NDLI: Symmetry-Assisted Adversaries for Quantum State Generation

Content Provider	IEEE Xplore Digital Library
Author	Ambainis, A. Magnin, L. Roetteler, M. Roland, J.
Copyright Year	2011
Abstract	We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target quantum states. There has been hope for quite some time that quantum state generation might be a route to tackle the GRAPH-ISOMORPHISM problem. We show that for the related problem of INDEX-ERASURE our method leads to a lower bound of square root of N which matches an upper bound obtained via reduction to quantum search on N elements. This closes an open problem first raised by Shi [FOCS'02]. Our approach is based on two ideas: (i) on the one hand we generalize the known additive and multiplicative adversary methods to the case of quantum state generation, (ii) on the other hand we show how the symmetries of the underlying problem can be leveraged for the design of optimal adversary matrices and dramatically simplify the computation of adversary bounds. Taken together, these two ideas give the new result for INDEX-ERASURE by using the representation theory of the symmetric group. Also, the method can lead to lower bounds even for small success probability, contrary to the standard adversary method. Furthermore, we answer an open question due to Spalek [CCC'08] by showing that the multiplicative version of the adversary method is stronger than the additive one for any problem. Finally, we prove that the multiplicative bound satisfies a strong direct product theorem, extending a result by Spalek to quantum state generation problems.
Starting Page	167
Ending Page	177
File Size	414883
Page Count	11
File Format	PDF
ISBN	9781457701795
ISSN	10930159
DOI	10.1109/CCC.2011.24
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-08
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Registers Additives Complexity theory Indexes Quantum mechanics Quantum computing Computational modeling index-erasure quantum query complexity adversary method strong direct product theorem
Content Type	Text
Resource Type	Article

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

A Strong Direct Product Theorem for Quantum Query Complexity

The Multiplicative Quantum Adversary

A strong direct product theorem for quantum query complexity

The multiplicative quantum adversary (2007).

The Multiplicative Quantum Adversary (2007)

Strong direct product theorems for quantum communication and query complexity (2011)

Negative weights make adversaries stronger

A Direct Product Theorem for Discrepancy

A new quantum lower bound method, with an application to strong direct product theorem for quantum search (2005)

Symmetry-Assisted Adversaries for Quantum State Generation

Similar Documents

A Strong Direct Product Theorem for Quantum Query Complexity

The Multiplicative Quantum Adversary

A strong direct product theorem for quantum query complexity

The multiplicative quantum adversary (2007).

The Multiplicative Quantum Adversary (2007)

Strong direct product theorems for quantum communication and query complexity (2011)

Negative weights make adversaries stronger

A Direct Product Theorem for Discrepancy

A new quantum lower bound method, with an application to strong direct product theorem for quantum search (2005)

Symmetry-Assisted Adversaries for Quantum State Generation