# Quantum Fidelity Estimation in the Resource Theory of Nonstabilizerness

**Authors:** Zhiping Liu, Kun Wang, Xin Wang  
**arXiv:** [2506.12938](https://arxiv.org/abs/2506.12938)  
**Date:** 2025-06-15  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2506.12938v1/

## Key points

- Authors Zhiping Liu, Kun Wang, and Xin Wang focus on quantum fidelity estimation in the Resource Theory of Nonstabilizerness.
- Stabilizer operations are crucial in fault-tolerant quantum computing.
- Non-stabilizer resources play a key role in enabling universal quantum computation through state injection.
- Efficient fidelity estimation protocols are proposed for both quantum states and channels within the resource theory of nonstabilizerness, particularly for qudit systems with odd prime dimensions.
- The protocols require measuring only a constant number of phase-space point operator expectation values selected randomly based on an importance weighting scheme customized to the target state.
- Nonstabilizerness measures like Wigner rank and mana can quantify the sample complexity of the proposed protocols, providing operational insights into fidelity estimation tasks.
- There is a fundamental trade-off where fidelity estimation for general quantum states and channels may demand exponentially scaling resources with their nonstabilizerness, but remains tractable for states and channels allowing efficient classical simulation.
- The study enhances fidelity estimation techniques within nonstabilizer resources, offering practical implications for benchmarking quantum systems in noisy environments and advancing robust quantum computing methodologies.

## Summary

In their work titled "Quantum Fidelity Estimation in the Resource Theory of Nonstabilizerness," authors Zhiping Liu, Kun Wang, and Xin Wang delve into the crucial task of quantum fidelity estimation for benchmarking quantum states and processes on noisy quantum devices. They highlight the significance of stabilizer operations in fault-tolerant quantum computing, while also emphasizing the role of non-stabilizer resources in enabling universal quantum computation through state injection. The authors propose several efficient fidelity estimation protocols tailored for both quantum states and channels within the resource theory of nonstabilizerness, with a specific focus on qudit systems characterized by odd prime dimensions. These protocols are designed to require measuring only a constant number of phase-space point operator expectation values, with operators selected randomly based on an importance weighting scheme customized to the target state. One notable aspect of their work is the demonstration that mathematically defined nonstabilizerness measures such as Wigner rank and mana can quantify the sample complexity of the proposed protocols. This insight provides a clear operational interpretation in the fidelity estimation task, revealing a fundamental trade-off: while fidelity estimation for general quantum states and channels may demand resources that scale exponentially with their nonstabilizerness, the task remains tractable for states and channels that allow for efficient classical simulation. Overall, this study contributes valuable insights into enhancing fidelity estimation techniques within the realm of nonstabilizer resources, offering practical implications for benchmarking quantum systems in noisy environments and advancing towards more robust quantum computing methodologies.