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We initiate the study of quantum algorithms for optimizing approximately convex functions.
Quantum algorithm for estimating volumes of convex bodies, 2019
Shouvanik Chakrabarti, Andrew M. Childs, Shih-Han Hung, Tongyang Li, Chunhao Wang, and Xiaodi Wu · 1908
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On explicit L 2 L^{2} -convergence rate estimate for underdamped Langevin dynamics, 2019
Yu Cao, Jianfeng Lu, and Lihan Wang · 1908
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Quantum supremacy using a programmable superconducting processor
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, and Joseph C. Bardin et al · 1910
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Logarithmic concave measures with applications to stochastic programming
András Prékopa · 1971
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On logarithmic concave measures and functions
András Prékopa · 1973
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Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions
Robert L. Smith · 1984
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Hit-and-run algorithms for the identification of nonredundant linear inequalities
H.C.P. Berbee, C.G.E. Boender, A.H.G. Rinnooy Ran, C.L. Scheffer, Robert L. Smith, and Jan Telgen · 1987
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Hit-and-run algorithms for generating multivariate distributions
Claude J.P. Bélisle, H. Edwin Romeijn, and Robert L. Smith · 1993
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Performance of the Gibbs, hit-and-run, and Metropolis samplers
Ming-Hui Chen and Bruce Schmeiser · 1993
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Improving hit-and-run for global optimization
Zelda B. Zabinsky, Robert L. Smith, J. Fred McDonald, H. Edwin Romeijn, and David E. Kaufman · 1993
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Quantum measurements and the Abelian stabilizer problem, 1995
Alexei Yu Kitaev · 1995
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Hit-and-run mixes fast
László Lovász · 1999
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Quantum computation and quantum information
Michael A. Nielsen and Isaac L. Chuang · 2000
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Quantum walks on graphs
Dorit Aharonov, Andris Ambainis, Julia Kempe, and Umesh Vazirani · 2001
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Hit-and-run is fast and fun, 2003
László Lovász and Santosh Vempala · 2003
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Quantum speed-up of Markov chain based algorithms
Mario Szegedy · 2004
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Improved regret for zeroth-order adversarial bandit convex optimisation
Tor Lattimore · 2006
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Hit-and-run from a corner
László Lovász and Santosh Vempala · 2006
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The geometry of logconcave functions and sampling algorithms
László Lovász and Santosh Vempala · 2007
Cited alongside, same era.
Quantum SDP-solvers: Better upper and lower bounds
Joran van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf · 2017
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Hit-and-run for sampling and planning in non-convex spaces
Yasin Abbasi-Yadkori, Peter Bartlett, Victor Gabillon, and Alan Malek · 2017
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Quantum speed-ups for semidefinite programming
Fernando G.S.L. Brandão and Krysta Svore · 2017
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Faster quantum mixing for slowly evolving sequences of markov chains
Davide Orsucci, Hans J. Briegel, and Vedran Dunjko · 2018
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Chenyi Zhang, Jiaqi Leng, and Tongyang Li · 2007
Cited alongside, same era.
Pawel Wocjan and Anura Abeyesinghe · 2008
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Structured logconcave sampling with a restricted gaussian oracle
Varsha Dani, Thomas P. Hayes, and Sham M. Kakade · 2009
Cited alongside, same era.
Quantum algorithm for approximating partition functions
Pawel Wocjan, Chen-Fu Chiang, Daniel Nagaj, and Anura Abeyesinghe · 2009
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Quantum computational advantage using photons
Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, and Li-Chao Peng et al · 2012
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Escaping the local minima via simulated annealing: Optimization of approximately convex functions
Alexandre Belloni, Tengyuan Liang, Hariharan Narayanan, and Alexander Rakhlin · 2015
Cited alongside, same era.
Joran van Apeldoorn and András Gilyén · 2019
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Quantum SDP solvers: Large speed-ups, optimality, and applications to quantum learning
Fernando G.S.L. Brandão, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu · 2019
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Convex optimization using quantum oracles
Joran van Apeldoorn, András Gilyén, Sander Gribling, and Ronald de Wolf · 2020
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Quantum algorithms and lower bounds for convex optimization
Shouvanik Chakrabarti, Andrew M. Childs, Tongyang Li, and Xiaodi Wu · 2020
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Adaptive quantum simulated annealing for Bayesian inference and estimating partition functions
Aram W. Harrow and Annie Y. Wei · 2020
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Lecture notes on quantum algorithms
Andrew M. Childs · 2021
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Quantum Sub-Gaussian Mean Estimator
Yassine Hamoudi · 2021
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Improved regret for zeroth-order stochastic convex bandits
Tor Lattimore and Andras Gyorgy · 2021
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Quantum algorithms for sampling log-concave distributions and estimating normalizing constants, 2022
Andrew M. Childs, Tongyang Li, Jin-Peng Liu, Chunhao Wang, and Ruizhe Zhang · 2022
Closest in time.
Quantum multi-armed bandits and stochastic linear bandits enjoy logarithmic regrets, 2022
Zongqi Wan, Zhijie Zhang, Tongyang Li, Jialin Zhang, and Xiaoming Sun · 2022
Closest in time.