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Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data.
Two theorems on random polynomial time
Leonard Adleman · 1978
Earlier work this paper cites.
Why and how to establish a private code on a public network
Shafi Goldwasser, Silvio Micali, and Po Tong · 1982
Earlier work this paper cites.
How to generate cryptographically strong sequences of pseudorandom bits
Manuel Blum and Silvio Micali · 1984
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Rsa and rabin functions: Certain parts are as hard as the whole
Werner Alexi, Benny Chor, Oded Goldreich, and Claus P Schnorr · 1988
Earlier work this paper cites.
Random-self-reducibility of complete sets
Joan Feigenbaum and Lance Fortnow · 1993
Earlier work this paper cites.
Cryptographic limitations on learning boolean formulae and finite automata
Michael Kearns and Leslie Valiant · 1994
Earlier work this paper cites.
An introduction to computational learning theory
Michael Kearns and Umesh Vazirani · 1994
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Peter Shor · 1999
Earlier work this paper cites.
Quantum information processing in continuous time
Andrew Macgregor Childs · 2004
Earlier work this paper cites.
Equivalences and separations between quantum and classical learnability
Rocco Servedio and Steven J Gortler · 2004
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Blind quantum computation
Pablo Arrighi and Louis Salvail · 2006
Earlier work this paper cites.
Average-case complexity
Andrej Bogdanov and Luca Trevisan · 2006
Earlier work this paper cites.
Quantum computational complexity of the N-representability problem: Qma complete
Yi-Kai Liu, Matthias Christandl, and Frank Verstraete · 2007
Earlier work this paper cites.
Computational complexity: a modern approach
Sanjeev Arora and Boaz Barak · 2009
Earlier work this paper cites.
Quantum algorithm for linear systems of equations
Aram W Harrow, Avinatan Hassidim, and Seth Lloyd · 2009
Earlier work this paper cites.
Interacting boson problems can be qma hard
Tzu-Chieh Wei, Michele Mosca, and Ashwin Nayak · 2010
Earlier work this paper cites.
The computational complexity of linear optics
Scott Aaronson and Alex Arkhipov · 2011
Cited alongside, same era.
https://cstheory.stackexchange.com/questions/15066/ consequences-of-bqp-subseteq-p-poly
Scott Aaronson, Jan 2013 · 2013
Cited alongside, same era.
The bose-hubbard model is QMA-complete
Andrew M Childs, David Gosset, and Zak Webb · 2014
Cited alongside, same era.
Understanding machine learning: From theory to algorithms
Shai Shalev-Shwartz and Shai Ben-David · 2014
Cited alongside, same era.
Average-case complexity versus approximate simulation of commuting quantum computations
Michael J Bremner, Ashley Montanaro, and Dan J Shepherd · 2016
Cited alongside, same era.
Guest column: A survey of quantum learning theory
Srinivasan Arunachalam and Ronald de Wolf · 2017
Cited alongside, same era.
Optimal learning of quantum hamiltonians from high-temperature gibbs states
Jeongwan Haah, Robin Kothari, and Ewin Tang · 2021
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A rigorous and robust quantum speed-up in supervised machine learning
Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme · 2021
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Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments
Thomas O’Brien, LevC Ioffe, Yuan Su, David Fushman, Hartmut Neven, Ryan Babbush, and Vadim Smelyanskiy · 2021
Later among the works it cites.
Electronic structure in a fixed basis is qma-complete
Bryan O’Gorman, Sandy Irani, James Whitfield, and Bill Fefferman · 2021
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On the quantum versus classical learnability of discrete distributions
Ryan Sweke, Jean-Pierre Seifert, Dominik Hangleiter, and Jens Eisert · 2021
Later among the works it cites.
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Quantum machine learning
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd · 2017
Cited alongside, same era.
The complexity of antiferromagnetic interactions and 2d lattices
Stephen Piddock and Ashley Montanaro · 2017
Cited alongside, same era.
The discrete-logarithm problem with preprocessing
Henry Corrigan-Gibbs and Dmitry Kogan · 2018
Cited alongside, same era.
Bqp-completeness of scattering in scalar quantum field theory
Stephen P Jordan, Hari Krovi, Keith SM Lee, and John Preskill · 2018
Cited alongside, same era.
Sample-efficient learning of quantum many-body systems
Anurag Anshu, Srinivasan Arunachalam, Tomotaka Kuwahara, and Mehdi Soleimanifar · 2020
Cited alongside, same era.
Sequential minimal optimization for quantum-classical hybrid algorithms
Ken Nakanishi, Keisuke Fujii, and Synge Todo · 2020
Cited alongside, same era.
Effect of data encoding on the expressive power of variational quantum-machine-learning models
Maria Schuld, Ryan Sweke, and Johannes Jakob Meyer · 2021
Later among the works it cites.
Complexity of the guided local hamiltonian problem: improved parameters and extension to excited states
Chris Cade, Marten Folkertsma, and Jordi Weggemans · 2022
Later among the works it cites.
On establishing learning separations between classical and quantum machine learning with classical data
Casper Gyurik and Vedran Dunjko · 2022
Later among the works it cites.
Improved hardness results for the guided local hamiltonian problem
Sevag Gharibian, Ryu Hayakawa, François Le Gall, and Tomoyuki Morimae · 2022
Later among the works it cites.
Optimal learning of quantum hamiltonians from high-temperature gibbs states
Jeongwan Haah, Robin Kothari, and Ewin Tang · 2022
Later among the works it cites.
Provably efficient machine learning for quantum many-body problems
Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor V Albert, and John Preskill · 2022
Later among the works it cites.
Learning many-body hamiltonians with heisenberg-limited scaling
Hsin-Yuan Huang, Yu Tong, Di Fang, and Yuan Su · 2022
Later among the works it cites.
Multi-dimensional fourier series with quantum circuits
Berta Casas and Alba Cervera-Lierta · 2023
Closest in time.
Relation between quantum advantage in supervised learning and quantum computational advantage
Jordi Pérez-Guijarro, Alba Pagès-Zamora, and Javier R Fonollosa · 2023
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Guidable local hamiltonian problems with implications to heuristic ansatze state preparation and the quantum pcp conjecture
Jordi Weggemans, Marten Folkertsma, and Chris Cade · 2023
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