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Quantum speedup for nonreversible Markov chains
Baptiste Claudon1,2,3, Jean-Philip Piquemal4,5, Pierre Monmarché6,7,8,9
1Advanced Research Department, Qubit Pharmaceuticals, Paris, France. baptiste.claudon@qubit-pharmaceuticals.com.
Nature Communications
|November 28, 2025
Summary
This study introduces quantum algorithms to accelerate nonreversible Markov chains, offering an exponential speedup beyond previous quadratic gains for reversible chains. These quantum computing advancements promise significant impacts across diverse scientific and financial fields.
Area of Science:
- Quantum Computing
- Computational Mathematics
- Statistical Modeling
Background:
- Classical computing faces limitations in solving complex problems.
- Quantum algorithms offer potential speedups for specific computational tasks.
- Previous research focused on quantum acceleration for reversible Markov chains.
Purpose of the Study:
- To develop quantum algorithmic techniques for accelerating nonreversible Markov chain processes.
- To construct Markov chain reversibilizations for enhanced computational efficiency.
- To explore quantum speedups beyond quadratic acceleration for nonreversible processes.
Main Methods:
- Development of novel quantum algorithmic techniques.
- Construction of Markov chain reversibilizations.
- Analysis of quantum speedup for nonreversible processes.
Main Results:
- Achieved an up-to-exponential quantum speedup for nonreversible Markov chains.
- Demonstrated acceleration beyond quadratic gains predicted for reversible chains.
- Established methods for reversibilizing nonreversible Markov chains.
Conclusions:
- Quantum computing can significantly accelerate nonreversible Markov chain processes.
- The developed techniques offer substantial improvements over classical methods.
- Potential for broad applications in statistics, machine learning, and scientific modeling.
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