Open AccessPauli basis formalism in quantum computations
Author(s) -
V. V. Nikonov,
A. N. Tsirulev
Publication year - 2020
Publication title -
mathematical modelling and geometry
Language(s) - English
Resource type - Journals
ISSN - 2311-1275
DOI - 10.26456/mmg/2020-831
Subject(s) - pauli exclusion principle , theoretical physics , hilbert space , quantum mechanics , sic povm , physics , unitary state , mathematics , quantum operation , pure mathematics , algebra over a field , quantum , open quantum system , political science , law
This article deals with quantum computations in the Pauli basis whose elements are usually identified with the Pauli strings. This approach allows us to represent quantum states, observables, and unitary operators in the unified form of linear combination of Pauli strings, so that all operations can be reduced to the string compositions. Nevertheless a formal justification of the Pauli basis for quantum computations should be based on the strong results of complex linear algebra and the theory of Hilbert spaces. We briefly review the main features of Pauli strings for quantum states and unitary operators, and also the key operations with them, including an algorithm for string compositions and a transformation algorithm from the standard basis to the Pauli basis.