Pith. sign in

REVIEW

A Finite Presentation of CNOT-Dihedral Operators

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1701.00140 v5 pith:JFEXVAFP submitted 2016-12-31 quant-ph cs.ETcs.LO

A Finite Presentation of CNOT-Dihedral Operators

Matthew Amy (Institute for Quantum Computing , David R. Cheriton School of Computer Science , University of Waterloo , Waterloo , Canada) , Jianxin Chen (Institute for Advanced Computer Studies , Joint Center for Quantum Information , Computer Science
show 4 more authors
University of Maryland College Park USA) Neil J. Ross (Institute for Advanced Computer Studies
This is my paper
classification quant-ph cs.ETcs.LO
keywords cnot-dihedraloperatorsfiniteformnormalpresentationcircuitcnot
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

We give a finite presentation by generators and relations of the unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the {CNOT, T} gate set as a corollary.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.