I contributed to an article titled “Researchers Explore Quantum-Inspired Optimization” in the December 2021 edition of the Pure AI web site. See https://pureai.com/articles/2021/12/01/quantum-inspired-optimization.aspx.

Quantum-inspired optimization starts with a standard algorithm, such as particle swarm optimization or simulated annealing, and modifies the algorithm by using one of many ideas adapted from physics quantum behavior. Quantum-inspired optimization (QIO) is not the same as quantum computing (QC). QIO uses standard hardware and software, as opposed to QC which uses exotic hardware and highly specialized software.

Left: An example of standard simulated annealing to solve the Traveling Salesman Problem with n = 30 cities. Right: The same problem solved using quantum inspired simulated annealing.

Quantum-inspired annealing incorporates the idea of quantum particle tunneling. Briefly, a quantum particle will usually transition to an adjacent state. But sometimes a quantum particle will jump to a non-adjacent state. Motivated by this phenomenon, one possible realization of quantum-inspired annealing is:

create an initial random guess solution
set large starting temperature
set current time
loop many times
  with small probability based on current time
    create a tunneling non-adjacent candidate
  else
    create an adjacent candidate solution

  if candidate is better than current then
    replace the current solution with candidate
  else-if candidate is worse
    replace current anyway with probability
 based on current temperature
  end-if
  
  reduce temperature slightly
end-loop
return best solution found

I’m quoted in the article:

Dr. James McCaffrey from Microsoft Research works with combinatorial optimization and swarm optimization. McCaffrey commented, “Quantum-inspired optimization techniques have the potential to make a big impact in several fields.” He added, “Some of my colleagues and I believe that when more compute processing power becomes available, quantum-inspired optimization may provide significant breakthroughs for training deep neural networks with billions or trillions of weights.”

A quantum-related illustration by digital artist Olena Shmahalo from “Mathematicians Prove a 2D Version of Quantum Gravity Works” in Wired Magazine.