Reconstruction of quantum channel via convex optimization

Area of Science:

• Quantum Information Science
• Quantum Computing
• Machine Learning

Background:

• Quantum process tomography (QPT) is crucial for characterizing unknown quantum processes.
• Standard QPT can yield unphysical results, leading to information loss.
• Convex optimization offers a potential solution for robust and accurate QPT.

Purpose of the Study:

• To reconstruct quantum channels using convex optimization.
• To evaluate the performance of convex optimization against other methods.
• To demonstrate the applicability of convex optimization for analyzing quantum channel properties.

Main Methods:

• Reconstruction of the seawater channel using convex optimization.
• Testing the method on seven fundamental quantum gates.
• Comparison with standard-inversion and norm-optimization using cost function and state deviation.

Main Results:

• Convex optimization provides a more precise and robust estimation of process matrix elements.
• The method requires fewer preliminary resources compared to other approaches.
• Reconstructions of non-unitary channels achieved up to 99.5% accuracy.

Conclusions:

• Convex optimization is a superior method for quantum process tomography, ensuring physical results.
• This approach facilitates deeper analysis of quantum channel properties, including phase transitions and Hamiltonians.
• The integration of QPT with convex optimization paves the way for machine learning of quantum channels.