Learning Arbitrary Complex Matrices by Interlacing Amplitude and Phase Masks with Fixed Unitary Operations

• URL: http://arxiv.org/abs/2312.05648v1
• Date: Sat, 9 Dec 2023 19:27:57 GMT
• Title: Learning Arbitrary Complex Matrices by Interlacing Amplitude and Phase Masks with Fixed Unitary Operations
• Authors: Matthew Markowitz, Kevin Zelaya, Mohammad-Ali Miri
• Abstract summary: We introduce a novel architecture for physically implementing discrete linear operations. The proposed architecture enables the development of novel families of programmable photonic circuits for on-chip analog information processing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide range of applications as one of the most fundamental mathematical operations there has been a particular interest in programmable photonic circuits that perform matrix-vector multiplication. In this regard, there has been great interest in developing novel circuit architectures for performing matrix operations that are compatible with the existing photonic integrated circuit technology which can thus be reliably implemented. Recently, it has been shown that discrete linear unitary operations can be parameterized through diagonal phase parameters interlaced with a fixed operator that enables efficient photonic realization of unitary operations by cascading phase shifter arrays interlaced with a multiport component. Here, we show that such a decomposition is only a special case of a much broader class of factorizations that allow for parametrizing arbitrary complex matrices in terms of diagonal matrices alternating with a fixed unitary matrix. Thus, we introduce a novel architecture for physically implementing discrete linear operations. The proposed architecture is built on representing an $N \times N$ matrix operator in terms of $N+1$ amplitude-and-phase modulation layers interlaced with a fixed unitary layer that could be implemented via a coupled waveguide array. The proposed architecture enables the development of novel families of programmable photonic circuits for on-chip analog information processing.

Related papers

• Low-depth, compact and error-tolerant photonic matrix-vector multiplication beyond the unitary group [0.0]
  We introduce a novel architecture of photonic circuits capable of implementing non-unitary transfer matrices. Our architecture exploits compact low-depth beam-splitter meshes rather than bulky fully connected mixing blocks. We have shown that photonic circuits designed with our architecture have lower depth than their standard counterparts and are extremely tolerant to hardware errors.
  arXiv  Detail & Related papers  (2024-08-01T16:06:51Z)
• Multivariate trace estimation using quantum state space linear algebra [13.175145217328534]
  We present a quantum algorithm for approximating multivariate traces, i.e. the traces of matrix products. Our approach operates independently of the availability of specialized hardware like QRAM.
  arXiv  Detail & Related papers  (2024-05-02T08:54:28Z)
• How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations [98.7450564309923]
  This paper takes initial steps on understanding in-context learning (ICL) in more complex scenarios, by studying learning with representations. We construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size.
  arXiv  Detail & Related papers  (2023-10-16T17:40:49Z)
• Universal Unitary Photonic Circuits by Interlacing Discrete Fractional Fourier Transform and Phase Modulation [0.0]
  We introduce a novel parameterization of complex unitary matrices, which allows for the efficient implementation of arbitrary linear discrete unitary operators. We show that such a configuration can represent arbitrary unitary operators with $N+1$ phase layers. We propose an integrated photonic circuit realization of this architecture with coupled waveguide arrays and reconfigurable phase modulators.
  arXiv  Detail & Related papers  (2023-07-14T00:23:14Z)
• All-Photonic Artificial Neural Network Processor Via Non-linear Optics [0.0]
  We propose an all-photonic artificial neural network processor. Information is encoded in the amplitudes of frequency modes that act as neurons. Our architecture is unique in providing a completely unitary, reversible mode of computation.
  arXiv  Detail & Related papers  (2022-05-17T19:55:30Z)
• All-optical graph representation learning using integrated diffractive photonic computing units [51.15389025760809]
  Photonic neural networks perform brain-inspired computations using photons instead of electrons. We propose an all-optical graph representation learning architecture, termed diffractive graph neural network (DGNN) We demonstrate the use of DGNN extracted features for node and graph-level classification tasks with benchmark databases and achieve superior performance.
  arXiv  Detail & Related papers  (2022-04-23T02:29:48Z)
• Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO with Lens Arrays [54.43962058166702]
  millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays have received great attention. In this work, we investigate the joint design of a beam precoding matrix for mmWave MU-MIMO systems with DLA.
  arXiv  Detail & Related papers  (2021-01-05T03:55:04Z)
• Rapid characterisation of linear-optical networks via PhaseLift [51.03305009278831]
  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. We present a novel technique to reconstruct the transfer matrix of linear optical networks.
  arXiv  Detail & Related papers  (2020-10-01T16:04:22Z)
• Multi-View Spectral Clustering with High-Order Optimal Neighborhood Laplacian Matrix [57.11971786407279]
  Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data. This paper proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix. Our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base.
  arXiv  Detail & Related papers  (2020-08-31T12:28:40Z)
• Thermal phase shifters for femtosecond laser written photonic integrated circuits [58.720142291102135]
  Photonic integrated circuits (PICs) are acknowledged as an effective solution to fulfill the demanding requirements of many practical applications in both classical and quantum optics. Phase shifters integrated in the photonic circuit offer the possibility to dynamically reconfigure its properties in order to fine tune its operation or to produce adaptive circuits. We show how thermal shifters to reconfigure photonic circuits can be solved by a careful design of the thermal shifters and by choosing the most appropriate way to drive them.
  arXiv  Detail & Related papers  (2020-04-23T20:09:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.