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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Pushing the boundary of quantum advantage in hard combinatorial optimization with probabilistic computers.

Shuvro Chowdhury1, Navid Anjum Aadit2, Andrea Grimaldi3,4

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Probabilistic computers, using Monte Carlo algorithms, offer a scalable classical solution for complex optimization problems. These methods, including adaptive parallel tempering, outperform current quantum annealers, establishing a baseline for quantum advantage.

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Area of Science:

  • Computational physics
  • Quantum computing
  • Optimization algorithms

Background:

  • Quantum computing shows promise but lacks real-world advantage.
  • Classical methods are needed to solve complex optimization problems.

Purpose of the Study:

  • To present probabilistic computers as a scalable classical solution for optimization.
  • To benchmark classical algorithms against quantum annealers.

Main Methods:

  • Co-designing probabilistic computers with hardware for Monte Carlo algorithms.
  • Implementing discrete-time simulated quantum annealing and adaptive parallel tempering.
  • Benchmarking against a leading quantum annealer for 3D spin glasses.

Main Results:

  • Simulated quantum annealing shows improved scaling with increasing replicas.
  • Adaptive parallel tempering scales favorably and outperforms simulated quantum annealing.
  • Field-Programmable Gate Arrays (FPGAs) and specialized chips accelerate algorithms and improve energy efficiency.

Conclusions:

  • Probabilistic computers provide a scalable classical pathway for hard optimization problems.
  • Rigorous classical baselines are established for assessing practical quantum advantage.
  • Adaptive parallel tempering is a promising algorithm for real-world optimization challenges.