Study of producing resourceful quantum states via modular combinations of two-qubit circuits
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Physics (MPPHS), MSc
Publicerad
2024
Författare
Maltesson, Alex
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Quantum computers, Modular magic synthesis, Magic state distillation, Clifford gates, post-selection