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Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any other quantum many body system.
“Detailed Analysis of Circuit-to-Hamiltonian Mappings”, 2019
James. Watson · 1910
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“Quantum Mechanical Computers”
Richard. Feynman · 1985
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“Universal Quantum Simulators”
S. Lloyd · 1996
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“Nonbinary quantum codes”, 1997
Eric. Rains · 1997
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“84.57 Solving General Linear Diophantine Equations”
Michael Fox · 2000
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“Universal Translationally-Invariant Hamiltonians”, 2020
Stephen Piddock and Johannes Bausch · 2001
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“Classical and quantum computing”
Alexei. Kitaev, Alexander Shen and Mikhail. Vyalyi · 2002
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“Chapter - Universal Codes”
Peter Fenwick · 2003
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“Efficient quantum algorithms for simulating sparse Hamiltonians”, 2005
Dominic. Berry, Graeme Ahokas, Richard Cleve and Barry. Sanders · 2005
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“The complexity of quantum spin systems on a two-dimensional square lattice”
Roberto. Oliveira and Barbara. Terhal · 2005
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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 · 2007
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“The power of quantum systems on a line”
Dorit Aharonov, Daniel Gottesman, Sandy Irani and Julia Kempe · 2009
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“The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems”
Daniel Gottesman and Sandy Irani · 2013
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“The Local Hamiltonian problem on a line with eight states is QMA-complete”
Sean Hallgren, Daniel Nagaj and Sandeep Narayanaswami · 2013
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“Absolutely Maximally Entangled Qudit Graph States”, 2013
Wolfram Helwig · 2013
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“Local Tests of Global Entanglement and a Counterexample to the Generalized Area Law”
Dorit Aharonov, Aram. Harrow, Zeph Landau, Daniel Nagaj, Mario Szegedy and Umesh Vazirani · 2014
Cited alongside, same era.
“Complexity Classification of Local Hamiltonian Problems”
Toby. Cubitt and Ashley Montanaro · 2014
Cited alongside, same era.
“Causality and holographic entanglement entropy”
Matthew Headrick, Veronika. Hubeny, Albion Lawrence and Mukund Rangamani · 2014
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“Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence”
Fernando Pastawski, Beni Yoshida, Daniel Harlow and John Preskill · 2015
Cited alongside, same era.
“Undecidability of the spectral gap”
“The complexity of translationally invariant low-dimensional spin lattices in 3D”
Johannes Bausch and Stephen Piddock · 2017
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“Dynamics for holographic codes”, 2017
Tobias. Osborne and Deniz. Stiegemann · 2017
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“Universal Quantum Hamiltonians”
Toby Cubitt, Ashley Montanaro and Stephen Piddock · 2018
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“Hamiltonian sparsification and gap-simulations”, 2018
Dorit Aharonov and Leo Zhou · 2018
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Chinmay Nirkhe, Umesh Vazirani and Henry Yuen · 2018
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Toby. Cubitt, David Perez-Garcia and Michael. Wolf · 2015
Cited alongside, same era.
Toby Cubitt, David Perez-Garcia and Michael. Wolf · 2015
Cited alongside, same era.
“Hamiltonian simulation with nearly optimal dependence on all parameters”, 2015
Dominic. Berry, Andrew. Childs and Robin Kothari · 2015
Cited alongside, same era.
“Holographic duality from random tensor networks”
Patrick Hayden, Sepehr Nezami, Xiao-Liang Qi, Nathaniel Thomas, Michael Walter and Zhao Yang · 2016
Cited alongside, same era.
“Simple universal models capture all classical spin physics”
Gemma De Cuevas and Toby. Cubitt · 2016
Cited alongside, same era.
“The Complexity of Translationally Invariant Spin Chains with Low Local Dimension”
Johannes Bausch, Toby Cubitt and Maris Ozols · 2017
Cited alongside, same era.
“Nonunitary quantum computation in the ground space of local Hamiltonians”
Na“”iri Usher, Matty. Hoban and Dan. Browne · 2017
Cited alongside, same era.
“History-state Hamiltonians are critical”, 2018
Carlos. Gonz“’alez-Guill“’en and Toby. Cubitt · 2018
Later among the works it cites.
“Analysis and limitations of modified circuit-to-Hamiltonian constructions”
Johannes Bausch and Elizabeth Crosson · 2018
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“Undecidability of the Spectral Gap in One Dimension”, 2018
Johannes Bausch, Toby Cubitt, Angelo Lucia and David Perez-Garcia · 2018
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“A Complete Characterization of Unitary Quantum Space”
Bill Fefferman and Cedric Yen-Yu Lin · 2018
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“Toy models of holographic duality between local Hamiltonians”
Tamara Kohler and Toby Cubitt · 2019
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“Translationally Invariant Universal Classical Hamiltonians”
Tamara Kohler and Toby Cubitt · 2019
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“Hamiltonian sparsification and gap-simulations”, 2018
Dorit Aharonov and Leo Zhou · 2019
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“Perturbation Gadgets: Arbitrary Energy Scales from a Single Strong Interaction”
Johannes Bausch · 2019
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“General conditions for universality of Quantum Hamiltonians”, 2021
Tamara Kohler, Stephen Piddock, Johannes Bausch and Toby Cubitt · 2021
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