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.FSTTCS.2014.469
URN: urn:nbn:de:0030-drops-48646
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4864/
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O'Donnell, Ryan ; Cem Say, A. C.

One Time-traveling Bit is as Good as Logarithmically Many

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Abstract

We consider computation in the presence of closed timelike curves (CTCs), as proposed by Deutsch. We focus on the case in which the CTCs carry classical bits (as opposed to qubits). Previously, Aaronson and Watrous showed that computation with polynomially many CTC bits is equivalent in power to PSPACE. On the other hand, Say and Yakaryilmaz showed that computation with just 1 classical CTC bit gives the power of "postselection", thereby upgrading classical randomized computation (BPP) to the complexity class BPP_path and standard quantum computation (BQP) to the complexity class PP. It is natural to ask whether increasing the number of CTC bits from 1 to 2 (or 3, 4, etc.) leads to increased computational power. We show that the answer is no: randomized computation with logarithmically many CTC bits (i.e., polynomially many CTC states) is equivalent to BPP_path. (Similarly, quantum computation augmented with logarithmically many classical CTC bits is equivalent to PP.) Spoilsports with no interest in time travel may view our results as concerning the robustness of the class BPP_path and the computational complexity of sampling from an implicitly defined Markov chain.

BibTeX - Entry

@InProceedings{odonnell_et_al:LIPIcs:2014:4864,
  author =	{Ryan O'Donnell and A. C. Cem Say},
  title =	{{One Time-traveling Bit is as Good as Logarithmically Many}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{469--480},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4864},
  URN =		{urn:nbn:de:0030-drops-48646},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.469},
  annote =	{Keywords: Time travel, postselection, Markov chains, randomized computation}
}

Keywords: Time travel, postselection, Markov chains, randomized computation
Collection: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 12.12.2014

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