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We give a quantum logspace algorithm for powering contraction matrices, that is, matrices with spectral norm at most~1.
Positive functions on c*-algebras
W Forrest Stinespring · 1955
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Irreversibility and heat generation in the computing process
R. Landauer · 1961
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𝖡𝖯𝖧𝖲𝖯𝖠𝖢𝖤 ( s ) ⊆ 𝖣𝖲𝖯𝖠𝖢𝖤 ( s 3 / 2 ) \mathsf{BPHSPACE}(s)\subseteq\mathsf{DSPACE}(s^{3/2})
Michael Saks and Shiyu Zhou · 1999
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Space-bounded quantum complexity
John Watrous · 1999
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Reversible space equals deterministic space
Klaus-Jörn Lange, Pierre McKenzie, and Alain Tapp · 2000
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Notes on landauer’s principle, reversible computation, and maxwell’s demon
Charles Bennett · 2003
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Both toffoli and controlled-not need little help to do universal quantum computing
Yaoyun Shi · 2003
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Transformation of quantum states using uniformly controlled rotations
Mikko Möttönen, Juha J Vartiainen, Ville Bergholm, and Martti M Salomaa · 2005
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Quantum arthur–merlin games
Chris Marriott and John Watrous · 2005
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Time-space tradeoff in derandomizing probabilistic logspace
Jin-Yi Cai, Venkatesan T Chakaravarthy, and Dieter van Melkebeek · 2006
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Contractivity of positive and trace-preserving maps under l p norms
David Perez-Garcia, Michael M Wolf, Denes Petz, and Mary Beth Ruskai · 2006
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On random unitary channels
Koenraad MR Audenaert and Stefan Scheel · 2008
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Quantum algorithm for linear systems of equations
Aram W Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
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Quantum Computation and Quantum Information
Michael A Nielsen and Isaac L Chuang · 2010
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Matrix theory: basic results and techniques
Fuzhen Zhang · 2011
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Time-space efficient simulations of quantum computations
Dieter van Melkebeek and Thomas Watson · 2012
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Inverting well conditioned matrices in quantum logspace
Amnon Ta-Shma · 2013
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Fundamental limits of online and distributed algorithms for statistical learning and estimation
Ohad Shamir · 2014
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Simulating hamiltonian dynamics with a truncated taylor series
Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma · 2015
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A complete characterization of unitary quantum space
Bill Fefferman and Cedric Yen-Yu Lin · 2018
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Extractor-based time-space lower bounds for learning
Sumegha Garg, Ran Raz, and Avishay Tal · 2018
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Entropy samplers and strong generic lower bounds for space bounded learning
Dana Moshkovitz and Michal Moshkovitz · 2018
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Fast learning requires good memory: A time-space lower bound for parity learning
Ran Raz · 2018
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The theory of quantum information
John Watrous · 2018
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The power of block-encoded matrix powers: Improved regression techniques via faster hamiltonian simulation
Shantanav Chakraborty, András Gilyén, and Stacey Jeffery · 2019
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