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Journal of the Optical Society of America B

Analysis of the multiport beam splitter transfer matrix in photonic integrated devices

Diego G. Barreto, Marcos Cordeiro, Eduardo Cesar Rodrigues de Lima, Gabriel Aragao, Luciano Soares da Cruz, Breno Marques

Published Jan 2, 2026• 0 citations
Publisher

Abstract

The use of silicon photonics in the context of quantum technologies has been widely discussed in the fields of communication, engineering, computation, biology, chemistry, and metrology due to its scalability, stability, room-temperature control, and system miniaturization capabilities. In this paper, in the context of using photonic chips for application in quantum information protocols, we focus on multiple waveguide encoding of qudits, that is, a multi-level quantum computational unit, instead of the usual two-level qubit. Given the complexity of constructing control gates and designing systems using qubits, we show a method where we use coupled-mode theory in the small perturbation approximation, so that we can describe the coupling matrix of n-waveguides that can be used in the context of interferometers in photonic chips, to find optimal parameters for describing operations using qudits.

DOI
10.1364/josab.580046

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The use of silicon photonics in the context of quantum technologies has been widely discussed in the fields of communication, engineering, computation, biology, chemistry, and metrology due to its scalability, stability, room-temperature control, and system miniaturization capabilities. In this paper, in the context of using photonic chips for application in quantum information protocols, we focus on multiple waveguide encoding of qudits, that is, a multi-level quantum computational unit, instead of the usual two-level qubit. Given the complexity of constructing control gates and designing systems using qubits, we show a method where we use coupled-mode theory in the small perturbation approximation, so that we can describe the coupling matrix of n-waveguides that can be used in the context of interferometers in photonic chips, to find optimal parameters for describing operations using qudits.
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Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing [1], photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. [3]), measurement (eg. [4]) and other quantum technologies [5]. However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturisation and scalability [6]. Here we report high-fidelity silica-on-silicon integrated optical realisations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate [7]. We have demonstrated controlled manipulation of up to four photons on-chip, including high-fidelity single qubit operations, using a lithographically patterned resistive phase shifter [8]. We have used this architecture to implement a small-scale compiled version of Shorʼs quantum factoring algorithm [9] and demonstrated heralded generation of tuneable four photon entangled states from a six photon input [10]. We have combined waveguide photonic circuits with superconducting single photon detectors [11]. We describe complex quantum interference behaviour in multi-mode interference devices with up to eight inputs and outputs [12], and quantum walks of correlated particles in arrays of coupled waveguides [13]. Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [14,15] and single photon sources [16,17].
Optical chips for quantum photonics are cutting-edge technology, merging photonics and quantum mechanics to manipulate light at the quantum level. These chips are crucial for advancing quantum computing, secure communication, and precision sensing by integrating photonic components such as waveguides, beam splitters, and detectors to manipulate single photons, the fundamental carriers of quantum information. Key advancements in optical chips include low-loss waveguides, efficient single-photon sources, and high-fidelity quantum gates, all essential for scalable quantum circuits. Integrating these circuits on a chip offers significant advantages in miniaturization, stability, and reproducibility over traditional bulk optics setups. Recent breakthroughs in materials science and nanofabrication have propelled the field forward, enabling the production of chips with higher precision and lower defect rates. Silicon photonics, in particular, has become a prominent platform due to its compatibility with existing semiconductor manufacturing processes, facilitating the integration of quantum photonic circuits with classical electronic systems. Here, we share our vision of the future of optical chips for quantum photonics, which hold promise for various applications. In quantum computing, they enable the development of compact and scalable quantum processors. In communication, they provide the foundation for ultra-secure quantum networks through quantum key distribution. In sensing, they allow for high-precision measurements that surpass classical limits. As research progresses, optical chips are expected to play a critical role in realizing the full potential of quantum technologies.
Silicon-on-insulator (SOI) wafers have been developed for electronic integrated circuits, but are also one of the most promising platforms in photonic integrated circuits due to its low loss, high refractive index, ability to fast phase modulation, and well-developed fabrication technologies. With advantages to handle light with a small volume and high modulation speed, silicon photonics has been intensively investigated as the next generation platform of signal processing, interconnection, and communication devices. Recently, silicon photonics has been attracted great interests in quantum optics communities as optical quantum systems for linear optical quantum computing are achievable using silicon photonic components including beam splitters, phase modulators, and filters and the small footprint of a silicon photonic quantum system has unprecedented performances of high stability and scalability. Here we show our recent results on the fabrication of silicon photonic elements for quantum applications. We fabricated low-loss optical waveguides, efficient fiber-to-waveguide grating couplers, resonator-based optical filters, and tunable beam splitters and tested their performances. A micro-sized heater is attached on a Mach-Zehnder interferometer, showing stable operation as a slow phase modulator. In addition, phase modulators using plasma dispersion effects are under investigation. Finally, the quantum characteristics of photon pairs generated by spontaneous four-wave mixing in silicon waveguides are investigated. These results will be an essential cornerstone for the realization of quantum optical computing and quantum communication devices.
The impact of quantum technology will be profound and far-reaching: secure communication networks for consumers, corporations and government; precision sensors for biomedical technology and environmental monitoring; quantum simulators for the design of new materials, pharmaceuticals and clean energy devices; and ultra-powerful quantum computers for addressing otherwise impossibly large datasets for machine learning and artificial intelligence applications. However, engineering quantum systems and controlling them is an immense technological challenge: they are inherently fragile; and information extracted from a quantum system necessarily disturbs the system itself. Of the various approaches to quantum technologies, photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturization and scalability. We will described our latest progress in generating, manipulating and interacting single photons in waveguide circuits on silicon chips.
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