Fetching the paper…
Reading the bibliography…
We study the problem of learning a local quantum Hamiltonian $H$ given copies of its Gibbs state $\rho = e^{-\beta H}/\textrm{tr}(e^{-\beta H})$ at a known inverse temperature $\beta>0$.
“Markov field on finite graphs and lattices” Available at http://www.statslab.cam.ac.uk/~grg/books/hammfest/hamm-cliff.pdf , 1971
J.M. Hammersley and P. Clifford · 1971
Earlier work this paper cites.
“The finite group velocity of quantum spin systems”
Elliott. Lieb and Derek. Robinson · 1972
Earlier work this paper cites.
“The ellipsoid method and its consequences in combinatorial optimization”
Martin Grötschel, László Lovász and Alexander Schrijver · 1981
Earlier work this paper cites.
“An approach to obtaining global extremums in polynomial mathematical programming problems”
Naum Shor · 1987
Earlier work this paper cites.
“Squared functional systems and optimization problems”
Yurii Nesterov · 2000
Earlier work this paper cites.
“Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization”, 2000
Pablo. Parrilo · 2000
Earlier work this paper cites.
“Complexity of Positivstellensatz proofs for the knapsack”
Dima Grigoriev · 2001
Earlier work this paper cites.
“Distinguishing Separable and Entangled States”
A.. Doherty, Pablo. Parrilo and Federico. Spedalieri · 2002
Earlier work this paper cites.
“Series expansion methods for strongly interacting lattice models”
Jaan Oitmaa, Chris Hamer and Weihong Zheng · 2006
Earlier work this paper cites.
“Entanglement in many-body systems”
Luigi Amico, Rosario Fazio, Andreas Osterloh and Vlatko Vedral · 2008
Earlier work this paper cites.
“Sums of squares, moment matrices and optimization over polynomials”
Monique Laurent · 2008
Earlier work this paper cites.
“Efficient quantum state tomography”
Marcus Cramer et al · 2010
Earlier work this paper cites.
Matthew Hastings · 2010
Earlier work this paper cites.
“A quasipolynomial-time algorithm for the quantum separability problem”
Fernando.S.L. Brandão, Matthias Christandl and Jon Yard · 2011
Earlier work this paper cites.
“Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators”
M. Endres et al · 2011
Earlier work this paper cites.
“Practical characterization of quantum devices without tomography”
Marcus. da Silva, Olivier Landon-Cardinal and David Poulin · 2011
Earlier work this paper cites.
“Hypercontractivity, sum-of-squares proofs, and their applications”
Boaz Barak et al · 2012
Earlier work this paper cites.
“Reconstruction of Markov random fields from samples: Some observations and algorithms”
Guy Bresler, Elchanan Mossel and Allan Sly · 2013
Earlier work this paper cites.
“Quantum simulation”
I.0.167emM. Georgescu, S. Ashhab and Franco Nori · 2014
Earlier work this paper cites.
“Suppressing qubit dephasing using real-time Hamiltonian estimation”
M.. Shulman et al · 2014
Earlier work this paper cites.
“Hamiltonian learning and certification using quantum resources”
Nathan Wiebe, Cassandra Granade, Christopher Ferrie and D.0.167emG. Cory · 2014
Earlier work this paper cites.
“Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method”
Boaz Barak, Jonathan. Kelner and David Steurer · 2015
Earlier work this paper cites.
“Efficiently learning Ising models on arbitrary graphs”
Guy Bresler · 2015
Earlier work this paper cites.
“Quantum Hamiltonian complexity”
Sevag Gharibian, Yichen Huang, Zeph Landau and Seung Shin · 2015
Cited alongside, same era.
“Solutions of the two-dimensional Hubbard model: benchmarks and results from a wide range of numerical algorithms”
J… LeBlanc et al · 2015
Cited alongside, same era.
“Computational implications of reducing data to sufficient statistics”, 2015
Andrea Montanari · 2015
Cited alongside, same era.
“Connecting global and local energy distributions in quantum spin models on a lattice”
Itai Arad, Tomotaka Kuwahara and Zeph Landau · 2016
Cited alongside, same era.
“Proofs, beliefs, and algorithms through the lens of sum-of-squares”, 2016
Boaz Barak and David Steurer · 2016
Cited alongside, same era.
