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Quantum Comb Tomography via Learning Isometries on Stiefel Manifold
Ze-Tong Li1,2,3, Xin-Lin He1,2, Cong-Cong Zheng1,2
1Southeast University, State Key Laboratory of Millimeter Waves, Nanjing 210096, China.
Physical Review Letters
|February 6, 2025
Summary
We present an efficient quantum comb tomography method using fewer parameters by learning isometries. This approach reduces computational burdens and enables dimension-reduced quantum comb tomography with high accuracy.
Area of Science:
- Quantum Information Science
- Quantum Computation
- Mathematical Physics
Background:
- Quantum combs are crucial for quantum information science.
- Current reconstruction methods face computational challenges due to high parameter requirements and physical constraints.
Purpose of the Study:
- To develop an efficient method for quantum comb tomography.
- To overcome computational encumbrances associated with existing techniques.
Main Methods:
- Propose a novel method for quantum comb tomography.
- Learn isometries on the Stiefel manifold through unconstrained optimization.
- Employ stepwise isometry estimation for truncated quantum comb information.
Main Results:
- Significantly reduced parameter requirements compared to existing methods.
- Demonstrated capability to provide information of truncated quantum combs.
- Achieved dimension-reduced quantum comb tomography with bounded error.
Conclusions:
- The proposed method offers high accuracy and efficiency for quantum comb tomography.
- This approach alleviates computational burdens in quantum information science.
- Enables more practical and scalable quantum comb reconstructions.
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