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Arbitrary linear transformations for photons in the frequency synthetic dimension.

ABSTRACT: Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a photonic architecture to achieve arbitrary linear transformations by harnessing the synthetic frequency dimension of photons. Our structure consists of dynamically modulated micro-ring resonators that implement tunable couplings between multiple frequency modes carried by a single waveguide. By inverse design of these short- and long-range couplings using automatic differentiation, we realize arbitrary scattering matrices in synthetic space between the input and output frequency modes with near-unity fidelity and favorable scaling. We show that the same physical structure can be reconfigured to implement a wide variety of manipulations including single-frequency conversion, nonreciprocal frequency translations, and unitary as well as non-unitary transformations. Our approach enables compact, scalable and reconfigurable integrated photonic architectures to achieve arbitrary linear transformations in both the classical and quantum domains using current state-of-the-art technology.

SUBMITTER: Buddhiraju S

PROVIDER: S-EPMC8065043 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Most connectivity metrics in neuroimaging research reduce multivariate activity patterns in regions-of-interests (ROIs) to one dimension, which leads to a loss of information. Importantly, it prevents us from investigating the transformations between patterns in different ROIs. Here, we applied linear estimation theory in order to robustly estimate the linear transformations between multivariate fMRI patterns with a cross-validated ridge regression approach. We used three functional connectivity metrics that describe different features of these voxel-by-voxel mappings: goodness-of-fit, sparsity and pattern deformation. The goodness-of-fit describes the degree to which the patterns in an input region can be described as a linear transformation of patterns in an output region. The sparsity metric, which relies on a Monte Carlo procedure, was introduced in order to test whether the transformation mostly consists of one-to-one mappings between voxels in different regions. Furthermore, we defined a metric for pattern deformation, i.e. the degree to which the transformation rotates or rescales the input patterns. As a proof of concept, we applied these metrics to an event-related fMRI data set consisting of four subjects that has been used in previous studies. We focused on the transformations from early visual cortex (EVC) to inferior temporal cortex (ITC), fusiform face area (FFA) and parahippocampal place area (PPA). Our results suggest that the estimated linear mappings explain a significant amount of response variance in the three output ROIs. The transformation from EVC to ITC shows the highest goodness-of-fit, and those from EVC to FFA and PPA show the expected preference for faces and places as well as animate and inanimate objects, respectively. The pattern transformations are sparse, but sparsity is lower than would have been expected for one-to-one mappings, thus suggesting the presence of one-to-few voxel mappings. The mappings are also characterised by different levels of pattern deformations, thus indicating that the transformations differentially amplify or dampen certain dimensions of the input patterns. While our results are only based on a small number of subjects, they show that our pattern transformation metrics can describe novel aspects of multivariate functional connectivity in neuroimaging data.

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Arbitrary linear transformations for photons in the frequency synthetic dimension.

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