Analog Programmable-Photonic Computation (APC) leverages programmable integrated photonics (PIP) to perform high-speed matrix operations using optical waves. However, the continuous nature of optical waves that implement the analog bits or anbits - the fundamental unit of information in APC - makes computational results intrinsically sensitive to physical noise. Here, we establish and experimentally validate a comprehensive noise analysis in APC platforms using the geometric representation of the anbit in the Generalized Bloch Sphere (GBS). By modeling the physical noise sources in PIP circuits as random photocurrent fluctuations at the output of the opto-electrical (O/E) converter, and using error propagation theory, the noise statistics can be projected onto the GBS. This approach leads to specific noise maps in the GBS for each noise source, enabling the identification of the dominant noise sources within the APC system. Analytical predictions are numerically and experimentally validated on a fabricated silicon PIP chip. Beyond statistical characterization of system noise, the proposed model provides quantitative design criteria for noise-adapted analog constellations in the GBS, advancing APC towards scalable and robust optical computing systems, with potential applications in emerging paradigms such as photonic neuromorphic computing.
Analog Programmable-Photonic Computation (APC) leverages programmable integrated photonics (PIP) to perform high-speed matrix operations using optical waves. However, the continuous nature of optical waves that implement the analog bits or anbits - the fundamental unit of information in APC - makes computational results intrinsically sensitive to physical noise. Here, we establish and experimentally validate a comprehensive noise analysis in APC platforms using the geometric representation of the anbit in the Generalized Bloch Sphere (GBS). By modeling the physical noise sources in PIP circuits as random photocurrent fluctuations at the output of the opto-electrical (O/E) converter, and using error propagation theory, the noise statistics can be projected onto the GBS. This approach leads to specific noise maps in the GBS for each noise source, enabling the identification of the dominant noise sources within the APC system. Analytical predictions are numerically and experimentally validated on a fabricated silicon PIP chip. Beyond statistical characterization of system noise, the proposed model provides quantitative design criteria for noise-adapted analog constellations in the GBS, advancing APC towards scalable and robust optical computing systems, with potential applications in emerging paradigms such as photonic neuromorphic computing.
The limitations of digital electronics in handling real-time matrix operations for emerging computational tasks—such as artificial intelligence, drug design, and medical imaging—have prompted renewed interest in analog computing. Programmable integrated photonics (PIP) has emerged as a promising technology for scalable, low-power, and high-bandwidth analog computation. Although prior work has explored PIP implementations of quantum and neuromorphic computing, both approaches face significant limitations due to misalignments between their mathematical models and the native capabilities of photonic hardware. Building on the recently proposed analog programmable-photonic computation (APC)—a computation theory explicitly matched to the technological features of PIP—we introduce its critical missing component: an information theory. We present analog programmable-photonic information (API), a mathematical framework that addresses fundamental concepts beyond APC by examining the amount of information that can be generated, computed, and recovered in a PIP platform. API also demonstrates the robustness of APC against errors arising from system noise and hardware imperfections, enabling scalable computation without the extensive error correction overhead required in quantum computing. Together, APC and API provide a unified foundation for on-chip photonic computing, offering a complementary alternative to digital, quantum, and neuromorphic paradigms, and positioning PIP as a cornerstone technology for next-generation information processing.
The limitations of digital electronics in handling real-time matrix operations for emerging computational tasks - such as artificial intelligence, drug design, and medical imaging - have prompted renewed interest in analog computing. Programmable Integrated Photonics (PIP) has emerged as a promising technology for scalable, low-power, and high-bandwidth analog computation. While prior work has explored PIP implementations of quantum and neuromorphic computing, both approaches face significant limitations due to misalignments between their mathematical models and the native capabilities of photonic hardware. Building on the recently proposed Analog Programmable-Photonic Computation (APC) - a computation theory explicitly matched to the technological features of PIP - we introduce its critical missing component: an information theory. We present Analog Programmable-Photonic Information (API), a mathematical framework that addresses fundamental concepts beyond APC by examining the amount of information that can be generated, computed and recovered in a PIP platform. API also demonstrates the robustness of APC against errors arising from system noise and hardware imperfections, enabling scalable computation without the extensive error-correction overhead required in quantum computing. Together, APC and API provide a unified foundation for on-chip photonic computing, offering a complementary alternative to digital, quantum and neuromorphic paradigms, and positioning PIP as a cornerstone technology for next-generation information processing.
The precise characterization of spatial optical coherence is fundamental to emerging applications in optical communications and computational imaging. However, extracting the full coherence matrix traditionally requires phase-sensitive interferometry, which is highly vulnerable to environmental noise and poses severe scalability challenges for integrated photonics. Here, we introduce an architecture-agnostic framework for analyzing and controlling partially coherent light on programmable photonic circuits. By leveraging the Schur-Horn theorem, our approach systematically diagonalizes the incident coherence matrix, relying solely on output intensity measurements and entirely circumventing the need for complex phase retrieval. We experimentally validate this black-box protocol on a low-depth, non-universal photonic integrated circuit, successfully reconstructing the hidden eigenvalues of mixed states generated from up to four mutually incoherent sources. Furthermore, we demonstrate active, in-situ statistical light control by introducing non-unitary amplitude modulation to significantly enhance interference visibility, exposing a fundamental physical trade-off between coherence enhancement and optical loss. Inherently resilient to hardware constraints and experimental noise, this scalable paradigm establishes a robust pathway for realizing ultra-compact, on-chip spatial coherence analyzers.
General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach–Zehnder interferometers, these systems have demonstrated significant potential in microwave photonic applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach–Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3 × 3 and 4 × 4 random unitary matrices yields fidelities >98% and bit precisions over five bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.
The quantum random number generation based on laser phase noise, which is featured with high random number generation rate and ease for photonic integration, has been extensively investigated and demonstrated. Despite these advancements, a theoretical model to achieve optimal performance in terms of maximizing the random number generation rate is still incomplete. In this work, a comprehensive physical model for this scheme is introduced to accurately predict the power spectrum of entropy source and probability distribution of raw data, based on which the entropy source bandwidth and extractable randomness can be accordingly estimated and thus the system performance can be quantitatively evaluated and optimized. The model is sufficiently validated through both simulation and experiment with significant agreement under various typical setups. Furthermore, our proposal enables the proactive design of experimental parameters to achieve optimal system performance, which is crucial for the design and practical implementation of photonics integrated quantum random number generations.
Programmable integrated photonics (PIP) has emerged as a powerful on-chip platform for optical signal processing and computing, enabling the implementation of reconfigurable N×N unitary matrix transformations through meshes of tunable interferometers, which realize 2$\times2unitarymatrices.However,theenergyconsumptionassociatedwithphase−shifteractuationisbecomingamajorlimitationtothescalabilityofPIPplatforms.Here,weintroduceageometricframeworkforenergyoptimizationinPIPcircuitsbyexploitingtherepresentationof2\times2unitarymatricesasconcatenationsofbasicEulerrotationsontheBlochsphere.WeshowthatequivalentimplementationsofthesameN\times$N unitary matrix (N ≥ 2) can exhibit markedly different energy costs depending on the rotation trajectories on the Bloch sphere implemented by each interferometer. Leveraging this insight, we identify minimum-energy configurations by systematically selecting the shortest rotation trajectories. We experimentally and numerically validate the proposed approach in diverse silicon PIP architectures, including feedforward and multipurpose hexagonal meshes, neural network accelerators, and photonic quantum-gate implementations. These results establish a general route toward more energy-efficient large-scale PIP processors for classical and quantum signal processing and computing applications.