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We investigate state designs for continuous-variable quantum systems using the aid of lattice-like quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that for an n-mode system, the set of all GKP states forms a rigged continuous-variable state 2-design. We use these lattice state designs to construct a continuous variable shadow tomography protocol, derive sample complexity bounds for both global- and local GKP shadows under reasonable physical assumptions, and provide the physical gadgets needed to implement this protocol., Comment: 7+31 pages, 3 figures, comments welcome!

We investigate the effect of three-dimensionality on the synchronization characteristics of the wake behind an oscillating circular cylinder at Re = 300. Cylinder oscillations in rotation, transverse translation, and streamwise translation are considered. We utilize phase-reduction analysis, which quantifies the phase-sensitivity function of periodic flows, to examine the synchronization properties. Here, we present an ensemble-based framework for phase-reduction analysis to handle three-dimensional wakes that are not perfectly time-periodic. Based on the phase-sensitivity functions, synchronizability to three types of cylinder oscillations is evaluated. In spite of similar trends, we find that phase-sensitivity functions involving three-dimensional wakes are lower in magnitude compared to those of two-dimensional wakes, which leads to narrower conditions for synchronization to weak cylinder oscillations. We unveil that the difference between the phase-sensitivity functions of two- and three-dimensional flows is strongly correlated to the amplitude variation of the three-dimensional flow by the cylinder motions. This finding reveals that the cylinder motion modifies the three-dimensionality of the wake as well as the phase of vortex shedding, which leads to reduced phase modulation. The synchronization conditions of three-dimensional wakes, predicted by phase-reduction analysis, agree with the identification by parametric studies using direct numerical simulations for forced oscillations with small amplitudes. This study presents the potential capability of phase-reduction to study synchronization characteristics of complex flows., Comment: 21 pages, 15 figures

Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state -- a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry -- we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback., Comment: 21+12 pages, 10+4 figures

In this paper, we present a computational algorithm for constructing all boundaries and defects of topological generalized Pauli stabilizer codes in two spatial dimensions. Utilizing the operator algebra formalism, we establish a one-to-one correspondence between the topological data-such as anyon types, fusion rules, topological spins, and braiding statistics-of (2+1)D bulk stabilizer codes and (1+1)D boundary anomalous subsystem codes. To make the operator algebra computationally accessible, we adapt Laurent polynomials and convert the tasks into matrix operations, e.g., the Hermite normal form for obtaining boundary anyons and the Smith normal form for determining fusion rules. This approach enables computers to automatically generate all possible gapped boundaries and defects for topological Pauli stabilizer codes through boundary anyon condensation and topological order completion. This streamlines the analysis of surface codes and associated logical operations for fault-tolerant quantum computation. Our algorithm applies to $Z_d$ qudits, including both prime and nonprime $d$, thus enabling the exploration of topological quantum codes beyond toric codes. We have applied the algorithm and explicitly demonstrated the lattice constructions of 2 boundaries and 6 defects in the $Z_2$ toric code, 3 boundaries and 22 defects in the $Z_4$ toric code, 1 boundary and 2 defects in the double semion code, 1 boundary and 22 defects in the six-semion code, 6 boundaries and 270 defects in the color code, and 6 defects in the anomalous three-fermion code. In addition, we investigate the boundaries of two specific bivariate bicycle codes within a family of low-density parity-check (LDPC) codes. We demonstrate that their topological orders are equivalent to 8 and 10 copies of $Z_2$ toric codes, with anyons restricted to move by 12 and 1023 lattice sites in the square lattice, respectively., Comment: 36+17 pages, 41 figures; v2: typos fixed, figures updated; v3: format changed

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism's components, leading to self-modelling "tangled hierarchies". Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the G\"odel--Turing--Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time., Comment: 30 pages, 13 figures

Digital twins in manufacturing serve as a crucial bridge between the industrial age and the digital age, offering immense value. Current additive manufacturing processes are able to generate vast amounts of in-process data, which, when effectively ingested, can be transformed into insightful decisions. Data-driven methods from reduced order modeling and system identification are particularly promising in managing this data deluge. This study focuses on Laser Powder Directed Energy Deposition (LP-DED) equipped with in-situ process measurements to develop a compact virtual test-bed. This test-bed can accurately ingest arbitrary process inputs and report in-process observables as outputs. This virtual test-bed is derived using Dynamic Mode Decomposition with Control (DMDc) and is coupled with uncertainty quantification techniques to ensure robust predictions., Comment: 22 pages, 12 figures

In this study, we report a tetragonal perovskite structure of SrIrO$_3$ (P4/mmm, a = 3.9362(9) \r{A}, c = 7.880(3) \r{A}) synthesized at 6 GPa and 1400 $\deg$C, employing the ambient pressure monoclinic SrIrO$_3$ with distorted 6H structure as a precursor. The crystal structure of tetragonal SrIrO3 was evaluated on the basis of single crystal and powder X-ray diffraction. A cubic indexing was observed attributed to overlooked superlattice reflections. Weak fractional peaks in the H and K dimensions suggest possible structure modulation by oxygen defects. Magnetization study reveals weak paramagnetic behavior down to 2 K, indicative of the interplay between spin-orbit coupling, electron correlations, and crystal electric field. Additionally, measurements of electrical resistivity display metallic behavior with an upturn at about 54 K, ascribed to weak electron localization and possible structural defects., Comment: 31 pages, 12 figures

