License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2017.48
URN: urn:nbn:de:0030-drops-81826
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8182/
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Chao, Rui ; Reichardt, Ben W. ; Sutherland, Chris ; Vidick, Thomas

Overlapping Qubits

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LIPIcs-ITCS-2017-48.pdf (0.9 MB)

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 <= epsilon in n^{O(1/epsilon^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.

BibTeX - Entry

@InProceedings{chao_et_al:LIPIcs:2017:8182,
  author =	{Rui Chao and Ben W. Reichardt and Chris Sutherland and Thomas Vidick},
  title =	{{Overlapping Qubits}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{48:1--48:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8182},
  URN =		{urn:nbn:de:0030-drops-81826},
  doi =		{10.4230/LIPIcs.ITCS.2017.48},
  annote =	{Keywords: Quantum computing, Qubits, Dimension test}
}

Keywords: Quantum computing, Qubits, Dimension test
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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