[Paper Review] Efficient Quantum Tomography with Fidelity Estimation.

Zhaoyu Han, Jun Wang+5 more|arXiv (Cornell University)|Dec 8, 2017

Quantum Information and Cryptography3 citations

TL;DR

This paper proposes a machine learning-based quantum tomography scheme for pure states that enables efficient reconstruction with built-in fidelity estimation. It achieves sub-exponential measurement scaling, making large-scale quantum state tomography feasible in practice.

ABSTRACT

We propose a quantum tomography scheme for pure states which adopts machine learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic state. We prove the validity of the scheme theoretically and perform numerically simulated experiments on several typical target quantum states such as W, cluster and dimer states. We find that the required number of measurements to meet the convergence criterion does not grow exponentially in the number of qubits, thus the scheme achieves high efficiency that is crucial for large-scale quantum states tomography in a laboratory.

Motivation & Objective

• Address the challenge of high resource overhead in quantum state tomography for large-scale quantum systems.
• Develop a method that maintains high fidelity in reconstructed quantum states while minimizing measurement requirements.
• Integrate a reliable fidelity estimation mechanism to assess the reliability of reconstructed states without full tomography.
• Enable scalable tomography of complex entangled states such as W, cluster, and dimer states in realistic experimental settings.

Proposed method

• Employ machine learning techniques to reconstruct pure quantum states from measurement data.
• Design a fidelity estimation module that evaluates the reliability of the reconstructed state using only a subset of measurement outcomes.
• Use a variational approach to optimize the state reconstruction process, reducing the number of required measurements.
• Formulate the reconstruction problem as an optimization task with fidelity as a regularizing constraint.
• Validate the method numerically on benchmark entangled states including W, cluster, and dimer states.
• Ensure theoretical validity of the scheme through rigorous proof of convergence and fidelity estimation accuracy.

Experimental results

Research questions

• RQ1 Can machine learning reduce the number of measurements required for pure state tomography without sacrificing fidelity?
• RQ2 How accurately can the fidelity of a reconstructed quantum state be estimated using only partial measurement data?
• RQ3 Does the proposed scheme scale efficiently with increasing qubit number, avoiding exponential measurement growth?
• RQ4 Can the method reliably reconstruct complex entangled states such as W and cluster states in simulation?
• RQ5 Is the fidelity estimation mechanism robust and self-consistent across different types of target quantum states?

Key findings

• The proposed scheme achieves convergence with a number of measurements that does not grow exponentially with the number of qubits.
• Fidelity estimation is successfully integrated into the reconstruction process, enabling real-time reliability assessment.
• Numerical simulations confirm accurate reconstruction of W, cluster, and dimer states with high fidelity.
• The method demonstrates scalability, making large-scale quantum tomography practically feasible.
• The theoretical validity of the scheme is rigorously proven, supporting its reliability in experimental applications.
• The approach significantly reduces resource overhead compared to standard quantum tomography protocols.