Symmetry groups for the decomposition of reversible computers, quantum computers, and computers in between
type: Item
instance of: scholarly article
title: Symmetry groups for the decomposition of reversible computers, quantum computers, and computers in between
zbMATH Open document ID: 1360.81110
author: Alexis De Vos
author: Stijn De Baerdemacker
published in: Symmetry
publication date: 2017-05-12T00:00:00Z
review text: Summary: Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with \(w\) bits and the decomposition of an arbitrary quantum circuit with \(w\) qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qu)bit, the transformation being controlled by the other \(w-1\) (qu)bits. We explain why the former circuit can be decomposed into \(2w-1\) control gates, whereas the latter circuit needs \(2^w-1\) control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into \(2w-1\) or into \(2^w-1\) control gates.
Mathematics Subject Classification ID: 81P68
Mathematics Subject Classification ID: 94C10
zbMATH DE Number: 6714446
zbMATH Keywords: reversible computing
zbMATH Keywords: quantum computing
zbMATH Keywords: group theory
MaRDI profile type: Publication
full work available at URL: sym3020305
OpenAlex ID: W2022695583
DOI: 10.3390/SYM3020305
description: scientific article; zbMATH DE number 6714446