Quantum computing has emerged as one of the most exciting frontiers in modern physics and computer science, promising to revolutionize problem-solving in fields ranging from cryptography to materials science. Among the many challenges in quantum computing, one particularly complex problem is determining the ground state of quantum many-body systems—systems with multiple interacting quantum particles. This problem is computationally demanding even for the most advanced classical computers, as the number of possible configurations grows exponentially with the number of particles involved.
A fascinating aspect of these systems is their interaction with thermal baths, environments with a fixed temperature that can influence their energy states. When a quantum system is placed in a thermal bath, it cools down over time, gradually lowering its energy. However, instead of always reaching its true ground state—the lowest possible energy level—the system may get trapped in a local minimum, where its energy is lower than nearby configurations but not at the absolute minimum. This phenomenon makes optimization particularly challenging, as classical algorithms often struggle to escape these local traps.
In a groundbreaking study published in Nature Physics, researchers at the California Institute of Technology and the AWS Center for Quantum Computing have demonstrated that while finding local minima in quantum systems is classically difficult, quantum computers may have a significant advantage. Their work introduces a new quantum algorithm that simulates natural cooling processes, allowing quantum computers to efficiently identify these local minima.
The research was driven by a fundamental question: Should physicists focus only on ground states, even though they are often difficult to achieve in real-world conditions? According to Hsin-Yuan (Robert) Huang, one of the lead authors of the study, this question challenges conventional wisdom in quantum physics. In classical machine learning, practical algorithms often rely on local minima rather than absolute global minima, leading the researchers to consider whether quantum many-body systems could benefit from a similar approach.
To address this challenge, the researchers combined insights from multiple fields, including quantum thermodynamics, optimization theory, and computational complexity. Their key innovation was defining quantum local minima using thermal perturbations, a concept grounded in real-world physics. When a system cools naturally, it experiences small fluctuations in energy, allowing it to explore different states. By mimicking this process, the researchers devised a method for quantum computers to locate stable low-energy configurations more efficiently than classical methods.
The study revealed that cooling to local minima is classically hard but quantumly easy. To establish this result, the researchers constructed specific quantum systems where any local minimum encodes a universal quantum computation—a problem widely believed to be classically intractable. This finding highlights a fundamental difference between classical and quantum optimization: while classical computers struggle with these energy landscapes, quantum computers can exploit quantum superposition and tunneling to explore multiple configurations simultaneously.
At the heart of the study is the quantum thermal gradient descent algorithm, a novel method that allows quantum computers to simulate natural cooling processes. Unlike classical algorithms, which are often constrained by the landscape of energy states, this quantum approach can move through energy barriers more efficiently, reaching solutions that classical methods fail to find. One of the greatest technical challenges the researchers faced was proving that certain classically hard Hamiltonians (mathematical representations of quantum systems) lack suboptimal local minima, meaning their energy landscapes are smooth and bowl-like. To do this, they used advanced techniques from quantum complexity theory and mathematical physics.
One of the most significant implications of this work is that cooling quantum systems to local minima is a universal quantum computation problem. This means that a quantum computer can efficiently find local minima in energy landscapes, while classical computers cannot—assuming that quantum computers are indeed more powerful than classical ones. This result challenges traditional approaches to studying quantum many-body systems, suggesting that analyzing local minima and the overall energy landscape may be as important as focusing on ground states. By optimizing over the entire landscape, researchers could even discover new physical phenomena, such as anomalous local minima with unexpected properties.
Another major takeaway is that these quantum algorithms can dramatically enhance energy optimization, with potential applications in materials science, chemistry, and physics. For example, when classical algorithms find what they consider the best possible solution, this quantum approach could push beyond those limits, discovering even lower-energy states. This has profound implications for designing new materials, understanding superconductors, and improving chemical reaction modeling.
Looking ahead, the researchers plan to further test and refine their algorithm, applying it to a broader range of scenarios. Their next steps include identifying physically relevant quantum systems with favorable energy landscapes, where their approach could offer practical quantum advantages. Additionally, they are exploring whether these techniques could extend beyond quantum many-body systems to improve classical optimization problems, potentially influencing fields like logistics, finance, and artificial intelligence.
Another exciting avenue of research is the experimental demonstration of these algorithms using near-term quantum devices. While large-scale, fault-tolerant quantum computers are still in development, current quantum hardware may already be able to implement these cooling-based optimization techniques. Moreover, the researchers aim to engineer synthetic quantum processes that outperform even natural cooling, opening up possibilities for new types of quantum simulations and optimizations.
Ultimately, this research represents a significant step toward bridging the gap between theoretical quantum advantage and practical applications. By pioneering new ways to understand and control quantum many-body systems, the team at Caltech and AWS has laid the foundation for future breakthroughs in quantum computing, materials science, and beyond. The ability to efficiently find local minima could reshape how scientists approach quantum optimization, leading to new discoveries and technological advancements that were previously thought to be out of reach.
More information: Chi-Fang Chen et al, Local minima in quantum systems, Nature Physics (2025). DOI: 10.1038/s41567-025-02781-4.