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Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
Here we develop a new scheme of projective quantum Monte-Carlo (QMC) simulation combining unbiased zero-temperature (projective) determinant QMC and variational Monte-Carlo based on Gutzwiller projection wave function, dubbed as…
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem,…
We present a strategy to alleviate the sign problem in continuous-time quantum Monte Carlo (CTQMC) simulations of the dynamical-mean-field-theory (DMFT) equations for the spin-orbit-coupled multiorbital Hubbard model. We first identify the…
We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign…
Quantum Monte Carlo (QMC) simulations constitute nowadays one of the most powerful methods to study strongly correlated quantum systems, provided that no "sign problem" arises. However, many systems of interest, including highly frustrated…
The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces…
We consider bipartite SU($N$) spin Hamiltonians with a fundamental representation on one sublattice and a conjugate to fundamental on the other sublattice. By mapping these antiferromagnets to certain classical loop models in one higher…
We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$…
Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…
We review a recently proposed approach to the problem of alternating signs for fermionic many body Monte Carlo simulations in finite temperature simulations. We derive an estimate for fermion wandering lengths and introduce the notion of…
A powerful way to guarantee the absence of a sign problem in determinantal quantum Monte Carlo simulations is imposing a particular type of anti-unitary symmetries. It is shown that these same symmetries give rise to constraints on…
We combine the recent $\eta-$ensemble path integral Monte Carlo (PIMC) approach to the free energy [T.~Dornheim \textit{et al.}, \textit{Phys.~Rev.~B} \textbf{111}, L041114 (2025)] with a recent fictitious partition function technique based…
We revisit the infinite variance problem in fermionic Monte Carlo simulations, which is widely encountered in areas ranging from condensed matter to nuclear and high-energy physics. The different algorithms, which we broadly refer to as…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
We present a quantum Monte Carlo method which allows calculations on many-fermion systems at finite temperatures without any sign decay. This enables simulations of the grand-canonical ensemble at large system sizes and low temperatures.…
This work shows that the recently discovered operator contraction identity for solving the discreet Path Integral of the harmonic oscillator can be applied equally to fermions in any dimension. This then yields an exactly solvable model for…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…
Quantum Monte Carlo (QMC) methods for the frustrated quantum spin systems occasionally suffer from the negative sign problem, which makes simulations exponentially harder for larger systems at lower temperatures and severely limits QMC's…
It is commonly believed that in quantum Monte Carlo approaches to fermionic many- body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point…