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

Sammanfattning

Quantum computers are a technology that has garnered much attention throughout the lastdecades. This interest can partially be attributed to the realization that quantum computersseemingly can accomplish some computational tasks more efficiently than classical computers.The computational components that a quantum computer requires for these speed-ups arecalled resources. In this thesis, we implement and study an algorithm that aims to obtain aset 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 magicsynthesis (MMS) and is inspired by a method proposed by Sergey Bravyi and Alexei Kitaev inRef. [1], which can obtain magic states that are arbitrarily close to the target with a processnamed magic state distillation (MSD). The quality of the output state from the algorithms ischaracterized by fidelity, where MMS and MSD are both implemented to obtain an output statewith a higher fidelity to the target by a similar optimization procedure of consuming severalfaulty input magic states in multiple optimization rounds. The defining characteristic of theMMS algorithm, which deviates from the MSD method, is that MMS only requires two statesas inputs for each round of optimization, whereas the MSD algorithm needs at least five inputstates for distillation. The results we acquired from implementing the MMS algorithm showedthat it could not increase the fidelity of the input state to the T state, while some improvementof the input state to the H state appeared feasible. However, the MMS algorithm could onlyincrease the fidelity of the input state to the H state up to a certain point. It is because of thisimportant realization that we do not consider the MMS algorithm as a genuine “distillation”method, and instead refer to it as a “synthesis” algorithm.