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APL Photonics

Toward the information-theoretic limit of programmable photonics

Ryan Hamerly, Jasvith Raj Basani, Alexander Sludds, Sri Krishna Vadlamani, Dirk Englund

Published Nov 1, 2025• 6 citations
Publisher

Abstract

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.

DOI
10.1063/5.0269741

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•Sep 1, 2026•0 citations
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.
The scalability of many programmable photonic circuits is limited by the 2π2π2π 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\ll 2π≪2π. We derive a universal information-theoretic limit to the phase-shift efficiency of universal multiport interferometers, and propose a "3-MZI" architecture that approaches this limit to within a factor of 2×2\times2×, approximately a 10×10\times10× reduction in average phase shift over the prior art, where the average phase shift scales inversely with system size as O(1/N)O(1/\sqrt{N})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\lesssim 0.2≲0.2 radians without loss of accuracy.
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.
Programmable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programming method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programmable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes, and low-depth non-unitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programming produces phase distribution shrinking as the matrix size increases. Identified reference point allows for the subtraction to be carried out electronically after detection, avoiding the interferometric subtraction loss. We further quantify the trade-off between reduced phase range and the intrinsic overhead introduced by the subtraction architecture, and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programming as a conditional but potentially useful route toward more scalable programmable photonic matrix processors.
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.