Tomography of Quantum States from Structured Measurements via quantum-aware transformer

TL;DR

This paper introduces a quantum-aware transformer model for quantum state tomography that leverages the structured nature of quantum measurements, achieving high-fidelity reconstructions and robustness against noise through innovative architecture and loss functions.

Contribution

The paper proposes a novel quantum-aware transformer architecture that explicitly incorporates quantum measurement structure and fidelity metrics for improved quantum state reconstruction.

Findings

Outperforms existing methods in fidelity of reconstructed states

Demonstrates robustness against experimental noise

Validated through simulations and IBM quantum computer experiments

Abstract

Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized function to translate experimentally measured statistics into physical density matrices. However, the specific structure of quantum measurements for characterizing a quantum state has been neglected in previous work. In this paper, we explore the similarity between highly structured sentences in natural language and intrinsically structured measurements in QST. To fully leverage the intrinsic quantum characteristics involved in QST, we design a quantum-aware transformer (QAT) model to capture the complex relationship between measured frequencies and density matrices. In particular, we query quantum operators in the architecture to facilitate informative representations of quantum data and integrate the Bures distance into the loss function to evaluate quantum state fidelity, thereby enabling the reconstruction of quantum states from measured data with high fidelity. Extensive simulations and experiments (on IBM quantum computers) demonstrate the superiority of the QAT in reconstructing quantum states with favorable robustness against experimental noise.