“Temperature scaling law for quantum annealing optimizers”
“Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature”
Tomotaka Kuwahara, Kohtaro Kato and Fernando… Brandão · 2020
Later among the works it cites.
“List decodable learning via sum of squares”
Prasad Raghavendra and Morris Yau · 2020
Later among the works it cites.
“Efficient learning of commuting Hamiltonians on lattices”, 2021
Anurag Anshu, Srinivasan Arunachalam, Tomotaka Kuwahara and Mehdi Soleimanifar · 2021
Later among the works it cites.
“List-decodable subspace recovery: Dimension independent error in polynomial time”
Ainesh Bakshi and Pravesh. Kothari · 2021
Later among the works it cites.
“Robust linear regression: optimal rates in polynomial time”
Ainesh Bakshi and Adarsh Prasad · 2021
Later among the works it cites.
“Theoretical and experimental perspectives of quantum verification”
Jose Carrasco et al · 2021
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Tameem Albash, Victor Martin-Mayor and Itay Hen · 2017
Cited alongside, same era.
“Quantum entanglement, sum of squares, and the log rank conjecture”
Boaz Barak, Pravesh. Kothari and David Steurer · 2017
Cited alongside, same era.
“Quantum simulations with ultracold atoms in optical lattices”
Christian Gross and Immanuel Bloch · 2017
Cited alongside, same era.
“Information theoretic properties of Markov random fields, and their algorithmic applications”
Linus Hamilton, Frederic Koehler and Ankur Moitra · 2017
Cited alongside, same era.
“Learning graphical models using multiplicative weights”
Adam Klivans and Raghu Meka · 2017
Cited alongside, same era.
“Mixture models, robustness, and sum of squares proofs”
Samuel. Hopkins and Jerry Li · 2018
Cited alongside, same era.
“Efficient algorithms for outlier-robust regression”
Adam Klivans, Pravesh. Kothari and Raghu Meka · 2018
Cited alongside, same era.
Later among the works it cites.
“Improved thermal area law and quasilinear time algorithm for quantum Gibbs states”
Tomotaka Kuwahara, Álvaro. Alhambra and Anurag Anshu · 2021
Later among the works it cites.
“Entanglement Hamiltonian tomography in quantum simulation”
Christian Kokail et al · 2021
Later among the works it cites.
“Settling the robust learnability of mixtures of Gaussians”
Allen Liu and Ankur Moitra · 2021
Later among the works it cites.
“Application of the Level-2 Quantum Lasserre Hierarchy in Quantum Approximation Algorithms”
Ojas Parekh and Kevin Thompson · 2021
Later among the works it cites.
“SoS degree reduction with applications to clustering and robust moment estimation”
David Steurer and Stefan Tiegel · 2021
Later among the works it cites.
“Optimal short-time measurements for Hamiltonian learning”
Assaf Zubida, Elad Yitzhaki, Netanel. Lindner and Eyal Bairey · 2021
Later among the works it cites.
“Robustly learning mixtures of k k arbitrary Gaussians”
Ainesh Bakshi et al · 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.
“Optimizing strongly interacting fermionic Hamiltonians”
Matthew. Hastings and Ryan O’Donnell · 2022
Later among the works it cites.
“A survey on the complexity of learning quantum states”
Anurag Anshu and Srinivasan Arunachalam · 2023
Closest in time.
“Quantum many-body systems in thermal equilibrium”
Álvaro. Alhambra · 2023
Closest in time.
“Field Theory and The Sum-of-Squares for Quantum Systems”
Matthew Hastings · 2023
Closest in time.
“Magnetically mediated hole pairing in fermionic ladders of ultracold atoms”
Sarah Hirthe et al · 2023
Closest in time.
“Learning many-body Hamiltonians with Heisenberg-limited scaling”
Hsin-Yuan Huang, Yu Tong, Di Fang and Yuan Su · 2023
Closest in time.
“Practical Hamiltonian learning with unitary dynamics and Gibbs states”
Andi Gu, Lukasz Cincio and Patrick. Coles · 2024
Closest in time.
“A CS guide to the quantum singular value transformation”
Ewin Tang and Kevin Tian · 2024
Closest in time.
“Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators”
Adam Watts et al · 2024
Closest in time.