Structured light, light tailored in its internal degrees of freedom, has become topical in numerous quantum and classical information processing protocols. In this work, we harness the high dimensional nature of structured light modulated in the transverse spatial degree of freedom to realize an adaptable scheme for learning unitary operations. Our approach borrows from concepts in variational quantum computing, where a search or optimization problem is mapped onto the task of finding a minimum ground state energy for a given energy/goal function. We achieve this by a pseudo-random walk procedure over the parameter space of the unitary operation, implemented with optical matrix-vector multiplication enacted on arrays of Gaussian modes by exploiting the partial Fourier transforming capabilities of a cylindrical lens in the transverse degree of freedom for the measurement. We outline the concept theoretically, and experimentally demonstrate that we are able to learn optical unitary matrices for dimensions d = 2, 4, 8, and 16 with average fidelities of >90%. Our work advances high dimensional information processing and can be adapted to both process and quantum state tomography of unknown states and channels.
Structured light, light tailored in its internal degrees of freedom, has become topical in numerous quantum and classical information processing protocols. In this work, we harness the high dimensional nature of structured light modulated in the transverse spatial degree of freedom to realize an adaptable scheme for learning unitary operations. Our approach borrows from concepts in variational quantum computing, where a search or optimization problem is mapped onto the task of finding a minimum ground state energy for a given energy/goal function. We achieve this by a pseudo-random walk procedure over the parameter space of the unitary operation, implemented with optical matrix-vector multiplication enacted on arrays of Gaussian modes by exploiting the partial Fourier transforming capabilities of a cylindrical lens in the transverse degree of freedom for the measurement. We outline the concept theoretically, and experimentally demonstrate that we are able to learn optical unitary matrices for dimensions d = 2, 4, 8, and 16 with average fidelities of >90%. Our work advances high dimensional information processing and can be adapted to both process and quantum state tomography of unknown states and channels.
Structured light, light tailored in its internal degrees of freedom, has become topical in numerous quantum and classical information processing protocols. In this work, we harness the high dimensional nature of structured light modulated in the transverse spatial degree of freedom to realise an adaptable scheme for learning unitary operations. Our approach borrows from concepts in variational quantum computing, where a search or optimisation problem is mapped onto the task of finding a minimum ground state energy for a given energy/goal function. We achieve this by a pseudo-random walk procedure over the parameter space of the unitary operation, implemented with optical matrix-vector multiplication enacted on arrays of Gaussian modes by exploiting the partial Fourier transforming capabilities of a cylindrical lens in the transverse degree of freedom for the measurement. We outline the concept theoretically, and experimentally demonstrate that we are able to learn optical unitary matrices for dimensions d = 2, 4, 8 and 16 with average fidelities of >90%. Our work advances high dimensional information processing and can be adapted to both process and quantum state tomography of unknown states and channels.
Optical computing harnesses the speed of light to perform vector-matrix operations efficiently. It leverages interference, a cornerstone of quantum computing algorithms, to enable parallel computations. In this work, we interweave quantum computing with classical structured light by formulating the process of photonic matrix multiplication using quantum mechanical principles such as state superposition and subsequently demonstrate a well-known algorithm, namely, Deutsch–Jozsa’s algorithm. This is accomplished by elucidating the inherent tensor product structure within the Cartesian transverse degrees of freedom of light, which is the main resource for optical vector-matrix multiplication. To this end, we establish a discrete basis using localized Gaussian modes arranged in a lattice formation and demonstrate the operation of a Hadamard gate. Leveraging the reprogrammable and digital capabilities of spatial light modulators, coupled with Fourier transforms by lenses, our approach proves adaptable to various algorithms. Therefore, our work advances the use of structured light for quantum information processing.
Structured light has become topical of late, where controlling light in all its degrees of freedom has offered novel states of light long predicted, enhanced functionality in applications, and a modern toolbox for probing fundamental science. Structuring light as single photons and entangled states allows the spatial modes of light to be used to encode a large alphabet, accessing high dimensional Hilbert spaces for fundamental tests of quantum mechanics and improved quantum information processing tasks. In this tutorial, we outline the basic concepts of high dimensional quantum states expressed in a basis of spatial modes (structured light) and explain how to create, control, and detect such quantum states in the laboratory with a focus on transverse spatial modes such as the orbital angular momentum and pixel (position) modes. Finally, we highlight some example applications of such quantum structured light, from communications to imaging.
