Quantum Functional Information Metric Reveals Rarer States Outperform Near-perfect Fidelity Circuits in Random Circuit Evolution

The quest to build powerful quantum computers demands not only accurate calculations, but also efficient and robust circuit designs. Rodrigo Pasti and Jonas Krause, both from the Pontifical Catholic University of Paran ́a, now introduce Functional Information, a novel metric that assesses both the usefulness and the rarity of quantum states and circuits. Their work reveals that circuits achieving near-perfect accuracy are not necessarily the most valuable, as slightly imperfect, yet rarer, states can offer significant advantages. By testing this metric through both random circuit sampling and evolutionary optimisation, the researchers demonstrate that prioritising Functional Information sustains exploration, generates more diverse structures, and ultimately favours circuits that are both highly accurate and remarkably robust, positioning it as a powerful tool for advancing quantum computing.

Rarity and Functionality in Quantum States

Scientists have developed a new metric, Quantum Functional Information (QFI), to assess both the usefulness and rarity of quantum states and circuits, moving beyond traditional measures like fidelity or entropy. This work establishes a framework to evaluate how probable a quantum state is while also performing a specific task, linking rarity, structure, and usefulness within the quantum realm. The algebraic definition of QFI proves it is bounded, interpretable, and tunable, providing a precise mathematical foundation for evaluating quantum systems. To validate this metric, the research team employed random circuit sampling and evolutionary algorithms.

Random circuit sampling involved generating millions of quantum circuits and assessing their ability to achieve desired target states, allowing researchers to observe the spontaneous emergence of functional configurations within a vast possibility space. This process established a baseline for the rarity of functional states and provided data for computing QFI curves. Complementing this approach, the team implemented an evolutionary algorithm to efficiently explore the circuit space, guiding the search for circuits that maximize functionality as defined by the QFI metric. Experiments utilizing simulations built within the Qiskit framework enabled precise control over circuit parameters and accurate measurement of fidelity distributions.

By comparing the performance of circuits evolved under fidelity-only optimization with those optimized using QFI, scientists demonstrated that QFI sustains exploration, generates richer structures, and favors robust circuits with high fidelity. Results show that circuits with near-perfect fidelity are less informational than slightly suboptimal, yet rarer, states, highlighting the importance of considering both performance and rarity. This work provides a precise algebraic definition of QFI, proving it is bounded, interpretable, and tunable, opening pathways for future applications in quantum algorithm design and benchmarking.

Rarity Drives Functional Information in Quantum Systems

Scientists have introduced Quantum Functional Information (QFI), a new metric designed to quantify both the usefulness and rarity of quantum states and circuits, moving beyond standard measures like fidelity or entropy. This work establishes a framework to assess how probable quantum states are while also performing a specific task, linking rarity, structure, and usefulness within the quantum domain. The research demonstrates that high fidelity, while desirable, does not necessarily equate to high informational value; instead, slightly suboptimal yet rarer states often possess greater functional information. This finding challenges conventional optimization approaches that prioritize fidelity alone, as these can reduce diversity and robustness in quantum systems.

The researchers validated this metric through both random circuit sampling and evolutionary algorithms, revealing a trade-off between fidelity and rarity. Evolutionary experiments showed that optimizing for Quantum Functional Information sustains exploration, generates richer structures, and favors robust circuits that also achieve high fidelity, unlike fidelity-only optimization which converges quickly but limits diversity. This work positions Quantum Functional Information as a practical tool for circuit design, benchmarking, and exploring emergent patterns within quantum systems, offering a new perspective on the relationship between performance and informational content.