The Pfaffian phase in BFSS becomes an O(9) pseudoscalar operator in a bosonic matrix integral, requiring 10-loop order in the high-T expansion before the sign problem is detectable in the 't Hooft regime.
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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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
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.
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An effective field theory approach to the sign problem in BFSS
The Pfaffian phase in BFSS becomes an O(9) pseudoscalar operator in a bosonic matrix integral, requiring 10-loop order in the high-T expansion before the sign problem is detectable in the 't Hooft regime.
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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
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.