Understanding the way cells communicate, co-locate, and interrelate is essential to furthering our understanding of how the body functions. H&E is widely available, however, cell subtyping often requires expert knowledge and the use of specialized stains. To reduce the annotation burden, AI has been proposed for the classification of cells on H&E. For example, the recent Colon Nucleus Identification and Classification (CoNIC) Challenge focused on labeling 6 cell types on H&E of the colon. However, the CoNIC Challenge was unable to classify epithelial subtypes (progenitor, enteroendocrine, goblet), lymphocyte subtypes (B, helper T, cytotoxic T), and connective subtypes (fibroblasts). We use inter-modality learning to label previously un-labelable cell types on H&E. We take advantage of multiplexed immunofluorescence (MxIF) histology to label 14 cell subclasses. We performed style transfer on the same MxIF tissues to synthesize realistic virtual H&E which we paired with the MxIF-derived cell subclassification labels. We evaluated the efficacy of using a supervised learning scheme where the input was realistic-quality virtual H&E and the labels were MxIF-derived cell subclasses. We assessed our model on private virtual H&E and public real H&E. On virtual H&E, we were able to classify helper T cells and epithelial progenitors with positive predictive values of $0.34 \pm 0.15$ (prevalence $0.03 \pm 0.01$) and $0.47 \pm 0.1$ (prevalence $0.07 \pm 0.02$) respectively, when using ground truth centroid information. On real H&E we could classify helper T cells and epithelial progenitors with upper bound positive predictive values of $0.43 \pm 0.03$ (parent class prevalence 0.21) and $0.94 \pm 0.02$ (parent class prevalence 0.49) when using ground truth centroid information. This is the first work to provide cell type classification for helper T and epithelial progenitor nuclei on H&E., Comment: arXiv admin note: text overlap with arXiv:2401.05602

Quantifying relationships between components of a complex system is critical to understanding the rich network of interactions that characterize the behavior of the system. Traditional methods for detecting pairwise dependence of time series, such as Pearson correlation, Granger causality, and mutual information, are computed directly in the space of measured time-series values. But for systems in which interactions are mediated by statistical properties of the time series (`time-series features') over longer timescales, this approach can fail to capture the underlying dependence from limited and noisy time-series data, and can be challenging to interpret. Addressing these issues, here we introduce an information-theoretic method for detecting dependence between time series mediated by time-series features that provides interpretable insights into the nature of the interactions. Our method extracts a candidate set of time-series features from sliding windows of the source time series and assesses their role in mediating a relationship to values of the target process. Across simulations of three different generative processes, we demonstrate that our feature-based approach can outperform a traditional inference approach based on raw time-series values, especially in challenging scenarios characterized by short time-series lengths, high noise levels, and long interaction timescales. Our work introduces a new tool for inferring and interpreting feature-mediated interactions from time-series data, contributing to the broader landscape of quantitative analysis in complex systems research, with potential applications in various domains including but not limited to neuroscience, finance, climate science, and engineering., Comment: 20 pages, 7 figures

Genuine quantum-mechanical effects are readily observable in modern optomechanical systems comprising bosonic ("classical") optical resonators. Here we describe unique features and advantages of optical two-level systems, or qubits, for optomechanics. The qubit state can be coherently controlled using both phonons and resonant or detuned photons. We experimentally demonstrate this using charge-controlled InAs quantum dots (QDs) in surface-acoustic-wave resonators. Time-correlated single-photon counting measurements reveal the control of QD population dynamics using engineered optical pulses and mechanical motion. As a first example, at moderate acoustic drive strengths, we demonstrate the potential of this technique to maximize fidelity in quantum microwave-to-optical transduction. Specifically, we tailor the scheme so that mechanically assisted photon scattering is enhanced over the direct detuned photon scattering from the QD. Spectral analysis reveals distinct scattering channels related to Rayleigh scattering and luminescence in our pulsed excitation measurements which lead to time-dependent scattering spectra. Quantum-mechanical calculations show good agreement with our experimental results, together providing a comprehensive description of excitation, scattering and emission in a coupled QD-phonon optomechanical system., Comment: 19 pages, 4 main figures, 7 supplementary figures

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian Boson Sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this work, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various R\'enyi-$\alpha$ entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for $\alpha = 1$ (i.e. the von Neumann entropy), and, more generally, for all positive integer $\alpha$, in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the R\'enyi-$\alpha$ variance for integers $\alpha > 1$, and we are able to show that these entropies are weakly typical., Comment: 7+11 pages, 1+2 figures

