Fidelity Estimation for Qudits Reveals Resource Scaling with Nonstabilizerness.

Researchers develop efficient fidelity estimation protocols for quantum states and channels utilising qudit systems with odd prime dimensions. These protocols, requiring measurement of a constant number of operators, demonstrate that metrics quantifying nonstabilizerness, such as Wigner rank and mana, directly relate to the complexity of fidelity estimation.

The accurate characterisation of quantum states and the processes that manipulate them represents a persistent challenge in the development of quantum technologies. Achieving reliable performance necessitates precise benchmarking, yet the inherent fragility of quantum information demands efficient methods for fidelity estimation, particularly on devices susceptible to noise. Researchers at The Hong Kong University of Science and Technology (Guangzhou), including Zhiping Liu, Kun Wang, and Xin Wang, address this need in their work, “Quantum Fidelity Estimation in the Resource Theory of Nonstabilizerness”. They propose novel protocols for estimating fidelity in qudit systems—quantum systems generalising qubits—with odd prime dimensions, leveraging concepts from the resource theory of nonstabilizerness. This framework examines the computational power afforded by quantum states and operations that extend beyond those stabilised by specific symmetries, offering a pathway to more efficient fidelity assessment. Their protocols require measuring only a limited number of quantum properties, with the complexity of the estimation directly linked to mathematically defined measures of nonstabilizerness, such as Wigner rank and mana, providing a clear relationship between theoretical resources and practical implementation.

Quantum fidelity estimation, a critical process for validating and benchmarking quantum devices, benefits from newly developed protocols that demonstrate enhanced efficiency, particularly when applied to qudits – quantum systems possessing d distinct levels. Researchers establish a direct correlation between the resource requirements for accurate fidelity estimation and the non-stabilizerness of the quantum state or channel under investigation. Non-stabilizerness, a measure of how far a quantum state or channel deviates from being describable by a stabiliser state, dictates the computational complexity of determining how closely a realised quantum state matches the intended one.

The protocols achieve fidelity estimation utilising a fixed number of measurements, a significant improvement over methods whose resource demands scale with system size. Crucially, the resource requirements increase exponentially with the non-stabilizerness, indicating that more complex quantum systems necessitate proportionally greater computational effort for accurate characterisation. This relationship provides a quantifiable link between the inherent complexity of a quantum system and the practical challenges of verifying its performance.

These methods remain computationally tractable, meaning they are efficiently implementable, for quantum states and channels possessing efficient classical representations. This constraint acknowledges the limitations of current computational resources and focuses on systems where classical simulation, even if approximate, is feasible. The protocols employ an importance weighting scheme during measurement selection, prioritising those measurements that yield the most information about the fidelity. This strategic approach optimises the efficiency of the estimation process, reducing the number of measurements required to achieve a given level of accuracy.

The findings have direct implications for the development of robust benchmarking strategies for quantum devices. Accurate fidelity estimation is essential for validating device performance, identifying sources of error, and ultimately, building reliable quantum technologies. Ongoing research extends these protocols to encompass more complex quantum systems and incorporates realistic noise models, aiming to enhance their practical applicability and address the challenges posed by imperfect quantum hardware.