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Condens. Matter 2017, 2(4), 33; doi:10.3390/condmat2040033

A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo

1
Department of Physics and Astronomy, University College London, WC1E 6BT London, UK
2
Extreme Light Infrastructure—Nuclear Physics (ELI-NP),Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, 30 Reactorului St, 077125 Bucharest-Magurele, Romania
Received: 18 August 2017 / Revised: 17 September 2017 / Accepted: 18 October 2017 / Published: 19 October 2017
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Abstract

I present here a new method that allows the introduction of a discrete auxiliary symmetry in a theory in such a way that the eigenvalue spectrum of the fermion functional determinant is made up of complex conjugated pairs. The method implies a particular way of introducing and integrating over auxiliary fields related to a set of artificial shift symmetries. Gauge fixing the artificial continuous shift symmetries in the direct and dual sectors leads to the appearance of direct and dual Becchi–Rouet–Stora–Tyutin (BRST)-type global symmetries and of a symplectic structure over the field space. Such a method may allow the extension of the applicability of quantum Monte Carlo methods to some problems plagued by the fermionic sign problem. View Full-Text
Keywords: quantum monte carlo; sign problem; P/NP quantum field computing quantum monte carlo; sign problem; P/NP quantum field computing
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Patrascu, A.T. A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo. Condens. Matter 2017, 2, 33.

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