Year: 2021
Type: dissertation
Abstract: Universal quantum computation can be achieved by a quantum device capable of acting with quantum gates, drawn from a universal gate set, on a specified input state and finally performing several measurements to produce an output. Alternatively, a universal gate set can be realized by supplementing certain non-universal gate sets, such as Clifford gates and matchgates, with resourceful so-called magic states. Whereas this is typically described using pure magic states, one also has to consider which mixed states can be used to achieve universality in a realistic setting. A common approach to identifying such states is through purification protocols, which comprise only free operations. Due to their importance in practical applications, mixed magic states for Clifford circuits have been the subject of extensive research. On the other hand, much less is known in the case of matchgate circuits.\n\nOne particular magic state for matchgate circuits is given by the four-qubit GHZ-state. In [S. Bravyi, Phys. Rev. A 73 (042313), 2006], a protocol was proposed which allows for the purification of this state, provided that the initial states have an even parity and satisfy a threshold condition. We present some variants of this protocol, which allow us to identify different sets of mixed magic states. During this investigation, we find classes of states in which each state can either be purified or ruled out from being resourceful. Some methods we use can be employed to disprove the existence of certain purification protocols, which would allow for the purification of an even larger class of states. Another method allows for an easy determination of new matchgate circuits based on a list of conditions between the input and output state of a circuit.
Author: Langer, Marc Mathurin
Institution: Universität Innsbruck
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6992931238