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We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band.
On the product of semi-groups of operators
Hale F Trotter · 1959
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Generalized trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems
Masuo Suzuki · 1976
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Quantum measurements and the abelian stabilizer problem
A Yu Kitaev · 1995
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Universal quantum simulators
Seth Lloyd · 1996
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A quantum adiabatic evolution algorithm applied to random instances of an np-complete problem
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda · 2001
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Michael A Nielsen and Isaac Chuang · 2002
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An elementary proof of the quantum adiabatic theorem
Andris Ambainis and Oded Regev · 2004
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Bounds for the adiabatic approximation with applications to quantum computation
Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler · 2007
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Adiabatic quantum computation is equivalent to standard quantum computation
Dorit Aharonov, Wim Van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev · 2008
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The magnus expansion and some of its applications
Sergio Blanes, Fernando Casas, JA Oteo, and José Ros · 2009
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Complexity of stoquastic frustration-free hamiltonians
Sergey Bravyi and Barbara Terhal · 2010
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Donny Cheung, Peter Høyer, and Nathan Wiebe · 2011
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Criticality without frustration for quantum spin-1 chains
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Dominic W Berry, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma · 2015
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Digitized adiabatic quantum computing with a superconducting circuit
Rami Barends, Alireza Shabani, Lucas Lamata, Julian Kelly, Antonio Mezzacapo, Urtzi Las Heras, Ryan Babbush, Austin G Fowler, Brooks Campbell, Yu Chen, et al · 2016
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Nearly optimal lattice simulation by product formulas
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Earl Campbell · 2019
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Hamiltonian simulation by qubitization
Guang Hao Low and Isaac L Chuang · 2019
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Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization
Ian D Kivlichan, Craig Gidney, Dominic W Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, et al · 2020
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Fast digital methods for adiabatic state preparation
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As usual in trotterization, the guideline for the decomposition is that one has a way to implement e i t H j e^{itH_{j}} efficiently for each H j H_{j} . A sufficient condition for this is for each H j H_{j} to be a sum of pairwise commuting local terms
Cited in the paper.
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Optimal protocols in quantum annealing and qaoa problems
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Quantum approximate optimization of the long-range ising model with a trapped-ion quantum simulator
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