Krylov Shadow Tomography: Efficient Estimation of Quantum Fisher Information

Area of Science:

• Quantum Information Science
• Applied Mathematics
• Quantum Computing

Background:

• Estimating quantum Fisher information (QFI) is crucial for quantum technologies.
• High nonlinearity poses challenges for QFI estimation in large quantum systems.

Purpose of the Study:

• To develop a resource-efficient and experimentally feasible method for estimating QFI in large quantum systems.
• To formulate a hierarchy of nonpolynomial lower bounds on QFI.

Main Methods:

• Integration of the Krylov subspace method with shadow tomography, termed Krylov shadow tomography.
• Formulation of nonpolynomial lower bounds on QFI expressed as expected values of Hankel matrix inverses.
• Utilizing shadow tomography to access these matrix inverses.

Main Results:

• A strict hierarchy of nonpolynomial lower bounds on QFI is established.
• The highest bound derived through Krylov shadow tomography precisely matches the QFI.
• All bounds are shown to be accessible via shadow tomography.

Conclusions:

• Krylov shadow tomography offers an efficient and experimentally viable approach for QFI estimation.
• This method enables the calculation of both nonpolynomial QFI bounds and the exact QFI.
• The technique addresses the long-standing challenge of QFI estimation in large quantum systems.