Scalable Quantum Tomography with Fidelity Estimation

Abstract

We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We prove the validity of the scheme theoretically, and we perform numerically simulated experiments on several target states including three typical quantum information states and randomly initiated states, demonstrating its efficiency and robustness. The number of replicas required by a certain convergence criterion grows in the manner of low-degree polynomial when the system scales, thus the scheme achieves high scalability that is crucial for practical quantum state tomography.

5 pages of main text including 5 figures, appended by 4 appendices including 1 figure. GitHub: https://github.com/congzlwag/BornMachineTomo

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• Hamiltonian-Driven Shadow Tomography of Quantum States
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• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Quantum State Tomography for Matrix Product Density Operators
• Neural networks in quantum many-body physics: a hands-on tutorial
• Observing Schrödinger's Cat with Artificial Intelligence: Emergent Classicality from Information Bottleneck
• Learning topological states from randomized measurements using variational tensor network tomography
• Quantum state tomography with disentanglement algorithm
• On the connection between least squares, regularization, and classical shadows
• Learning quantum symmetries with interactive quantum-classical variational algorithms
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States
• Quantum Machine Learning for State Tomography Using Classical Data