Built on

Low-depth quantum metropolis algorithm
Original
Jonathan E Moussa · 1903
Earlier work this paper cites.
Quenched vs Annealed: Glassiness from SK to SYK
Original
CL Baldwin and B Swingle · 1911
Earlier work this paper cites.
Solvable Model of a Spin-Glass
David Sherrington and Scott Kirkpatrick · 1975
Earlier work this paper cites.
Random-energy model: Limit of a family of disordered models
B. Derrida · 1980
Earlier work this paper cites.
Gapless spin-fluid ground state in a random, quantum heisenberg magnet
Subir Sachdev and Jinwu Ye · 1993
Earlier work this paper cites.
Adaptive estimation of a quadratic functional by model selection
Beatrice Laurent and Pascal Massart · 2000
Earlier work this paper cites.
Problem of equilibration and the computation of correlation functions on a quantum computer
Barbara M Terhal and David P DiVincenzo · 2000
Earlier work this paper cites.
Classical and quantum computation
Alexei Yu Kitaev, Alexander Shen, Mikhail N Vyalyi, and Mikhail N Vyalyi · 2002
Earlier work this paper cites.
Contractivity of positive and trace-preserving maps under L p L_{p} norms
David Pérez-García, Michael M Wolf, Denes Petz, and Mary Beth Ruskai · 2006
Earlier work this paper cites.
A sparse model of quantum holography
Original
Shenglong Xu, Leonard Susskind, Yuan Su, and Brian Swingle · 2008
Earlier work this paper cites.
Quantum metropolis sampling
Original
Kristan Temme, Tobias J Osborne, Karl G Vollbrecht, David Poulin, and Frank Verstraete · 2011
Earlier work this paper cites.
User-friendly tail bounds for sums of random matrices
Original
Joel A Tropp · 2012
Earlier work this paper cites.
A quantum–quantum Metropolis algorithm
Original
Man-Hong Yung and Alán Aspuru-Guzik · 2012
Earlier work this paper cites.
Phase transition in the density of states of quantum spin glasses
Original
László Erdős and Dominik Schröder · 2014
Earlier work this paper cites.

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A simple model of quantum holography, 2015
Alexei Kitaev · 2015
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Efficient quantum algorithms for simulating Lindblad evolution
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Richard Cleve and Chunhao Wang · 2016
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Remarks on the Sachdev–Ye–Kitaev model
Juan Maldacena and Douglas Stanford · 2016
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Extremal eigenvalues of local Hamiltonians
Aram W. Harrow and Ashley Montanaro · 2017
Cited alongside, same era.
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
Original
András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2019
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Fast thermalization from the eigenstate thermalization hypothesis

Then

An improved approximation algorithm for quantum max-cut on triangle-free graphs
Original
Robbie King · 2023
Later among the works it cites.
Szegedy walk unitaries for quantum maps
Original
Pawel Wocjan and Kristan Temme · 2023
Later among the works it cites.
Strongly interacting fermions are non-trivial yet non-glassy
Original
Eric R Anschuetz, Chi-Fang Chen, Bobak T Kiani, and Robbie King · 2024
Closest in time.
Bounds on the ground state energy of quantum p p -spin hamiltonians
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Quantum computational advantage with constant-temperature Gibbs sampling
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2024

Optimizing random local Hamiltonians by dissipation

Basso, Joao, Chen, Chi-Fang, Dalzell, Alexander M.

Understand

A central challenge in quantum simulation is to prepare low-energy states of strongly interacting many-body systems.

In this work, we study the problem of preparing a quantum state that optimizes a random all-to-all, sparse or dense, spin or fermionic $k$-local Hamiltonian.
We prove that a simplified quantum Gibbs sampling algorithm achieves a $\Omega(\frac{1}{k})$-fraction approximation of the optimum, giving an exponential improvement on the $k$-dependence over the prior best (both classical and quantum) algorithmic guarantees.
Combined with the circuit lower bound for such states, our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.

Built on

Low-depth quantum metropolis algorithm
Original
Jonathan E Moussa · 1903
Earlier work this paper cites.
Quenched vs Annealed: Glassiness from SK to SYK
Original
CL Baldwin and B Swingle · 1911
Earlier work this paper cites.
Solvable Model of a Spin-Glass
David Sherrington and Scott Kirkpatrick · 1975
Earlier work this paper cites.
Random-energy model: Limit of a family of disordered models
B. Derrida · 1980
Earlier work this paper cites.
Gapless spin-fluid ground state in a random, quantum heisenberg magnet
Subir Sachdev and Jinwu Ye · 1993
Earlier work this paper cites.
Adaptive estimation of a quadratic functional by model selection
Beatrice Laurent and Pascal Massart · 2000
Earlier work this paper cites.
Problem of equilibration and the computation of correlation functions on a quantum computer
Barbara M Terhal and David P DiVincenzo · 2000
Earlier work this paper cites.
Classical and quantum computation
Alexei Yu Kitaev, Alexander Shen, Mikhail N Vyalyi, and Mikhail N Vyalyi · 2002
Earlier work this paper cites.
Contractivity of positive and trace-preserving maps under L p L_{p} norms
David Pérez-García, Michael M Wolf, Denes Petz, and Mary Beth Ruskai · 2006
Earlier work this paper cites.
A sparse model of quantum holography
Original
Shenglong Xu, Leonard Susskind, Yuan Su, and Brian Swingle · 2008
Earlier work this paper cites.
Quantum metropolis sampling
Original
Kristan Temme, Tobias J Osborne, Karl G Vollbrecht, David Poulin, and Frank Verstraete · 2011
Earlier work this paper cites.
User-friendly tail bounds for sums of random matrices
Original
Joel A Tropp · 2012
Earlier work this paper cites.
A quantum–quantum Metropolis algorithm
Original
Man-Hong Yung and Alán Aspuru-Guzik · 2012
Earlier work this paper cites.
Phase transition in the density of states of quantum spin glasses
Original
László Erdős and Dominik Schröder · 2014
Earlier work this paper cites.

Similar

A simple model of quantum holography, 2015
Alexei Kitaev · 2015
Cited alongside, same era.
Efficient quantum algorithms for simulating Lindblad evolution
Original
Richard Cleve and Chunhao Wang · 2016
Cited alongside, same era.
Remarks on the Sachdev–Ye–Kitaev model
Juan Maldacena and Douglas Stanford · 2016
Cited alongside, same era.
Extremal eigenvalues of local Hamiltonians
Aram W. Harrow and Ashley Montanaro · 2017
Cited alongside, same era.
Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
Original
András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe · 2019
Cited alongside, same era.
Fast thermalization from the eigenstate thermalization hypothesis