Demonstration of robust and efficient quantum property learning with shallow shadows

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum State Tomography

Background:

• Efficient information extraction from quantum systems is vital for quantum information processing.
• Classical shadows offer a method for predicting quantum state properties with limited measurements.
• Standard methods like single-qubit measurements struggle with nonlocal observables.

Purpose of the Study:

• To develop a robust and sample-efficient method for quantum state characterization.
• To address noise limitations in shallow random quantum circuits used for quantum state learning.
• To enhance the prediction of diverse quantum state properties on near-term quantum hardware.

Main Methods:

• Proposed robust shallow shadows protocol utilizing Bayesian inference for noise mitigation.
• Analyzed noise effects on sample complexity and optimal circuit depth.
• Provided theoretical guarantees for error mitigation under various noise models.

Main Results:

• Demonstrated improved sample efficiency for learning high-weight Pauli observables and low-rank properties.
• Experimental validation on a superconducting quantum processor confirmed the method's advantage.
• Successfully predicted state properties like fidelity and entanglement entropy in the presence of realistic noise.

Conclusions:

• Robust shallow shadows offer a scalable and sample-efficient approach for quantum state characterization.
• The protocol effectively mitigates noise, outperforming standard single-qubit measurements.
• This method is suitable for near-term quantum devices, advancing quantum information processing capabilities.