Proposal for Quantum Simulation via All-Optically Generated Tensor Network States

We devise an all-optical scheme for the generation of entangled multimode photonic states encoded in temporal modes of light. The scheme employs a nonlinear down-conversion process in an optical loop to generate one- and higher-dimensional tensor network states of light. We illustrate the principle with the generation of two different classes of entangled tensor network states and report on a variational algorithm to simulate the ground-state physics of many-body systems. We demonstrate that state-of-the-art optical devices are capable of determining the ground-state properties of the spin-1/2 Heisenberg model. Finally, implementations of the scheme are demonstrated to be robust against realistic losses and mode mismatch.Comment: 6 pages main text plus 6 pages Supplementary Material and many figures. Updated to published version. Comments welcom

Area-Specific Information Processing in Prefrontal Cortex during a Probabilistic Inference Task: A Multivariate fMRI BOLD Time Series Analysis

<div><p>Introduction</p><p>Discriminating spatiotemporal stages of information processing involved in complex cognitive processes remains a challenge for neuroscience. This is especially so in prefrontal cortex whose subregions, such as the dorsolateral prefrontal (DLPFC), anterior cingulate (ACC) and orbitofrontal (OFC) cortices are known to have differentiable roles in cognition. Yet it is much less clear how these subregions contribute to different cognitive processes required by a given task. To investigate this, we use functional MRI data recorded from a group of healthy adults during a “Jumping to Conclusions” probabilistic reasoning task.</p><p>Methods</p><p>We used a novel approach combining multivariate test statistics with bootstrap-based procedures to discriminate between different task stages reflected in the fMRI blood oxygenation level dependent signal pattern and to unravel differences in task-related information encoded by these regions. Furthermore, we implemented a new feature extraction algorithm that selects voxels from any set of brain regions that are jointly maximally predictive about specific task stages.</p><p>Results</p><p>Using both the multivariate statistics approach and the algorithm that searches for maximally informative voxels we show that during the Jumping to Conclusions task, the DLPFC and ACC contribute more to the decision making phase comprising the accumulation of evidence and probabilistic reasoning, while the OFC is more involved in choice evaluation and uncertainty feedback. Moreover, we show that in presumably non-task-related regions (temporal cortices) all information there was about task processing could be extracted from just one voxel (indicating the unspecific nature of that information), while for prefrontal areas a wider multivariate pattern of activity was maximally informative.</p><p>Conclusions/Significance</p><p>We present a new approach to reveal the different roles of brain regions during the processing of one task from multivariate activity patterns measured by fMRI. This method can be a valuable tool to assess how area-specific processing is altered in psychiatric disorders such as schizophrenia, and in healthy subjects carrying different genetic polymorphisms.</p></div

Multivariate test statistics.

<p>(<i>A</i>) Hotelling’s Generalized T² for prefrontal (blue) and non-task-related (black) temporal regions normalized by the corresponding bootstraps; n.s. = not significant w.r.t. bootstraps. (<i>B</i>) Mahalanobis distances (MDs) to the first fish drawn before decision (normalized w.r.t. bootstraps) clearly revealed a distinct "decision" point, which was significantly more pronounced in prefrontal regions (blue). (<i>C</i>) Differences in normalized Mahalanobis distances during the <i>decision making</i> and the <i>decision evaluation</i> phases for the ACC, DLPFC and OFC; N = 11; Error bars = SEM across participants.</p

PFC subregions comparison.

<p>The fraction of most informative voxels selected during the (<i>A</i>) <i>decision making</i> and (<i>B</i>) <i>decision evaluation</i> phases from the DLFPC and the OFC for all of the 11 participants. (<i>C</i>) The fraction of most informative voxels selected during <i>decision making</i> and (<i>D</i>) <i>decision evaluation</i> phases from the ACC and the OFC for all participants. The blue and red lines represent the priors for the DLPFC/ACC and OFC masks, respectively.</p

Voxel selection algorithm.

<p>(<i>A</i>) Penalized cross validation error for task-related (blue) and non-task-related (red) ROIs. (<i>B</i>) Penalized prediction error curve for the left DLPFC, smoothed by a Gaussian kernel (cyan). A minimum (non-penalized) prediction error of 0.327 = 0.505/(1 + ξ<i>p</i>/log<i>n</i>) was obtained for the overall separation of the six cognitive task stages; <i>p</i> is the number of voxels for this ROI (left DLPFC), <i>n</i> is the number of time points, and ξ = 1. (<i>C</i>) The most predictive voxels (marked in red) selected from a combined ROI mask (blue regions) were distributed across the DLPFC, OFC, ACC and hippocampus.</p

Means and standard deviations.

<p><b>A:</b> Number of fish viewed per block before the decision was taken (draws to decision = DTD). <b>B:</b> Confidence ratings per block. (grey = classical version, black = monetary incentive version of the task).</p

Jumping To Conclusions Paradigm, schematic of one of 8 task blocks: The schematic depicts the monetary incentive version where subjects saw the amount of money left for them to win in case they chose the right lake.

<p>For more detailed description of the task see the Methods section.</p

Activation and deactivation during JTC versus control blocks: control>JTC.

<p>Significance threshold: p<.05, FWE (family wise error) corrected for the whole brain. BA = Brodmann area, Tmax = maximal t-value in the cluster, coordinates = MNI (Montreal Neurological Institute) coordinates of the peak voxel in the cluster. k = cluster-size, superscript letters indicate joint clusters.</p

Sequence of the color of fish in each block.

<p>T = color of the target lake, O = color of the other lake. To introduce variety, colors changed in each block.</p

Activation during presentation of the last versus all preceding fish (event related regressors): last >preceding fish.

<p>Significance threshold: p<.05, FWE (family wise error) corrected for the whole brain. BA = Brodmann area, Tmax = maximal t-value in the cluster, coordinates = MNI (Montreal Neurological Institute) coordinates of the peak voxel in the cluster. k = cluster-size, superscript letters indicate joint clusters.</p