Rapid characterisation of linear-optical networks via PhaseLift

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 energyefficient 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.

Architecture agnostic algorithm for reconfigurable optical interferometer programming

“…The J F R Frobenius metric requires exact measurement of the unitary elements' modulus and phase. Several reconstruction methods have been proposed and verified [16,21,[28][29][30]. Some of them [21,28] provide only partial information about the transformation matrix of the interferometer omitting phases which are impossible to reconstruct using the methodspecific dataset.…”

“…Several reconstruction methods have been proposed and verified [16,21,[28][29][30]. Some of them [21,28] provide only partial information about the transformation matrix of the interferometer omitting phases which are impossible to reconstruct using the methodspecific dataset. Any method will inevitably suffer from the path-dependent optical loss which is impossible to distinguish and attribute to the particular path inside the circuit.…”

“…This brings us to the first step of our learning algorithm -the reconstruction of the parameters of the basis matrices utilizing the information from the training set T gathered from the device of interest (see Fi.1b)). The set T includes M pairs ( Ū (i) , Φ(i) ) obtained by seeding the device with random phase shifts Φ(i) and applying the unitary reconstruction procedure of choice [16,21] to get the Ū (i) . The basis matrices U are then determined as the solution of the optimization problem…”

“…The basis matrices U are sampled randomly from the Haar-uniform distribution using the QR decomposition [22]. In the real-life setting the elements of T are the outcomes Ū (i) rec of the unitary reconstruction [16,21] algorithms applied to the reconfigurable interferometer programmed with the phases Φ(i) . The subtleties of gathering the appropriate training set experimentally are discussed in Sec.…”

Characterization of multimode linear optical networks

“…In addition, it cannot be used in the presence of mode-dependent losses in the collection stages. Other black-box algorithms based on coherent light measurements always require high phase stability during the scan in the input and output sections, [31][32][33] thus making them not viable for optical setups with in-fiber connections, which are nevertheless typical for integrated photonic devices. The last classes we mention are machine-learning algorithms, 34,35 which need large sets of data to learn the correct transformation.…”