Machine-learning Augmented Shadow Tomography (Part I)

With the rapid advancement of quantum computing devices, characterization and validation of many-body quantum states realized on such devices remains an essential challenge. While the full tomographic reconstruction of the density matrix would offer complete characterization of a quantum state, such reconstruction is prohibitively costly for systems larger than a few qubits. Alternatives to tomographic reconstruction are estimating operator expectation values using classical shadows [1] and generative modeling using neural networks such as attention based quantum state tomography (AQT) [2, 3]. We propose to combine the best of both approaches by using AQT-augmented data for classical shadow: Machine-learning Augmented Shadow Tomography (MAST). In this first talk, we present the classical shadow element and the AQT element of the MAST. We also discuss merits of various metrics and subtleties in using traditional metrics designed for full tomography on the classical shadow and on AQT.

1. Huang et al, Nature Physics 16, 1050 (2020)

2. Carrasquilla et al, Nat. Mach. Int. 1, 155 (2019)

3. Cha et al, arxiv:2006.12469