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Overlapping Qubits

Chao, Rui and Reichardt, Ben W. and Sutherland, Chris and Vidick, Thomas (2017) Overlapping Qubits. In: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics. No.67. Dagstuhl Publishing , Wadern, Germany, Art. No. 48. ISBN 9783959770293. http://resolver.caltech.edu/CaltechAUTHORS:20171011-113818136

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Abstract

An ideal system of n qubits has 2^n dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, n qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be ≤ ϵ in n^(O(1/ϵ^2)) dimensions.) Thus, even before considering issues like noise, a real system of n qubits might inherently lack any potential for exponential power. On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.4230/LIPIcs.ITCS.2017.48DOIArticle
https://arxiv.org/abs/1701.01062arXivDiscussion Paper
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2017 Rui Chao, Ben W. Reichardt, Chris Sutherland, and Thomas Vidick; licensed under Creative Commons License CC-BY. R.C., B.R. and C.S. supported by NSF grant CCF-1254119 and ARO grant W911NF-12-1-0541. T.V. supported by NSF CAREER grant CCF-1553477, an AFOSR YIP award, and the IQIM, an NSF Physics Frontiers Center (NFS Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-1254119
Army Research Office (ARO)W911NF-12-1-0541
NSFCCF-1553477
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Subject Keywords:Quantum computing, Qubits, Dimension test
Classification Code:1998 ACM Subject Classification: F.1.1 Models of Computation
Record Number:CaltechAUTHORS:20171011-113818136
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20171011-113818136
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82284
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Oct 2017 18:46
Last Modified:04 Apr 2019 21:25

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