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

Sanjay Sharma1, Shyam Akashe2, Govind Murari Upadhyay3

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Summary
This summary is machine-generated.

Classical shadows offer an efficient method for quantum state reconstruction, reducing measurement complexity. This technique accurately estimates quantum states, like Bell states, with high fidelity, even on noisy hardware.

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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.