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We give a simple proof of a Chernoff bound for the spectrum of a $k$-local Hamiltonian based on Weyl's inequalities.
Hermann Weyl · 1912
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Probability Inequalities for Sums of Bounded Random Variables
Wassily Hoeffding · 1963
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The complexity of the local Hamiltonian problem
Julia Kempe, Alexei Kitaev, and Oded Regev · 2006
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Quantum simulation of many-body Hamiltonians using perturbation theory with bounded-strength interactions
Sergey Bravyi, David P DiVincenzo, Daniel Loss, and Barbara M Terhal · 2008
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A short proof of the Hajnal–Szemerédi theorem on equitable colouring
Hal A Kierstead and Alexandr V Kostochka · 2008
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Computational difficulty of computing the density of states
Brielin Brown, Steven T Flammia, and Norbert Schuch · 2011
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Some applications of hypercontractive inequalities in quantum information theory
Ashley Montanaro · 2012
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Guest Column: The Quantum PCP Conjecture
Dorit Aharonov, Itai Arad, and Thomas Vidick · 2013
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Spectra and Eigenstates of Spin Chain Hamiltonians
J. P. Keating, N. Linden, and H. J. Wells · 2015
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Concentration bounds for quantum states with finite correlation length on quantum spin lattice systems
Anurag Anshu · 2016
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Product-state Approximations to Quantum Ground States
Fernando G. S. L. Brandão and Aram W. Harrow · 2016
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Connecting the probability distributions of different operators and generalization of the Chernoff–Hoeffding inequality
Tomotaka Kuwahara · 2016
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Spectrum estimation from samples
Weihao Kong, Gregory Valiant, and others · 2017
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Approximation algorithms for quantum many-body problems
Sergey Bravyi, David Gosset, Robert Koenig, and Kristan Temme · 2019
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Beyond Product State Approximations for a Quantum Analogue of Max Cut
Anurag Anshu, David Gosset, and Karen Morenz · 2020
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An approximation algorithm for the MAX-2-Local Hamiltonian problem
Sean Hallgren, Eunou Lee, and Ojas Parekh · 2020
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Classical algorithms, correlation decay, and complex zeros of partition functions of quantum many-body systems
Aram W Harrow, Saeed Mehraban, and Mehdi Soleimanifar · 2020
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Quantum Computation of Eigenvalues within Target Intervals
Phillip W. K. Jensen, Lasse Bjørn Kristensen, Jakob S. Kottmann, and Alán Aspuru-Guzik · 2020
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Gaussian concentration bound and Ensemble equivalence in generic quantum many-body systems including long-range interactions
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Aram W. Harrow
Cited in the paper.
Tomotaka Kuwahara and Keiji Saito · 2020
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