Classical and quantum algorithms for many-body problems by Ayral, Thomas

“…The many-body problem is central to many fields, such as condensed-matter physics and chemistry, but also to combinatorial optimization, which is nothing but a classical many-body problem. …”
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Kondo spectral functions at low-temperatures: A dynamical-exchange-correlation-field perspective by Zhen Zhao

“…Consequently, it can significantly reduce the complexity of the many-body problem faced by first-principles approaches to strongly correlated materials.…”
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Long-time error-mitigating simulation of open quantum systems on near term quantum computers by Brian Rost, Lorenzo Del Re, Nathan Earnest, Alexander F. Kemper, Barbara Jones, James K. Freericks

“…Our two examples show promise that the driven-dissipative quantum many-body problem can eventually be solved on quantum computers.…”
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Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning by Yuanran Zhu, Jia Yin, Cian C Reeves, Chao Yang, Vojtěch Vlček

“…Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N _t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. …”
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Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods by Raphaël Photopoulos, Antoine Boulet

“…Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. …”
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