26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Locally Purified Tensor Networks for Quantum Optics

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Poster AIP | Quantum Science and Technology (QST)

Speaker

Hugo Stackhouse (The University of Sydney)

Description

Tensor networks are well known for their ability to efficiently model dynamics of highly complex systems, from correlations in many-body quantum systems to rich structure in real-world machine-learning datasets. A key challenge of applying tensor-network techniques to quantum optics is that many physically interesting systems are open, and the standard tensor network standard compression schemes do not preserve positive semidefiniteness: an essential property of physically realistic mixed quantum states that is computationally intractable to check. We approach this problem using Locally Purified Tensor Networks (LPTNs), an ansatz that certifies positive semidefiniteness by modelling the Cholesky decomposition of a many-body density matrix. We present two paradigms where LPTNs efficiently model multi-modal states of light.

1) Recently, it has been shown that tensor-network machine learning is very efficient at reconstructing joint probability distributions from datasets of time-series measurements. A natural setting for this algorithm is homodyne tomography, where time traces of electric field quadratures are used to reconstruct optical quantum states to high fidelity. We combine maximum-likelihood homodyne tomography with state-of-the art tensor-network machine learning methods to reconstruct an LPTN representation of highly multi-modal, mixed states of light from homodyne quadrature measurements.

2) A very challenging, yet fundamental problem in quantum optics is the study of light transmitted through an array of atomic media. Light-matter systems involving unidirectional waveguides are of special interest, as they effectively model a large class of disordered 1D systems but with better computational scaling. Recent work has examined the scattering of states of squeezed vacuum off quantum emitters, demonstrating they can generate photonic states useful for quantum computing. We demonstrate an LPTN-based time evolution algorithm for simulating these light-matter interactions in a waveguide-QED formalism.