Photonic circuits are central to classical and quantum information processing. While integrated technologies dominate, free-space architectures are emerging as attractive alternatives, offering broad bandwidth and direct manipulation of optical modes without confinement in waveguides. A key challenge for scalability lies in circuit depth, as the number of layers manipulating the optical field typically grows with the system size. Here, we introduce a programmable free-space photonic platform that implements translation-invariant, high-dimensional unitary transformations using only three layers. Information is encoded in structured light modes defined by circular polarization and quantized transverse momenta, and processed with spatial light modulators interleaved with half-wave plates. We implement unitaries that are equivalent to quantum walks over up to 30 time steps, in one- and two-dimensional lattices, distributing a single input mode across more than 7,000 outputs, where conventional approaches would require tens or hundreds of layers. The platform supports diverse quantum walk dynamics, including disorder, synthetic gauge fields, and topological effects, previously explored only in separate experiments. Using coincidence detection with a time-tagging camera, we show compatibility with quantum optics protocols and provide examples of quantum walks of heralded single photons. These results contribute to establishing free-space optical processors as promising resources for high-dimensional quantum simulation and scalable optical information processing.
Photonic circuits are central to classical and quantum information processing. While integrated technologies dominate, free-space architectures are emerging as attractive alternatives, offering broad bandwidth and direct manipulation of optical modes without confinement in waveguides. A key challenge for scalability lies in circuit depth, as the number of layers manipulating the optical field typically grows with the system size. Here, we introduce a programmable free-space photonic platform that implements translation-invariant, high-dimensional unitary transformations using only three layers. Information is encoded in structured light modes defined by circular polarization and quantized transverse momenta, and processed with spatial light modulators interleaved with half-wave plates. We implement unitaries that are equivalent to quantum walks over up to 30 time steps, in one- and two-dimensional lattices, distributing a single input mode across more than 7,000 outputs, where conventional approaches would require tens or hundreds of layers. The platform supports diverse quantum walk dynamics, including disorder, synthetic gauge fields, and topological effects, previously explored only in separate experiments. Using coincidence detection with a time-tagging camera, we show compatibility with quantum optics protocols and provide examples of quantum walks of heralded single photons. These results contribute to establishing free-space optical processors as promising resources for high-dimensional quantum simulation and scalable optical information processing.
Photonic circuits, engineered to couple optical modes according to a specific map, serve as processors for classical and quantum light. The number of components typically scales with that of processed modes, thus correlating system size, circuit complexity, and optical losses. We present a photonic-circuit technology implementing large-scale unitary maps in free space, coupling a single input to hundreds of output modes in a two-dimensional compact layout. The map corresponds to a quantum walk of structured photons, realized through light propagation in three liquid-crystal metasurfaces, having their optic axes artificially patterned. Theoretically, the walk length and the number of connected modes can be arbitrary while keeping losses constant. The patterns can be designed to replicate multiple unitary maps. We also discuss limited reconfigurability by adjusting the overall birefringence and the relative displacement of the optical elements. These results lay the basis for the design of low-loss nonintegrated photonic circuits, primarily for manipulating multiphoton states in quantum regimes.
The possibility of fine-tuning the couplings between optical modes is a key requirement in photonic circuits for quantum simulations. In these architectures, emulating the long-time evolution of particles across large lattices requires sophisticated setups that are often intrinsically lossy. Here we report ultra-long photonic quantum walks across several hundred optical modes, obtained by propagating a light beam through very few closely stacked liquid-crystal metasurfaces. By exploiting spin–orbit effects, these implement space-dependent polarization transformations that mix circularly polarized optical modes carrying quantized transverse momentum. As each metasurface implements long-range couplings between distant modes, by using only a few of them we simulate quantum walks up to 320 discrete steps without any optical amplification, far beyond state-of-the-art experiments. To showcase the potential of this method, we experimentally demonstrate that in the long time limit a quantum walk affected by dynamical disorder generates maximal entanglement between two system partitions. Our platform grants experimental access to large-scale unitary evolutions while keeping optical losses at a minimum, thereby paving the way to massive multi-photon multi-mode quantum simulations.
