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Quantum Speedups for Multiproposal MCMC.

Chin-Yi Lin1, Kuo-Chin Chen2, Philippe Lemey3

  • 1Department of Physics, National Taiwan University, Taipei, Taiwan.

Bayesian Analysis
|September 25, 2025
PubMed
Summary
This summary is machine-generated.

Quantum parallel MCMC (QPMCMC2) offers significant speedups for sampling challenging distributions. This new strategy requires only O(1) target evaluations and O(log P) qubits, improving efficiency for complex models like bacterial evolutionary networks.

Keywords:
Bayesian phylogeneticsIsing modelsMCMCquantum algorithms

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Area of Science:

  • Quantum Computing
  • Computational Statistics
  • Statistical Physics

Background:

  • Multiproposal Markov chain Monte Carlo (MCMC) algorithms enhance sampling efficiency for complex target distributions.
  • Classical MCMC requires O(P) target evaluations per step with P proposals, limiting scalability.
  • Prior quantum MCMC (QPMCMC) achieved O(sqrt(P)) evaluations but retained O(P) overall complexity due to proposal generation.

Purpose of the Study:

  • Introduce a novel, faster quantum multiproposal MCMC strategy: QPMCMC2.
  • Achieve significant computational speedups by reducing target evaluations and qubit requirements.
  • Demonstrate the applicability and efficiency of QPMCMC2 on complex graphical models.

Main Methods:

  • Developed QPMCMC2 utilizing a Tjelmeland distribution for proposal generation close to the input state.
  • Analyzed QPMCMC2 complexity, showing O(1) target evaluations and O(log P) qubits for P proposals.
  • Ensured the QPMCMC2 Markov kernel maintains detailed balance exactly and is fully explicit for graphical models.

Main Results:

  • QPMCMC2 achieves a substantial reduction in computational cost compared to classical and previous quantum MCMC methods.
  • The algorithm was successfully applied to Ising-type models on bacterial evolutionary networks.
  • Significant speedups were observed in Bayesian ancestral trait reconstruction for a dataset of 248 Salmonella bacteria.

Conclusions:

  • QPMCMC2 represents a significant advancement in quantum MCMC, offering unprecedented efficiency for sampling.
  • The method's exact detailed balance and explicit nature broaden its applicability to various graphical models.
  • QPMCMC2 shows great promise for accelerating complex statistical inference tasks in fields like evolutionary biology.