Quantum- Inspired Structure- Preserving Probabilistic Inference

Abstract

Probabilistic methods serve as the underlying frame-work of various machine learning techniques. When using these models, a central problem is that of computing the partition function, whose computation is intractable for many models of interest. Here, we present the first quantum-inspired method that is especially designed for computing fast approximations to the partition function. Our approach uses a novel hardware solver for quadratic unconstrained binary optimization problems that relies on evolutionary computation. The specialized design allows us to assess millions of candidate solutions per second, leading to high quality maximum a-posterior (MAP) estimates, even for hard instances. We investigate the expected run-time of our solver and devise new ultra-sparse parity constraints to combine our device with the WISH approximation scheme. A SIMD-like packing strategy further allows us to solve multiple MAP instances at once, resulting in high efficiency and an additional speed-up. Numerical experiments show that our quantum-inspired approach produces accurate and robust results. While pure software implementations of the WISH algorithm typically run on large compute clusters with hundreds of CPUs, our results are achieved on two FPGA boards which both consume below 10 Watts. Moreover, our results extend seamlessly to adiabatic quantum computers.