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URN: urn:nbn:de:0030-drops-156726
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Eliminating Intermediate Measurements Using Pseudorandom Generators

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Abstract

We show that quantum algorithms of time T and space S ≥ log T with unitary operations and intermediate measurements can be simulated by quantum algorithms of time T ⋅ poly (S) and space {O}(S⋅ log T) with unitary operations and without intermediate measurements. The best results prior to this work required either Ω(T) space (by the deferred measurement principle) or poly(2^S) time [Bill Fefferman and Zachary Remscrim, 2021; Uma Girish et al., 2021]. Our result is thus a time-efficient and space-efficient simulation of algorithms with unitary operations and intermediate measurements by algorithms with unitary operations and without intermediate measurements.
To prove our result, we study pseudorandom generators for quantum space-bounded algorithms. We show that (an instance of) the INW pseudorandom generator for classical space-bounded algorithms [Russell Impagliazzo et al., 1994] also fools quantum space-bounded algorithms. More precisely, we show that for quantum space-bounded algorithms that have access to a read-once tape consisting of random bits, the final state of the algorithm when the random bits are drawn from the uniform distribution is nearly identical to the final state when the random bits are drawn using the INW pseudorandom generator. This result applies to general quantum algorithms which can apply unitary operations, perform intermediate measurements and reset qubits.

BibTeX - Entry

@InProceedings{girish_et_al:LIPIcs.ITCS.2022.76,
  author =	{Girish, Uma and Raz, Ran},
  title =	{{Eliminating Intermediate Measurements Using Pseudorandom Generators}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{76:1--76:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15672},
  URN =		{urn:nbn:de:0030-drops-156726},
  doi =		{10.4230/LIPIcs.ITCS.2022.76},
  annote =	{Keywords: quantum algorithms, intermediate measurements, deferred measurement, pseudorandom generator, INW generator}
}

Keywords: quantum algorithms, intermediate measurements, deferred measurement, pseudorandom generator, INW generator
Seminar: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue date: 2022
Date of publication: 25.01.2022


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