Researchers Define Time-Ordered Free Energy in Quantum Systems

Ruo Cheng Huang of the Nanyang Technological University and colleagues from Beyond Institute for Theoretical Science (BITS) and Institute of Advanced Intelligence and Computing (IAIC) have defined time-ordered free energy (TOFE) as the maximum work obtainable from temporally correlated quantum systems, constrained by knowledge of only past events.

The team developed a dynamic programming algorithm with linear time complexity relative to sequence length. This algorithm reveals that maximising energy gain at each step is not always optimal, with the key value identified as kBT ln 2. TOFE is a new metric quantifying the potential work obtainable from quantum systems evolving over time. The measurement accounts for an agent’s inability to foresee future states, limiting actions to responses based on past observations.

The team demonstrated that consistently maximising energy gain at each step does not guarantee the highest overall energy harvest; instead, a different approach proves more effective. This measurement considers an agent’s limitations, acting only on past events, mirroring scenarios where future prediction is impossible.

The team’s approach uses dynamic programming, solving complex problems by breaking them into simpler, overlapping subproblems. This finding challenges conventional approaches to sequential energy harvesting and opens questions about designing agents for temporally correlated quantum environments. Linear time complexity unlocks analysis of temporally correlated quantum systems A dynamic programming approach achieved linear scaling of time complexity with sequence length, a substantial improvement over previous exponential methods. This advancement enables the analysis of quantum state sequences previously considered intractable due to computational limitations, as sequences exceeding a few steps were beyond the reach of existing algorithms. Defining time-ordered free energy (TOFE) established a new benchmark for quantifying the maximum work obtainable from temporally correlated quantum systems operating under causal constraints. Work at Nanyang Technological University and A*STAR’s Centre for Quantum Technologies showed that enforcing temporal causality, restricting actions to utilise only past information, creates an unavoidable work deficit when harvesting quantum energy. Maximising long-term energy yield requires agents to forgo immediate gains to obtain predictive information about future extraction opportunities, revealing a trade-off. The current model assumes complete knowledge of the quantum source, and extending this to scenarios demanding simultaneous learning of both source dynamics and optimal extraction strategies presents a challenge. While these findings extend beyond theoretical understanding, the unavoidable work deficit indicates a fundamental limit to quantum energy harvesting, prompting investigation into strategies for lessening its effects. This also opens avenues for exploring the relationship between information acquisition and energy expenditure in quantum systems, potentially guiding the design of more efficient energy harvesting protocols. Time-ordered free energy as a metric for quantifying harvestable energy in Markovian systems Establishing a framework for quantifying energy harvesting from quantum systems offers potential benefits across diverse fields, ranging from nanoscale devices to advanced quantum technologies. However, the modelling relies on systems generated by hidden Markov machines, raising a critical question about the broader applicability of these findings. Do the observed benefits extend to more complex, non-Markovian processes where the future is not entirely dictated by the past? This metric, a way to quantify usable energy from changing quantum systems, provides a baseline for understanding energy harvesting potential in controlled environments. Establishing this benchmark allows researchers to accurately measure improvements as they incorporate more realistic dynamics, even if real-world quantum systems are more complex and unpredictable than these initial models. It is vital for developing autonomous machines operating with limited knowledge. By utilising dynamic programming, a technique breaking down complex problems into simpler steps, researchers achieved a linear relationship between computational time and the length of the quantum state sequence analysed. The research identified time-ordered free energy (TOFE) as a measure of the maximum work obtainable from temporally correlated quantum systems operating under causal constraints. Researchers demonstrated a method to determine the optimal strategy for energy extraction, with computational time scaling linearly with the length of the analysed quantum state sequence. The findings reveal a fundamental limit to quantum energy harvesting, indicated by an unavoidable work deficit, and suggest further investigation into minimising this effect. 👉 More information 🗞 Time-ordered free energy in correlated quantum systems: An agentic approach ✍️ Ruo Cheng Huang, Isha Singh Le Xue, Yuxuan Qu, Paul M. Riechers, Varun Narasimhachar and Mile Gu 🧠 ArXiv: https://arxiv.org/abs/2608.12942 Stay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: