Dorit Aharonov and Lior Eldar

On the complexity of Commuting Local Hamiltonians, and tight conditions for Topological Order in such systems

IEEE 52nd Annual Symposium on Foundations of Computer Science, 2011

Dorit Aharonov and Lior Eldar

The commuting local Hamiltonian on locally-expanding graphs is in NP

Quantum Information Processing, 2014

Dorit Aharonov, Oded Kenneth and Itamar Vigdorovich

On the Complexity of Two Dimensional Commuting Local Hamiltonians

Conference on the Theory of Quantum Computation, Communication and Cryptography, 2018

Dorit Aharonov, Daniel Gottesman, Sandy Irani and Julia Kempe

The Power of Quantum Systems on a Line

Communications in Mathematical Physics, 2009

Rupam Acharyya and Daniel Stefankovic

Glauber Dynamics for Ising Model on Convergent Dense Graph Sequences

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 2017

Francisco Barahona

On the computational complexity of Ising spin glass models

Journal of Physics A, 1982

Sergey Bravyi and Arvid J. Bessen and Barbara M. Terhal

Merlin–Arthur Games and Stoquastic Complexity

arXiv, 2006

Sergey Bravyi, David P. Divincenzo, Roberto Oliveira and Barbara M. Terhal

The Complexity of Stoquastic Local Hamiltonian Problems

Quantum Information and Computation, 2008

Sergey Bravyi and David Gosset

Polynomial-time classical simulation of quantum ferromagnets

Physical Review Letters, 2017

Sergey Bravyi and Matthew Hastings

On complexity of the quantum Ising model

Communications in Mathematical Physics, 2016

Jacob D. Biamonte and Peter J. Love

Realizable Hamiltonians for universal adiabatic quantum computers

American Physical Society, 78, 1, 2008

Vir B. Bulchandani and Stephen Piddock

The classical limit of Quantum Max–Cut

arXiv, 2024

Sergey Bravyi

Monte Carlo Simulation of Stoquastic Hamiltonians

Quantum Information and Computation, 2015

Sergey Bravyi and Mikhail Vyalyi

Commutative version of the $k$–local Hamiltonian problem and common eigenspace problem

arXiv, 2004

Yudong Cao, Ryan Babbush, Jacob Biamonte, and Sabre Kais

Hamiltonian gadgets with reduced resource requirements

Physical Review A, 2015

Christian Borgs, Jennifer Chayes, Tyler Helmuth, Will Perkins, and Prasad Tetali

Efficient sampling and counting algorithms for the Potts model on ℤᵈ at all temperatures

Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, 2020

Andrew M. Childs, David Gosset, and Zak Webb

The Bose–Hubbard Model is QMA–complete

International Colloquium on Automata, Languages, and Programming, 2014

Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, Jordi Weggemans

Improved Hardness Results for the Guided Local Hamiltonian Problem

International Colloquium on Automata, Languages, and Programming, 2023

Van Hao Can, Remco van der Hofstad, and Takashi Kumagai

Glauber dynamics for Ising models on random regular graphs: cut-off and metastability

arXiv, 2021

Toby Cubitt and Ashley Montanaro

Complexity classification of local Hamiltonian problems

SIAM Journal on Computing, 2016

Toby Cubitt, Ashley Montanaro and Stephen Piddock

Universal quantum Hamiltonians

Proceedings of the National Academy of Sciences, 2018

Jian Ding and Yuval Peres

Mixing time for the Ising model: a uniform lower bound for all graphs

Ann. Inst. H. Poincaré Probab. Statist., 2011

Roberto Fernández and Aldo Procacci

Cluster expansion for abstract polymer models. New bounds from an old approach

Communications in Mathematical Physics, 2007

Sacha Friedli and Yvan Velenik

Statistical mechanics of lattice systems: a concrete mathematical introduction

Cambridge University Press, 2017

Leslie Ann Goldberg and Heng Guo

The Complexity of Approximating complex-valued Ising and Tutte partition functions

Computational Complexity, 2017

Roy J. Glauber

Time Dependent Statistics of the Ising Model

Journal of Mathematical Physics, 1963

Andreas Galanis, Daniel Štefankovič, and Eric Vigoda

Inapproximability for antiferromagnetic spin systems in the tree nonuniqueness region

Journal of the ACM, 2015

Michel Goesmans and David Williamson

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

Journal of the ACM, 1995

Tyler Helmuth and Ryan L. Mann

Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature

Quantum, 2023

Sean Hallgren, Daniel Nagaj and Sandeep Narayanaswami

The Local Hamiltonian problem on a line with eight states is QMA–complete

Quantum Information and Computation, 2013

Thomas P. Hayes and Alistair Sinclair

A general lower bound for mixing of single-site dynamics on graphs

The Annals of Applied Probability, 2007

Sandy Irani and Jiaqing Jiang

Commuting Local Hamiltonian Problem on 2D beyond qubits

arXiv, 2023

Mark Jerrum and Alistair Sinclair

Polynomial-time approximation algorithms for the Ising model

SIAM Journal on Computing, 1993

Robbie King

An Improved Approximation Algorithm for Quantum Max–Cut on Triangle–Free Graphs

Quantum, 2023

Julia Kempe, Alexei Kitaev and Oded Regev

The Complexity of the Local Hamiltonian Problem

SIAM Journal on Computing, 2005

Roman Kotecký and David Preiss

Cluster expansion for abstract polymer models

Communications in Mathematical Physics, 1986

John Kallaugher and Ojas Parekh and Kevin Thompson and Yipu Wang and Justin Yirka

Complexity Classification of Product State Problems for Local Hamiltonians

arXiv, 2024

Julia Kempe and Oded Regev

3-Local Hamiltonian is QMA-complete

Quantum Information and Computation, 2003

Alexei Yu. Kitaev, Alexander Shen and Mikhail N. Vyalyi

Classical and Quantum Computation

American Mathematical Society, 2002

Ryan L. Mann and Tyler Helmuth

Efficient Algorithms for Approximating Quantum Partition Functions

Journal of Mathematical Physics, 2021

Ryan L. Mann and Romy M. Minko

Algorithmic Cluster Expansions for Quantum Problems

PRX Quantum, 2024

Elchanan Mossel and Allan Sly

Exact thresholds for Ising–Gibbs samplers on general graphs

The Annals of Probability, 2013

Daniel Nagaj

Local Hamiltonians in Quantum Computation

arXiv, 2008

Bryan O'Gorman and Sandy Irani and James Whitfield and Bill Fefferman

Intractability of Electronic Structure in a Fixed Basis

PRX Quantum, 2022

Roberto Oliveira and Barbara M. Terhal

The complexity of quantum spin systems on a two-dimensional square lattice

Quantum Information and Computation, 2008

Stephen Piddock

Complexity and Simulation of Many-Body Quantum Systems

University of Bristol, 2019

Stephen Piddock and Ashley Montanaro

The complexity of antiferromagnetic interactions and 2D lattices

Quantum Information and Computation, 2015

Edwin E. Salpeter

On Mayer's theory of cluster expansions

Annals of Physics, 1958

Allan Sly and Nike Sun

The computational hardness of counting in two-spin models on d-regular graphs

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, 2012

Alistair Sinclair, Piyush Srivastava, and Marc Thurley

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

Journal of Statistical Physics, 2014

Norbert Schuch and Frank Verstraete

Computational complexity of interacting electrons and fundamental limitations of density functional theory

Nature Physics, 2009

Norbert Schuch

Complexity of commuting Hamiltonians on a square lattice of qubits

arXiv, 2011

Gabriel Waite

Private communication, 2023