  We present evidence of the feasibility of using billion core approximate
computers to run simple U(1) sigma models, and discuss how the approach might
be extended to Lattice Quantum Chromodynamics (LQCD) models. This work is
motivated by the extreme time, power, and cost needed to run LQCD on current
computing hardware. We show that, using massively parallel approximate
hardware, at least some models can run with great speed and power efficiency
without sacrificing accuracy. As a test of accuracy, a 32 x 32 x 32 U(1) sigma
model yielded similar results using floating point and approximate
representations for the spins. A 20 million point 3D model, run on a
34,000-core single-board prototype approximate computer, showed encouraging
accuracy with a ~750 times improvement in speed and ~2500 times improvement in
speed/watt compared to a traditional CPU. These results suggest there is value
in future research to determine whether similar speed-ups and accuracies are
possible running full LQCD on the compact billion-core approximate computing
systems that are now practical.
