Quantum Algorithm Counts Optimization Optima Using Decoherence

Malay Marut Das, Mark A. Novotny, Yaroslav Koshka· August 18, 2026 View original

Key takeaways

  • CTPQsd# is a quantum algorithm for counting global optima in classical problems.
  • It uses decoherence of a small probe within a CTPQ state.
  • The algorithm avoids finding individual minima, simplifying the task.
  • It shows promise for #P-hard problems, with identified temperature thresholds for accuracy.

Who benefits

Quantum ComputingMaterials ScienceDrug DiscoveryLogisticsFinance

Summary

Researchers developed CTPQsd#, a quantum algorithm that counts the global optima of classical optimization problems by measuring the decoherence of a small probe within a canonical thermal pure quantum state, avoiding the need to find individual minima.

Counting the exact number of global optima in a classical optimization problem is a computationally intensive task, classified as #P-hard. A new quantum algorithm, named CTPQsd#, has been developed to tackle this challenge. This method leverages the properties of a canonical thermal pure quantum (CTPQ) state. The CTPQsd# algorithm determines the degeneracy of an optimization problem by measuring only a small "probe" system, rather than needing to identify each individual minimum. It exploits a subtle perturbative relationship between the decoherence of this probe and the problem's degeneracy when both are part of a CTPQ state. Numerical simulations, up to 20 problem qubits, have demonstrated the algorithm's ability to count global minima, even for highly unstructured problems. The study also quantifies the algorithm's sensitivity to various parameters like temperature, problem size, and energy range. It identifies specific temperature thresholds for exact degeneracy counting and for approximating near-degenerate minima within a defined tolerance. By focusing measurements on a small probe, the protocol significantly reduces the complexity compared to full tomography of the exponentially large problem space.

Why it matters

This breakthrough offers a novel quantum approach to a notoriously difficult computational problem, potentially accelerating solutions in fields like materials science, drug discovery, and logistics optimization once quantum hardware matures.

How to implement this in your domain

  1. 1Monitor advancements in quantum computing hardware capable of implementing CTPQsd# for practical applications.
  2. 2Explore potential use cases in your domain where counting optimal solutions is critical but currently intractable.
  3. 3Collaborate with quantum research teams to understand the algorithm's implications for specific optimization challenges.
  4. 4Evaluate the feasibility of encoding complex classical optimization problems into a quantum framework suitable for this algorithm.

Original post by Malay Marut Das, Mark A. Novotny, Yaroslav Koshka

"arXiv:2608.14941v1 Announce Type: new Abstract: Counting the global optima of a classical optimization problem is a #P-hard task. We develop the canonical thermal pure quantum (CTPQ) state-based degeneracy counting (CTPQsd#) algorithm that determines the number of global optima o…"

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Originally posted by Malay Marut Das, Mark A. Novotny, Yaroslav Koshka on X · view source

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