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arXiv:2109.05367 · Nature Communications

Asymptotically fault-tolerant programmable photonics

Ryan Hamerly, Saumil Bandyopadhyay, Dirk Englund

Published Nov 29, 2022• 70 citations
arXivHTMLPDF

Abstract

Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler-the Mach-Zehnder interferometer (MZI)-cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer degrades with increased mesh size, allowing scaling to arbitrarily large meshes. The proposed architectures support progressive self-configuration, are more compact than previous MZI-doubling schemes, and do not require additional phase shifters. This removes a key limitation to the development of very-large-scale programmable photonic circuits.

DOI
10.1038/s41467-022-34308-3

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physics.opticsCross-listedarXiv:2607.14759•Jul 17, 2026
Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler-the Mach-Zehnder interferometer (MZI)-cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer degrades with increased mesh size, allowing scaling to arbitrarily large meshes. The proposed architectures support progressive self-configuration, are more compact than previous MZI-doubling schemes, and do not require additional phase shifters. This removes a key limitation to the development of very-large-scale programmable photonic circuits.
Conventional multiport interferometers based on MZI meshes suffer from component imperfections, which limit their scaling. We introduce two new designs that overcome this limitation: a 3-splitter MZI for generic errors and a broadband MZI+Crossing design for more realistic correlated errors. These architectures, motivated by the correspondence between SU(2) and the Riemann sphere, are more error tolerant than the standard MZI mesh and support progressive self-configuration. Numerical simulations reveal orders-of-magnitude error reductions compared to the standard MZI mesh; moreover, the mesh is asymptotically perfect: the matrix error decreases with mesh size.
Universal linear programmable photonic circuits, composed of an array of Mach-Zehnder interferometers (MZIs), are fidelity-limited devices and are prohibitively difficult to scale. To address these limitations, we propose a compact and non-feedforward recurrent MZI topology wherein light can propagate in both directions. Our recurrent mesh achieves O ( N ) scaling by building imperfect beamsplitters in series to build perfect transformations. We theoretically examine the error tolerance of our proposed recurrent interferometer under imperfect mesh parameters. Our numerical results indicate that our proposed recurrent mesh permits more than an order of magnitude reduction in implementing unitary transformations.
In recent years, there has been growing interest in analog information processing and unconventional computing using Photonic Integrated Circuits (PICs) to address the increasing demands of next-generation computing. This has driven the development of on-chip architectures capable of implementing fundamental linear operations such as matrix-vector multiplication (MVM), which plays a central role in fields such as quantum information processing and the acceleration of deep neural networks. Within the feed-forward paradigm, interleaved meshes of Mach–Zehnder Interferometers (MZIs) have emerged as the leading architecture for programmable integrated photonics (PIP), enabling real-time implementation of arbitrary linear transformations using tunable phase shifter elements. More recently, an alternative class of programmable photonic architectures based on Multi-Plane Light Conversion (MPLC) has been proposed, consisting of alternating diagonal phase-shifter layers and multimode mixing elements. Although these architectures lack a deterministic synthesis algorithm for the phase actuators, they have been shown to offer several advantages over conventional MZI-based architectures. In this thesis we investigate the properties and universal capabilities of MPLC architectures utilizing unequally spaced coupled waveguide arrays (CWAs), with a particular emphasis on the well-known Jx-lattice. Defect tolerance and self-calibration properties are studied, demonstrating substantially greater robustness to imperfections than conventional MZI meshes. We further introduce several extensions of the MPLC architecture that demonstrate its flexibility, such as the redistribution of amplitude modulators and their interchangeable use with phase shifters to realize universal transformations with a near-minimal number of tunable units. Collectively, these results provide a broader understanding of the capabilities of MPLC architectures and establish a foundation for their application as a flexible alternative and complement to MZI-based designs.
The scalability of many programmable photonic circuits is limited by the 2π tuning range needed for the constituent phase shifters. To address this problem, we introduce the concept of a phase-efficient circuit architecture, where the average phase shift is ≪2π. We derive a universal information-theoretic limit to the phase-shift efficiency of universal multiport interferometers and, based on a modified Mach–Zehnder Interferometer (MZI) design, propose a “3-MZI” architecture that approaches this limit to within a factor of 2×, approximately a 10× reduction in average phase shift over the prior art, where the average phase shift scales inversely with system size N as O(1/N). For non-unitary circuits, we show that the 3-MZI saturates the theoretical bound for Gaussian-distributed target matrices. Using this architecture, we show optical neural network training with all phase shifters constrained to ≲0.2 radians without loss of accuracy.
Reconfigurable linear optical networks based on Mach-Zehnder interferometer (MZI) offer significant potential in optical information processing, particularly in emerging photonic quantum computing systems. However, device losses and calibration errors accumulate as network complexity grows, posing challenges in performing precise mapping of matrix operations. Existing architectures, such as Diamond and Bokun, introduce MZI redundancy into Reck and Clements architectures to improve reliability, which increases complexity and differential path losses that limit scalability. We propose a compact topology architecture that achieves 100% fidelity by employing a symmetrical MZI to decouple optical loss from power ratio and introducing extra MZIs to enforce uniform loss distributions. This multi-level optimization enables direct monitoring pathways while supporting precise calibration, and it approaches theoretical fidelity in practical deployments with direct implications for scalable and fault-tolerant photonic computing systems.
Programmable photonic interferometer meshes enable reconfigurable linear optical transformations, but their performance depends critically on accurate calibration of Mach-Zehnder interferometers and phase shifters. Conventional methods often require node isolation, dedicated routing paths, orthogonal training states, reference channels, or prior phase-voltage characterization, which become increasingly difficult in large thermally tuned meshes. We introduce a local variance-based self-calibration method using intensity-only measurements. Controlled phase perturbations are applied, and calibration points are identified from minima of the measured output-power variance. For Mach-Zehnder interferometers, the variance follows a characteristic |sin(theta)| dependence, allowing bar and cross operating points to be found without conventional node isolation. For phase shifters, balanced interference produces a complementary |cos(phi)| variance signature, enabling quadrature calibration through the same statistical principle. We validate the method experimentally on an 8 x 8 silicon nitride programmable photonic processor using a fully automated two-stage procedure. Starting from random phase settings, all Mach-Zehnder interferometers are calibrated first, followed by phase-shifter calibration under balanced-interference conditions. As a system-level test, we implement an embedded 4 x 4 Hadamard transformation on the 8 x 8 processor using a Clements decomposition. These results establish local output variance as a simple calibration observable for programmable photonic meshes. The method is compatible with discrete random phase ensembles and requires neither conventional node isolation nor orthogonal training fields, making it a practical calibration primitive for scalable self-stabilizing photonic processors.