A computationally efficient approach to quantum state reconstruction using robust classical shadows

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Measurement

Background:

• Quantum state tomography is essential for characterizing quantum systems but faces scalability challenges.
• Classical shadows provide a compressed quantum state representation using randomized measurements.
• This method reduces measurement complexity compared to full quantum tomography.

Purpose of the Study:

• To investigate classical shadows as an efficient alternative for reconstructing quantum states.
• To assess the fidelity and accuracy of classical shadows in estimating a Bell state.
• To demonstrate the scalability and feasibility of shallow shadow tomography on noisy quantum hardware.

Main Methods:

• A quantum circuit was used to generate a Bell state.
• 1000 snapshots were collected to construct the classical shadow.
• Reconstructed density matrices were evaluated using fidelity and norm difference metrics.

Main Results:

• Reconstruction fidelity stabilized around 0.98-1.0 as the number of snapshots increased.
• Norm difference decreased, indicating convergence towards the ideal Bell state.
• Shallow shadow tomography demonstrated up to fivefold measurement savings in experiments.

Conclusions:

• Classical shadows provide an efficient and accurate method for quantum state estimation.
• The technique is scalable and effective even with a limited number of snapshots.
• Shallow shadow tomography shows promise for characterizing quantum states on noisy quantum processors.