Rapid characterisation of linear-optical networks via PhaseLift
arXiv:2010.00517
Abstract
Linear-optical circuits are elementary building blocks for classical and quantum information processing with light. In particular, due to its monolithic structure, integrated photonics offers great phase-stability and can rely on the large scale manufacturability provided by the semiconductor industry. New devices, based on such optical circuits, hold the promise of faster and energy-efficient computations in machine learning applications and even implementing quantum algorithms intractable for classical computers. However, this technological revolution requires accurate and scalable certification protocols for devices that can be comprised of thousands of optical modes. Here, we present a novel technique to reconstruct the transfer matrix of linear optical networks that is based on the recent advances in low-rank matrix recovery and convex optimisation problems known as PhaseLift algorithms. Conveniently, our characterisation protocol can be performed with a coherent classical light source and photodiodes. We prove that this method is robust to noise and scales efficiently with the number of modes. We experimentally tested the proposed characterisation protocol on a programmable integrated interferometer designed for quantum information processing. We compared the transfer matrix reconstruction obtained with our method against the one provided by a more demanding reconstruction scheme based on two-photon quantum interference. For 5-dimensional random unitaries, the average circuit fidelity between the matrices obtained from the two reconstructions is 0.993.
arXiv commentmain document: 11 pages with 4 figures, appendix section: 15 pages
References in corpus (17)
- The NumPy array: a structure for efficient numerical computation
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Deep Learning with Coherent Nanophotonic Circuits
- All-Optical Machine Learning Using Diffractive Deep Neural Networks
- Universal Linear Optics
- Quantum process tomography of a controlled-NOT gate
- Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform
- Incoherence-Optimal Matrix Completion
- Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements
- A Partial Derandomization of PhaseLift using Spherical Designs
- Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns
- Quantum process tomography with coherent states
- Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage
- Super-stable tomography of any linear optical device
- On unitary reconstruction of linear optical networks
- Low rank matrix recovery from Clifford orbits
- Quantum Tomography From Few Full-Rank Observables