Efficient quantum state tomography.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Measurement

Background:

• Quantum state tomography (QST) is crucial for verifying quantum devices but becomes computationally intractable for large systems due to exponential scaling.
• Current QST methods require an exponentially increasing number of measurements and processing power with system size, limiting their application.

Purpose of the Study:

• To develop novel QST schemes that overcome the exponential scaling limitations of traditional methods.
• To enable efficient verification and benchmarking of larger quantum systems.

Main Methods:

• Introduced two QST schemes with favorable scaling properties compared to direct tomography.
• One scheme utilizes a constant number of subsystem unitary operations.
• The other scheme employs local measurements with advanced post-processing.

Main Results:

• Both presented schemes exhibit linear scaling in experimental operations and polynomial scaling in post-processing with system size.
• These methods are applicable to diverse quantum states, especially matrix product states.
• Rigorous certification of reconstructed state accuracy is possible without prior assumptions.

Conclusions:

• The developed QST schemes offer a practical solution for scaling quantum state verification.
• These advancements are vital for the progress of quantum computing and related technologies.
• The new methods significantly reduce the resource overhead for characterizing quantum systems.