In BFSS matrix theory, the sign problem is nonzero at large N but first appears at 10-loop order, giving ⟨cosθ⟩ ≈ exp(−9×10⁻⁹ N²(λβ³)⁵).
Approaches to the sign problem in lattice field theory
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abstract
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte-Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost fourty years, cannot be applied in this case. Various strategies to overcome this so-called Sign Problem or Complex Action Problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focussing on two more recent methods: Dualization to world-line type of representations and the density-of-states approach.
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The derivative of entanglement entropy with respect to subregion volume equals the thermal entropy density in the large-subregion limit, verified via lattice simulations of the finite-density O(4) model using dual worm algorithms.
Constrained symplectic quantization applied to the free scalar field reproduces the Feynman generating functional in the continuum limit and matches standard correlators, commutators, and Dyson-Schwinger equations in 1+1 dimensions via numerical evolution.
Constrained symplectic quantization recovers the Feynman generating functional with correct real-time prescription for relativistic QFT by analytic continuation of fields and action plus constraints on stable trajectories, tested via two-point functions and Dyson-Schwinger identities on a free scala
For diagonal quadratic evolutions, qubit encodings are asymptotically cheaper than qudit encodings in both Trotter and LCU settings, but small-dimension qudits can win under favorable synthesis or code-switching assumptions.
citing papers explorer
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An effective field theory approach to the sign problem in BFSS
In BFSS matrix theory, the sign problem is nonzero at large N but first appears at 10-loop order, giving ⟨cosθ⟩ ≈ exp(−9×10⁻⁹ N²(λβ³)⁵).
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Determination of thermodynamics from entanglement entropy in the finite-density O(N) model
The derivative of entanglement entropy with respect to subregion volume equals the thermal entropy density in the large-subregion limit, verified via lattice simulations of the finite-density O(4) model using dual worm algorithms.
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Constrained Symplectic Quantization II: The Free Scalar Field
Constrained symplectic quantization applied to the free scalar field reproduces the Feynman generating functional in the continuum limit and matches standard correlators, commutators, and Dyson-Schwinger equations in 1+1 dimensions via numerical evolution.
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Constrained Symplectic Quantization: Disclosing the Deterministic Framework Behind Quantum Field Theory
Constrained symplectic quantization recovers the Feynman generating functional with correct real-time prescription for relativistic QFT by analytic continuation of fields and action plus constraints on stable trajectories, tested via two-point functions and Dyson-Schwinger identities on a free scala
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
For diagonal quadratic evolutions, qubit encodings are asymptotically cheaper than qudit encodings in both Trotter and LCU settings, but small-dimension qudits can win under favorable synthesis or code-switching assumptions.