arXiv:1111.3633quant-ph
Quantum Algorithms for Quantum Field Theories
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
Abstract
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (phi-fourth theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
On point 1: I did not get your argument about NP hardness and equivalence to graph isomorphism. On the contrary, algorithms for efficiently simulating non-trivial QFTs on a non-relativistic quantum computers exist: https://arxiv.org/abs/1111.3633 Point 2: If "there is nothing…
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