The precise manipulation of quantum states of light lies at the heart of advancing photonic technologies, yet scalable solutions for hybrid photonic systems—where disparate optical modes such as polarization, time-bin, and frequency must coherently interact—remain a critical challenge. While current literature demonstrates various energy-conserving devices that effectively map between Hilbert spaces of unequal dimensions, there is a growing need for frameworks that address variable-dimensional transformations in a more unified manner. In this paper, we introduce an operator-level framework that systematically integrates both unitary and rectangular isometric energy-conserving transformations in multi-dimensional photonic systems. Unlike prior mode-specific approaches, our formalism enables modular modeling of hybrid optical modes within effective signal spaces, offering practical tools for scalable photonic quantum processors. By classifying these transformations into fixed- and variable-dimensional regimes, we derive universal design criteria for energy-conserving photonic signal processors. This work not only advances the fundamental understanding of photonic quantum processing but also delivers actionable tools for engineering next-generation scalable optical technologies, including multi-purpose, programmable photonic circuits, energy-efficient optical signal processing in reconfigurable networks, and high-dimensional quantum key distribution with hybrid mode encoding.
Abstract Photonic implementations of unitary processes on lattice structures, such as quantum walks, have been demonstrated across various architectures. However, few platforms offer the combined advantages of scalability, reconfigurability, and the ability to simulate dynamics on lattices with periodic boundary conditions, such as cyclic or toroidal geometries. Here, we employ a recently developed platform that enables the implementation of arbitrary translationally invariant unitary operations on one- and two-dimensional lattices, and demonstrate a natural mechanism for introducing periodic boundary conditions. Our approach leverages direct access to the reciprocal lattice, where discrete sampling of the unitary evolution effectively enforces the desired topology. We program our platform to realize quantum walks on 1D cyclic lattices and 2D lattices with cylindrical or toroidal topologies. The lattice size can be readily tuned by adjusting the sampling density in reciprocal space. By controlling reciprocal-space occupancy, we investigate the dynamics of localized states and wavepackets, observing refocusing behavior, breathing modes modulated by reciprocal-space discretizations, and wavepacket trajectories that reflect the underlying topology. We further demonstrate a form of dimensional reduction by mapping a 2D quantum walk on a cylinder to a 1D walk with a high-dimensional coin. These results establish a versatile platform for realizing a broad class of optical mode transformations within bounded Hilbert spaces.
Quantum technologies promise computational capabilities beyond the reach of classical systems. A forward-looking application lies in satellite missions, which increasingly depend on onboard computing under stringent constraints on size, weight and power. Quantum photonics is particularly attractive here: photon interference can enhance the machine-learning models needed to process large onboard data volumes, at fixed hardware resources. However, harnessing this interference requires more than generating single photons, as they must remain mutually indistinguishable: a fragile condition that is hard to maintain within the technically demanding framework of a space mission, which includes a rocket launch, strong thermal drifts, and radiation. This is why quantum states of light, though already generated and transmitted in orbit for secure communication and fundamental tests, have never been used as a computational resource. Here, we report a programmable quantum photonic platform operating on a nanosatellite, processing two photons in a six-mode universal integrated circuit. By programming distinct unitaries and tuning the photons into indistinguishability, we observe two-photon interference, establishing the on-board generation, manipulation and detection of non-classical light. This extends space-based technologies towards in-orbit quantum-assisted computing, for instance local encoding of Earth-observation data, or nodes in a distributed quantum network.
Qudits have proven to be a powerful resource for quantum information processing, offering enhanced channel capacities, improved robustness to noise, and highly efficient implementations of quantum algorithms. The encoding of photonic qudits in transverse-spatial degrees of freedom has emerged as a versatile tool for quantum information processing, allowing access to a vast information capacity within a single photon. We examine recent advances in quantum optical circuits with spatially structured light, focusing particularly on top-down approaches that employ complex mode-mixing transformations in free space and fibers. We highlight circuits based on platforms such as multi-plane light conversion, complex scattering media, multi-mode, and multi-core fibers. We discuss their applications for the manipulation and measurement of multi-dimensional and multi-mode quantum states. Furthermore, we discuss how these circuits have been employed to perform multi-party operations and multi-outcome measurements, thereby opening new avenues for scalable photonic quantum information processing.