close to the target with a process named magic state distillation (MSD). The quality of the output state from the algorithms is characterized by fidelity, where MMS and MSD are both implemented to obtain an output state with a higher fidelity to the target by a similar optimization procedure of consuming several faulty input magic states in multiple optimization rounds. The defining characteristic of the MMS algorithm, which deviates from the MSD method, is that MMS only requires two states as inputs for each round of optimization, whereas the MSD algorithm needs at least five input states for distillation. The results we acquired from implementing the MMS algorithm showed that it could not increase the fidelity of the input state to the T state, while some improvement of the input state to the H state appeared feasible. However, the MMS algorithm could only increase the fidelity of the input state to the H state up to a certain point. It is because of this important realization that we do not consider the MMS algorithm as a genuine “distillation” method, and instead refer to it as a “synthesis” algorithm.