Constrained shadow tomography for molecular simulation on quantum devices.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Computational Physics

Background:

• Quantum state tomography is essential for characterizing quantum systems but faces scalability challenges due to high measurement and computational costs.
• Classical shadows offer an efficient alternative for predicting observables using randomized measurements, but reconstructing detailed states remains difficult.

Purpose of the Study:

• To introduce a novel bi-objective semidefinite programming approach for constrained shadow tomography.
• To reconstruct the two-particle reduced density matrix (2-RDM) from noisy or incomplete classical shadow data.
• To enhance the accuracy, noise resilience, and scalability of quantum state reconstruction.

Main Methods:

• Developed a bi-objective semidefinite programming framework for constrained shadow tomography.
• Integrated N-representability constraints and nuclear-norm regularization into the optimization process.
• Reconstructed the two-particle reduced density matrix (2-RDM) by balancing fidelity to shadow measurements with energy minimization.

Main Results:

• The proposed method successfully reconstructs N-representable 2-RDMs from noisy or incomplete shadow data.
• The approach mitigates noise and sampling errors, ensuring physical consistency in reconstructed quantum states.
• Demonstrated significant improvements in accuracy, noise resilience, and scalability through numerical and hardware experiments.

Conclusions:

• The constrained shadow tomography method provides a robust foundation for physically consistent fermionic state reconstruction.
• This technique enhances the reliability of quantum simulations by improving the quality of reconstructed quantum states.
• The bi-objective optimization framework offers a scalable solution for advanced quantum information processing tasks.