NDLI: Contextuality Supplies the Magic for Quantum Computation

Content Provider	IEEE Xplore Digital Library
Author	Howard, M. Wallman, J. Veitch, V. Emerson, J.
Copyright Year	2015
Description	Author affiliation: Dept. of Stat., Univ. of Toronto, Toronto, ON, Canada (Veitch, V.) \|\| Dept. of Appl. Math, Univ. of Waterloo, Waterloo, ON, Canada (Howard, M.; Wallman, J.; Emerson, J.)
Abstract	We know that quantum mechanics enables the performance of computational and cryptographic tasks that are impossible (or impracticable) using only classical physics. It seems natural to examine manifestations of inherently quantum behaviour as potential sources of these capabilities. Here [1] we establish that quantum contextuality, a generalization of nonlocality identified by Bell [2] and Kochen-Specker [3] almost 50 years ago, is a critical resource for quantum speed-up within the leading model for fault-tolerant quantum computation, known as magic state distillation (MSD) [4], [5]. We consider the framework of fault-tolerant stabilizer quantum computation, which provides the most promising route to achieving robust universal quantum computation thanks to the discovery of high-threshold codes in two-dimensional geometries. In this framework, only a subset of quantum operations - namely, stabilizer operations - can be achieved via a fault-tolerant encoding. These operations define a closed subtheory (i.e. sets of states, transformations and measurements) of quantum theory - the stabilizer subtheory - which is not universal and in fact admits an efficient classical simulation. The stabilizer subtheory can be promoted to universal quantum computation through MSD which relies on a large number of ancillary resource states. Using d-level (where d is an odd prime) quantum systems - "qudits" - as the fundamental unit of information leads to mathematical and conceptual simplifications [6] (as well as improved efficiency and thresholds for the MSD subroutine). The term stabilizer refers to the fact that the states arising in our subtheory are simultaneous eigenstates of elements of the finite Heisenberg-Weyl (or, equivalently, the generalized Pauli-) group [7], [8], [9].If the input states to an MSD subroutine are unsuitable, then the overall computation remains classically efficiently simulable. We show that quantum contextuality plays a critical role in characterizing the suitability of quantum states for MSD. Our approach builds on recent work [10] that has established a remarkable connection between contextuality and graph-theory. We use this combinatorial framework to identify non-contextuality inequalities such that the onset of state-dependent contextuality, using stabilizer measurements, coincides exactly with the possibility of universal quantum computing via MSD.
Starting Page	96
Ending Page	96
File Size	112352
Page Count	1
File Format	PDF
ISBN	9781479917778
ISSN	0195623X
DOI	10.1109/ISMVL.2015.46
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-05-18
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Quantum computing Quantum mechanics Fault tolerance Fault tolerant systems Computational modeling Algorithms quantum computing
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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