Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2402.01039 · International Symposium on Lattice Field Theory (LATTICE)

Meron-Cluster Algorithms for Quantum Link Models

João C. Pinto Barros, Thea Budde, Marina Krstić Marinković

Published May 4, 2024• 4 citations
arXivHTMLPDF

Abstract

State-of-the-art algorithms for simulating fermions coupled to gauge fields often rely on integrating fermion degrees of freedom. While successful in simulating QCD at zero chemical potential, at finite density these approaches are hindered by the sign problem. We discuss the simulation of lattice gauge theories in the Hamiltonian formalism and present a generalized meron-cluster algorithm for the simulation of the $U\left(1\right)$ Quantum Link Model for spin $1/2$. This enables the study of models directly relevant to current quantum simulators and is a promising first step toward constructing new efficient algorithms for more complicated gauge theories.

DOI
10.22323/1.453.0024

Related papers

Quantum Monte Carlo for gauge fields and matter without the fermion determinant

Debasish Banerjee, Emilie Huffman

Monte Carlo simulations of strongly interacting fermionic systems are plagued by the fermion sign problem, making the nonperturbative study of many interesting regimes of dense quantum matter, or of theories of odd numbers of fermion flavors, challenging. Moreover, typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on the meron cluster algorithm, which can solve the fermion sign problem in a class of models without involving the determinant. We develop and benchmark new meron algorithms to simulate fermions coupled to Z2 and U(1) gauge fields in the presence of appropriate four-fermi interactions. Such algorithms can be used to uncover potential exotic properties of matter, particularly relevant for quantum simulator experiments. We demonstrate the emergence of the Gauss’ law at low temperatures for a U(1) model in (1+1)D . Published by the American Physical Society 2024

arXiv:2305.08917•Physical review. D/Physical review. D.•Feb 27, 2024•5 citations

Meron-Cluster Solution of Fermion Sign Problems

Shailesh Chandrasekharan A, U.‐J. Wiese

We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for nonrelativistic lattice fermions. A configuration of fermion world lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron clusters contribute $0$ to the path integral, while all other configurations contribute $1$. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.

arXiv:cond-mat/9902128•Physical Review Letters•Oct 18, 1999•223 citations

Interplay of Gauss Law and the Fermion Sign Problem in Quantum Link Models with Dynamical Matter

Anonymous, Debasish Banerjee, Emilie Huffman

Quantum Link Models with dynamical matter coupled to spin-$\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies $(G_e,G_o) = (d,\ -d)$, where $d$ is the spatial dimension and $e$ and $o$ are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.

International Symposium on Lattice Field Theory (LATTICE)•Jul 15, 2026•0 citations

Interplay of Gauss Law and the fermion sign problem in quantum link models with dynamical matter

Pallabi Dey, Debasish Banerjee, Emilie Huffman

Quantum Link Models with dynamical matter coupled to spin-$\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies $(G_e,G_o) = (d,\ -d)$, where $d$ is the spatial dimension and $e$ and $o$ are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.

arXiv:2602.22332•Feb 25, 2026•0 citations

Meron-Cluster Simulation of Quantum Spin Ladders in a Magnetic Field

Shailesh Chandrasekharan A, B. Scarlet, U.‐J. Wiese

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to quantum spin systems in an arbitrary external magnetic field, in which case standard cluster algorithms fail. As an example, we simulate antiferromagnetic quantum spin ladders in a uniform external magnetic field that competes with the spin-spin interaction. The numerical results are in agreement with analytic predictions for the magnetization as a function of the external field.

arXiv:cond-mat/9909451•Sep 30, 1999•2 citations

Review on Quantum Computing for Lattice Field Theory

Lena Funcke, Tobias Hartung, Karl Jansen +1 more

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.

arXiv:2302.00467•International Symposium on Lattice Field Theory (LATTICE)•Feb 1, 2023•39 citations
State-of-the-art algorithms for simulating fermions coupled to gauge fields often rely on integrating fermion degrees of freedom. While successful in simulating QCD at zero chemical potential, at finite density these approaches are hindered by the sign problem. We discuss the simulation of lattice gauge theories in the Hamiltonian formalism and present a generalized meron-cluster algorithm for the simulation of the U(1)U\left(1\right)U(1) Quantum Link Model for spin 1/21/21/2. This enables the study of models directly relevant to current quantum simulators and is a promising first step toward constructing new efficient algorithms for more complicated gauge theories.
Monte Carlo simulations of strongly interacting fermionic systems are plagued by the fermion sign problem, making the nonperturbative study of many interesting regimes of dense quantum matter, or of theories of odd numbers of fermion flavors, challenging. Moreover, typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on the meron cluster algorithm, which can solve the fermion sign problem in a class of models without involving the determinant. We develop and benchmark new meron algorithms to simulate fermions coupled to Z2 and U(1) gauge fields in the presence of appropriate four-fermi interactions. Such algorithms can be used to uncover potential exotic properties of matter, particularly relevant for quantum simulator experiments. We demonstrate the emergence of the Gauss’ law at low temperatures for a U(1) model in (1+1)D . Published by the American Physical Society 2024
We present a general strategy to solve the notorious fermion sign problem using cluster algorithms. The method applies to various systems in the Hubbard model family as well as to relativistic fermions. Here it is illustrated for nonrelativistic lattice fermions. A configuration of fermion world lines is decomposed into clusters that contribute independently to the fermion permutation sign. A cluster whose flip changes the sign is referred to as a meron. Configurations containing meron clusters contribute 000 to the path integral, while all other configurations contribute 111. The cluster representation describes the partition function as a gas of clusters in the zero-meron sector.
Quantum Link Models with dynamical matter coupled to spin-12 U(1)\frac{1}{2} \ \rm U(1)21​ U(1) gauge fields in $d=2+1 $ and 3+13+13+1 can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies (Ge,Go)=(d, −d)(G_e,G_o) = (d,\ -d)(Ge​,Go​)=(d, −d), where ddd is the spatial dimension and eee and ooo are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.
Quantum Link Models with dynamical matter coupled to spin-12 U(1)\frac{1}{2} \ \rm U(1)21​ U(1) gauge fields in $d=2+1 $ and 3+13+13+1 can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies (Ge,Go)=(d, −d)(G_e,G_o) = (d,\ -d)(Ge​,Go​)=(d, −d), where ddd is the spatial dimension and eee and ooo are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.
Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to quantum spin systems in an arbitrary external magnetic field, in which case standard cluster algorithms fail. As an example, we simulate antiferromagnetic quantum spin ladders in a uniform external magnetic field that competes with the spin-spin interaction. The numerical results are in agreement with analytic predictions for the magnetization as a function of the external field.
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the conventional Monte Carlo approach, such as the sign-problem afflicted regimes of finite baryon density, topological terms, and out-of-equilibrium dynamics. First proof-of-concept quantum computations of lattice gauge theories in (1+1) dimensions have been accomplished, and first resource-efficient quantum algorithms for lattice gauge theories in (1+1) and (2+1) dimensions have been developed. The path towards quantum computations of (3+1)-dimensional lattice gauge theories, including Lattice QCD, requires many incremental steps of improving both quantum hardware and quantum algorithms. After reviewing these requirements and recent advances, we discuss the main challenges and future directions.