The ability to prepare, control, and detect high-dimensional photonic quantum states is a key capability in modern quantum science. Spatially structured single- and bi-photon states provide access to large Hilbert spaces, enabling both fundamental studies and practical advances across quantum technologies. Precise control of these states is essential to characterising quantum light sources and to using spatial degrees of freedom for information encoding, with applications ranging from quantum imaging and simulation to high-capacity, noise-resilient quantum communication. In this talk, I will review recent experimental and theoretical progress in structured-light quantum information processing. I will discuss high-dimensional QKD with structured photons, strategies based on adaptive optics and tailored measurements to counter channel distortions, and protocols that exploit spatial mode structure. I will also describe how structured photonic states can be used to simulate linear and cyclic quantum systems, illustrating their potential as scalable platforms for high-dimensional quantum information processing.
The emergence and development of quantum optics as a discipline in the latter half of the twentieth century has established photons as one of the most promising candidates for future technologies in computing, metrology, communication, and imaging. In imaging and sensing, a series of recent theoretical works and proof-of-concept experiments have shown that by examining the mode structure of photons, one can build optical systems with resolutions below the Rayleigh–Abbe limit. Building upon these developments, in one of our works, we investigate the use of higher-order Hermite–Gauss (HG) modes for sensing optically induced transverse displacements. We show that projective measurements onto neighboring modes are optimal and sufficient in the small-displacement regime, and that the sensitivity—quantified by the Fisher information—scales linearly with the order of the mode used. We generalize the calculations to arbitrary displacements and varying degrees of coherence between the displaced modes, and perform a proof-of-concept experiment with higher-order HG modes, obtaining an order-of-magnitude enhancement in sensitivity compared to the fundamental mode. This approach enables enhanced displacement sensitivity with minimal measurements and highlights the potential of structured light for ultrasensitive displacement sensing, particularly for birefringence measurements with broadband or low-coherence light sources. We also consider displacement sensing in the light field originating from a biphoton source, which possesses rich high-dimensional correlations in its biphoton mode structure. We show that the Fisher information is proportional to the degree of entanglement, or equivalently, its Schmidt rank. In addition to sensing, photons structured in their transverse degrees of freedom also provide a convenient toolkit for quantum computing and communication due to the high dimensionality of their Hilbert space. In one of the works presented, we introduce a technique for nonlocal transfer of high-dimensional computational results using spatial correlations in photon pairs. We expect these findings to be useful in future photonic quantum networks, where computational resources are distributed and users can access the results of complex computations via a centrally located quantum processor. We also experimentally implement the protocol in down-converted photon pairs and demonstrate the transfer of unitaries in one-dimensional and two-dimensional transverse momentum spaces. In another work, we address the noise inherent in quantum computing circuits and simulate the interaction between a qubit and its environment by manipulating transverse momentum modes. This study, performed by fabricating three liquid-crystal metasurfaces, provides a practical solution for quantum state purification, demonstrating a versatile approach for simulating open-qubit dynamics. Combining the transverse spatial structure with polarization yields the so-called vector modes of photons. Structuring two-qubit interference, or the Hong–Ou–Mandel (HOM) effect, offers significant potential to extend the applications of such modes beyond the classical regime. We demonstrate the simultaneous generation of all four Bell states in polarization by exploiting HOM interference of vector modes. These results represent a significant step toward manipulating HOM interference within structured photons, offering promising applications in high-dimensional quantum information processing, quantum communication, and sensing. On the algorithmic side of photonic information processing, we propose a quantum pattern recognition algorithm to identify images obtained from quantum imaging techniques with correlated photons—such as “interaction-free” or “ghost” imaging. Interfacing these imaging techniques with quantum pattern recognition promises a significantly improved image acquisition and identification system, with potential applications in medical diagnostics and biological imaging.
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.