Gaussian Boson Sampling is a popular method for experimental demonstrations of quantum advantage, but many subtleties remain in fully understanding its theoretical underpinnings. An important component in the theoretical arguments for approximate average-case hardness of sampling is anticoncentration, which is a second-moment property of the output probabilities. In Gaussian Boson Sampling these are given by hafnians of generalized circular orthogonal ensemble matrices. In a companion work [arXiv:2312.08433], we develop a graph-theoretic method to study these moments and use it to identify a transition in anticoncentration. In this work, we find a recursive expression for the second moment using these graph-theoretic techniques. While we have not been able to solve this recursion by hand, we are able to solve it numerically exactly, which we do up to Fock sector $2n = 80$. We further derive new analytical results about the second moment. These results allow us to pinpoint the transition in anticoncentration and furthermore yield the expected linear cross-entropy benchmarking score for an ideal (error-free) device., Comment: 16+18 pages, 8+9 figures, 0+3 tables

Understanding the way cells communicate, co-locate, and interrelate is essential to understanding human physiology. Hematoxylin and eosin (H&E) staining is ubiquitously available both for clinical studies and research. The Colon Nucleus Identification and Classification (CoNIC) Challenge has recently innovated on robust artificial intelligence labeling of six cell types on H&E stains of the colon. However, this is a very small fraction of the number of potential cell classification types. Specifically, the CoNIC Challenge is unable to classify epithelial subtypes (progenitor, endocrine, goblet), lymphocyte subtypes (B, helper T, cytotoxic T), or connective subtypes (fibroblasts, stromal). In this paper, we propose to use inter-modality learning to label previously un-labelable cell types on virtual H&E. We leveraged multiplexed immunofluorescence (MxIF) histology imaging to identify 14 subclasses of cell types. We performed style transfer to synthesize virtual H&E from MxIF and transferred the higher density labels from MxIF to these virtual H&E images. We then evaluated the efficacy of learning in this approach. We identified helper T and progenitor nuclei with positive predictive values of $0.34 \pm 0.15$ (prevalence $0.03 \pm 0.01$) and $0.47 \pm 0.1$ (prevalence $0.07 \pm 0.02$) respectively on virtual H&E. This approach represents a promising step towards automating annotation in digital pathology.

In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to $\mathbb{Z}_d$ qudits, including instances where $d$ is a nonprime number. This capability allows the identification of topological orders that differ from the $\mathbb{Z}_d$ toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for $\mathbb{Z}_p$ qudits (with $p$ being a prime) are equivalent to finite copies of $\mathbb{Z}_p$ toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the 2d honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order., Comment: main text+appendix 29 pages, 27 figures

Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian Boson Sampling are understood to the same degree as for these other schemes, we understand relatively little about the statistical properties of its output distribution. The most relevant statistical property, from the perspective of demonstrating quantum advantage, is the anticoncentration of the output distribution as measured by its second moment. The degree of anticoncentration features in arguments for the complexity-theoretic hardness of Gaussian Boson Sampling, and it is also important to know when using cross-entropy benchmarking to verify experimental performance. In this work, we develop a graph-theoretic framework for analyzing the moments of the Gaussian Boson Sampling distribution. Using this framework, we show that Gaussian Boson Sampling undergoes a transition in anticoncentration as a function of the number of modes that are initially squeezed compared to the number of photons measured at the end of the circuit. When the number of initially squeezed modes scales sufficiently slowly with the number of photons, there is a lack of anticoncentration. However, if the number of initially squeezed modes scales quickly enough, the output probabilities anticoncentrate weakly., Comment: 5+13 pages, 2+3 figures

Toric $t$-designs, or equivalently $t$-designs on the diagonal subgroup of the unitary group, are sets of points on the torus over which sums reproduce integrals of degree $t$ monomials over the full torus. Motivated by the projective structure of quantum mechanics, we develop the notion of $t$-designs on the projective torus, which have a much more restricted structure than their counterparts on full tori. We provide various new constructions of toric and projective toric designs and prove bounds on their size. We draw connections between projective toric designs and a diverse set of mathematical objects, including difference and Sidon sets from the field of additive combinatorics, symmetric, informationally complete positive operator valued measures and complete sets of mutually unbiased bases (MUBs) from quantum information theory, and crystal ball sequences of certain root lattices. Using these connections, we prove bounds on the maximal size of dense $B_t \bmod m$ sets. We also use projective toric designs to construct families of quantum state designs. In particular, we construct families of (uniformly-weighted) quantum state $2$-designs in dimension $d$ of size exactly $d(d+1)$ that do not form complete sets of MUBs, thereby disproving a conjecture concerning the relationship between designs and MUBs (Zhu 2015). We then propose a modification of Zhu's conjecture and discuss potential paths towards proving this conjecture. We prove a fundamental distinction between complete sets of MUBs in prime-power dimensions versus in dimension $6$ (and, we conjecture, in all non-prime-power dimensions), the distinction relating to group structure of the corresponding projective toric design. Finally, we discuss many open questions about the properties of these projective toric designs and how they relate to other questions in number theory, geometry, and quantum information., Comment: 17+8 pages, 1 figure. V3: match journal version