The classical simulation of noisy quantum computers : a polyhedral approach

In this thesis we explored the consequences of considering generalised non-quantum notions of entanglement in the classical simulation of noisy quantum computers where the available measurements are restricted. Such noise rates serve as upper bounds to fault tolerance thresholds. These measurement r...

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Main Author: Ratanje, Nikhil
Published: University of Strathclyde 2017
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Online Access:https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.714723
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spelling ndltd-bl.uk-oai-ethos.bl.uk-7147232018-09-05T03:32:40ZThe classical simulation of noisy quantum computers : a polyhedral approachRatanje, Nikhil2017In this thesis we explored the consequences of considering generalised non-quantum notions of entanglement in the classical simulation of noisy quantum computers where the available measurements are restricted. Such noise rates serve as upper bounds to fault tolerance thresholds. These measurement restrictions come about either through imperfection, and/or by design to some limited set. By considering sets of operators that return positive measurement outcome probabilities for the restricted measurements, one can construct new single particle state spaces containing quantum and non-quantum operators. These state spaces can then be used with a modified version of Harrow and Nielsen’s classical simulation algorithm to efficiently simulate noisy quantum computers that are incapable of generating generalised entanglement with respect to the new state spaces. Through this approach we developed alternative methods of classical simulation, strongly connected to the study of non-local correlations, in that we constructed noisy quantum computers capable of performing non-Clifford operations and could generate some forms of multiparty quantum entanglement, but were classical in that they could be efficiently classically simulated and could not generate non-local statistics. We focused on magic state quantum computers (that are limited to only Pauli measurements), with ideal local gates, but noisy control-Pauli Z gates, and calculated the noise needed to ensure the control-Z gates became incapable of generating generalised entanglment for a variety of noise models and state space choice, with the aim of finding an optimal single particle state space requiring the least noise to remove the generalised entanglement. The state spaces were required to always return valid measurement probabilities, this meant they also had had to have octahedral symmetry to ensure local gates did not take states outside the state space. While we able to find to the optimal choice for highly imperfect measurements, were we unable to find the optimal in all cases. Our best candidate state space required less joint depolarising noise at [approximately equal to] 56% in comparison to noise levels of [approximately equal to] 67% required if the algorithm used quantum notions of separability. This suggests that generalised entanglement may offer more insight than quantum entanglement when discussing the power of Clifford operation based quantum computers.004.1University of Strathclydehttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.714723http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=27945Electronic Thesis or Dissertation
collection NDLTD
sources NDLTD
topic 004.1
spellingShingle 004.1
Ratanje, Nikhil
The classical simulation of noisy quantum computers : a polyhedral approach
description In this thesis we explored the consequences of considering generalised non-quantum notions of entanglement in the classical simulation of noisy quantum computers where the available measurements are restricted. Such noise rates serve as upper bounds to fault tolerance thresholds. These measurement restrictions come about either through imperfection, and/or by design to some limited set. By considering sets of operators that return positive measurement outcome probabilities for the restricted measurements, one can construct new single particle state spaces containing quantum and non-quantum operators. These state spaces can then be used with a modified version of Harrow and Nielsen’s classical simulation algorithm to efficiently simulate noisy quantum computers that are incapable of generating generalised entanglement with respect to the new state spaces. Through this approach we developed alternative methods of classical simulation, strongly connected to the study of non-local correlations, in that we constructed noisy quantum computers capable of performing non-Clifford operations and could generate some forms of multiparty quantum entanglement, but were classical in that they could be efficiently classically simulated and could not generate non-local statistics. We focused on magic state quantum computers (that are limited to only Pauli measurements), with ideal local gates, but noisy control-Pauli Z gates, and calculated the noise needed to ensure the control-Z gates became incapable of generating generalised entanglment for a variety of noise models and state space choice, with the aim of finding an optimal single particle state space requiring the least noise to remove the generalised entanglement. The state spaces were required to always return valid measurement probabilities, this meant they also had had to have octahedral symmetry to ensure local gates did not take states outside the state space. While we able to find to the optimal choice for highly imperfect measurements, were we unable to find the optimal in all cases. Our best candidate state space required less joint depolarising noise at [approximately equal to] 56% in comparison to noise levels of [approximately equal to] 67% required if the algorithm used quantum notions of separability. This suggests that generalised entanglement may offer more insight than quantum entanglement when discussing the power of Clifford operation based quantum computers.
author Ratanje, Nikhil
author_facet Ratanje, Nikhil
author_sort Ratanje, Nikhil
title The classical simulation of noisy quantum computers : a polyhedral approach
title_short The classical simulation of noisy quantum computers : a polyhedral approach
title_full The classical simulation of noisy quantum computers : a polyhedral approach
title_fullStr The classical simulation of noisy quantum computers : a polyhedral approach
title_full_unstemmed The classical simulation of noisy quantum computers : a polyhedral approach
title_sort classical simulation of noisy quantum computers : a polyhedral approach
publisher University of Strathclyde
publishDate 2017
url https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.714723
work_keys_str_mv AT ratanjenikhil theclassicalsimulationofnoisyquantumcomputersapolyhedralapproach
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