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Frontiers in Optics

Programable High-dimensional Quantum Gates via MPLC

Daniel S. Dahl, Martin Plöschner, Nicolas K. Fontaine, Jacquiline Romero, Joel A. Carpenter

Published Jan 1, 2024• 2 citations
Publisher

Abstract

We use multi-plane light conversion (MPLC) to implement a programmable high-dimensional quantum gate device for 17-dimensional qudits using Laguerre-Gaussian modes. Verified gates include X-gate, Z-gate, and Discrete Fourier Transform (DFT)-gate, enhancing quantum communication and computing.
DOI
10.1364/fio.2024.fm5c.5

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This thesis explores the development and application of multi-plane light conversion (MPLC) technol-ogy, focusing on its integration into experimental setups that push the boundaries of quantum opticsand spatial state tomography. Central to this study is a custom-built, research-grade MPLC devicedesigned around a programmable spatial light modulator (SLM), which facilitates two groundbreak-ing experiments: the manipulation of high-dimensional qudits for quantum gate operations, and thedevelopment of a high-dimensional Stokes-space spatial beam analyser for single-shot spatial statetomography.The first experiment involved implementing quantum gates — specifically the X-gate, Z-gate, andDFT-gate — for a 17-dimensional qudit, represented through the first 17 azimuthal Laguerre-Gaussianspatial modes on a MPLC device. This experiment not only demonstrated MPLC’s capability tohandle complex, high-dimensional quantum states but also underscored its potential to enhance thescalability and efficiency of quantum computing architectures. By leveraging the precise control overspatial modes afforded by MPLC and the programmability of SLM-based MPLC, the experimentdemonstrated high-dimensional gate operations, paving the way for more complex quantum computingoperations for qudits.The second project focused on using MPLC to develop a device capable of performing high-dimensional Stokes-space spatial beam analysis. This innovative instrument marks a significantbreakthrough in optical beam characterisation, providing a reference-free, single-shot technique forconducting spatial state tomography on beams characterisable by a six-mode or six-dimensional system.The device’s capacity to swiftly and precisely characterise the wavefront and coherence of opticalfields renders it an invaluable asset for advancing optical communication technologies and enhancingoptical sensing methodologies.Throughout this thesis, the theoretical foundations of MPLC technology are presented, with adetailed account of the MPLC device design and operational principles. Experimental results arepresented to validate the effectiveness of the MPLC device in both quantum gate operations andspatial state tomography. Comparisons with existing technologies highlight the MPLC’s enhancedperformance and versatility.This work not only expands the understanding and application of MPLC in quantum and opticalsciences but also sets the stage for future innovations in these fields. The continuous refinement andadaptation of MPLC technology promise to unlock new possibilities in both fundamental research andpractical applications.
High-dimensional entangled photons are a key resource for advanced quantum information processing. Efficient processing of high-dimensional entangled photons requires the ability to synthesize their state using general unitary transformations. The leading technology for processing photons in high-dimensions is integrated multiport interferometers. However, such devices are incompatible with free-space and fiber-based systems, and their architecture poses significant scaling challenges. Here we unlock these limitations by demonstrating a reconfigurable processor of entangled photons that is based on multi-plane light conversion (MPLC), a technology that was recently developed for multiplexing hundreds of spatial modes for classical free-space and fiber communication. To demonstrate the flexibility of MPLC, we perform four key tasks of quantum information processing using the same MPLC hardware: entanglement certification, tailored two-photon interference, arbitrary state transformations, and mode conversion. Based on the high degree of control we obtain, we expect MPLC will become a leading platform for future quantum technologies.
Photons can carry quantum information not only in two-level systems (qubits) but also in d-level systems known as qudits. A single photon distributed across d optical modes can encode up to log2(d) qubits of information, allowing for more efficient use of quantum resources and increased resilience to noise. This advantage, however, comes at a price: implementing quantum gates and performing measurements in high-dimensional Hilbert spaces is significantly more demanding than in the qubit case. To tackle these challenges, I will present our recent work developing new protocols and optical hardware that enable quantum communication and computation with high-dimensional qudits encoded in the temporal or spatial modes of single and entangled photons. I will discuss our experimental implementations of quantum key distribution using weak coherent pulses [Sulimany et al., NPJ Quantum Information 11, 16 (2025)], single photons from quantum dots [Halevi et al., Optica Quantum 2, 351 (2024)], and entangled photon pairs [Lib et al., Optica Quantum 3, 182 (2025)]. In the latter, we demonstrated projective measurements in two mutually unbiased bases for d=25d = 25d=25 using a multi-plane light converter (MPLC). I will also show how the same MPLC platform can be used to perform elementary operations in measurement-based quantum computation with high-dimensional cluster states [Lib and Bromberg, Nat. Photonics 18, 1218 (2024)]. Throughout the talk, I will discuss the tradeoffs between qubit- and qudit-based approaches and highlight the regimes where high-dimensional systems offer a practical advantage.
High-dimensional quantum key distribution (QKD) offers higher information capacity and stronger resilience to noise compared with its binary counterpart. However, these advantages are often hindered by the difficulty of realizing the required high-dimensional measurements and transformations. Here, we implement a large-scale multi-plane light converter (MPLC) and program it as a high-dimensional mode sorter of spatial modes for QKD. Using the MPLC, we demonstrate five-dimensional QKD with six mutually unbiased bases and 25-dimensional QKD with two mutually unbiased bases in the same experimental setup. Furthermore, we propose a construction of pairs of mutually unbiased bases that are robust to experimental errors, with measurement complexity scaling only with the square root of the encoded dimension. This approach paves the way for QKD implementations in higher dimensions.
High-dimensional entanglement offers a variety of advantages for both fundamental and applied applications in quantum information science. A central building block for such applications is a programmable processor of entangled states, which is crucial for the certification, manipulation, and distribution of high-dimensional entanglement. The leading technology for processing photons is integrated multiport interferometers. However, such devices are incompatible with structured light and their scaling is challenging. Here, we unlock these limitations by demonstrating a reconfigurable processor of entangled photons in high dimensions that is based on multiplane light conversion (MPLC), a technology that has recently been developed for multiplexing hundreds of spatial modes for classical communication. We use our programmable MPLC platform to certify three-dimensional entanglement in two mutually unbiased bases, perform 400 arbitrary random transformations on entangled photons, and convert the mode basis of entangled photons for entanglement distribution.