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The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving process on multiple instances of the same problem, by observing the process on one instance of the problem to inform initialization for other processes. We aim to take advantage of the VQE solution process to obtain useful information while disregarding information which we can predict to not be very useful. In particular, we find that the solution process produces lots of data with very little new information. Therefore, we can safely disregard much of this repetitive information with little effect on the outcome of the solution process., Comment: 4 pages, 5 figures, QCCC-24 conference

Current quantum devices face challenges when dealing with large circuits due to error rates as circuit size and the number of qubits increase. The circuit wire-cutting technique addresses this issue by breaking down a large circuit into smaller, more manageable subcircuits. However, the exponential increase in the number of subcircuits and the complexity of reconstruction as more cuts are made poses a great practical challenge. Inspired by ancilla-assisted quantum process tomography and the MUBs-based grouping technique for simultaneous measurement, we propose a new approach that can reduce subcircuit running overhead. The approach first uses ancillary qubits to transform all quantum input initializations into quantum output measurements. These output measurements are then organized into commuting groups for the purpose of simultaneous measurement, based on MUBs-based grouping. This approach significantly reduces the number of necessary subcircuits as well as the total number of shots. Lastly, we provide numerical experiments to demonstrate the complexity reduction., Comment: Accepted in IEEE International Conference on Quantum Computing and Engineering - QCE24

First-Person-View (FPV) holds immense potential for revolutionizing the trajectory of Unmanned Aerial Vehicles (UAVs), offering an exhilarating avenue for navigating complex building structures. Yet, traditional Neural Radiance Field (NeRF) methods face challenges such as sampling single points per iteration and requiring an extensive array of views for supervision. UAV videos exacerbate these issues with limited viewpoints and significant spatial scale variations, resulting in inadequate detail rendering across diverse scales. In response, we introduce FPV-NeRF, addressing these challenges through three key facets: (1) Temporal consistency. Leveraging spatio-temporal continuity ensures seamless coherence between frames; (2) Global structure. Incorporating various global features during point sampling preserves space integrity; (3) Local granularity. Employing a comprehensive framework and multi-resolution supervision for multi-scale scene feature representation tackles the intricacies of UAV video spatial scales. Additionally, due to the scarcity of publicly available FPV videos, we introduce an innovative view synthesis method using NeRF to generate FPV perspectives from UAV footage, enhancing spatial perception for drones. Our novel dataset spans diverse trajectories, from outdoor to indoor environments, in the UAV domain, differing significantly from traditional NeRF scenarios. Through extensive experiments encompassing both interior and exterior building structures, FPV-NeRF demonstrates a superior understanding of the UAV flying space, outperforming state-of-the-art methods in our curated UAV dataset. Explore our project page for further insights: https://fpv-nerf.github.io/., Comment: Accepted to ECCV 2024

Transformer-based architectures have become the de-facto standard models for diverse vision tasks owing to their superior performance. As the size of the models continues to scale up, model distillation becomes extremely important in various real applications, particularly on devices limited by computational resources. However, prevailing knowledge distillation methods exhibit diminished efficacy when confronted with a large capacity gap between the teacher and the student, e.g, 10x compression rate. In this paper, we present a novel approach named Automatic Multi-step Distillation (AMD) for large-scale vision model compression. In particular, our distillation process unfolds across multiple steps. Initially, the teacher undergoes distillation to form an intermediate teacher-assistant model, which is subsequently distilled further to the student. An efficient and effective optimization framework is introduced to automatically identify the optimal teacher-assistant that leads to the maximal student performance. We conduct extensive experiments on multiple image classification datasets, including CIFAR-10, CIFAR-100, and ImageNet. The findings consistently reveal that our approach outperforms several established baselines, paving a path for future knowledge distillation methods on large-scale vision models., Comment: 19 pages, 5 figures

It is common to compare state changes of multiple data items and identify which data items have changed more in various applications (e.g., annual GDP growth of different countries and daily increase of new COVID-19 cases in different regions). Grouped bar charts and slope graphs can visualize both state changes and their initial and final states of multiple data items, and are thus widely used for state change comparison. But they leverage implicit bar differences or line slopes to indicate state changes, which has been proven less effective for visual comparison. Both visualizations also suffer from visual scalability issues when an increasing number of data items need to be compared. This paper fills the research gap by proposing a novel radial visualization called Intercept Graph to facilitate visual comparison of multiple state changes. It consists of inner and outer axes, and leverages the lengths of line segments intercepted by the inner axis to explicitly encode the state changes. Users can interactively adjust the inner axis to filter large changes of their interest and magnify the difference of relatively-similar state changes, enhancing its visual scalability and comparison accuracy. We extensively evaluate the Intercept Graph in comparison with baseline methods through two usage scenarios, quantitative metric evaluations, and well-designed crowdsourcing user studies with 50 participants. Our results demonstrate the usefulness and effectiveness of the Intercept Graph.

In this work, we introduce the Prototypical Transformer (ProtoFormer), a general and unified framework that approaches various motion tasks from a prototype perspective. ProtoFormer seamlessly integrates prototype learning with Transformer by thoughtfully considering motion dynamics, introducing two innovative designs. First, Cross-Attention Prototyping discovers prototypes based on signature motion patterns, providing transparency in understanding motion scenes. Second, Latent Synchronization guides feature representation learning via prototypes, effectively mitigating the problem of motion uncertainty. Empirical results demonstrate that our approach achieves competitive performance on popular motion tasks such as optical flow and scene depth. Furthermore, it exhibits generality across various downstream tasks, including object tracking and video stabilization., Comment: 21 pages, 10 figures

With the rapid development of Quantum Machine Learning, quantum neural networks (QNN) have experienced great advancement in the past few years, harnessing the advantages of quantum computing to significantly speed up classical machine learning tasks. Despite their increasing popularity, the quantum neural network is quite counter-intuitive and difficult to understand, due to their unique quantum-specific layers (e.g., data encoding and measurement) in their architecture. It prevents QNN users and researchers from effectively understanding its inner workings and exploring the model training status. To fill the research gap, we propose VIOLET, a novel visual analytics approach to improve the explainability of quantum neural networks. Guided by the design requirements distilled from the interviews with domain experts and the literature survey, we developed three visualization views: the Encoder View unveils the process of converting classical input data into quantum states, the Ansatz View reveals the temporal evolution of quantum states in the training process, and the Feature View displays the features a QNN has learned after the training process. Two novel visual designs, i.e., satellite chart and augmented heatmap, are proposed to visually explain the variational parameters and quantum circuit measurements respectively. We evaluate VIOLET through two case studies and in-depth interviews with 12 domain experts. The results demonstrate the effectiveness and usability of VIOLET in helping QNN users and developers intuitively understand and explore quantum neural networks

Quantum computing offers significant speedup compared to classical computing, which has led to a growing interest among users in learning and applying quantum computing across various applications. However, quantum circuits, which are fundamental for implementing quantum algorithms, can be challenging for users to understand due to their underlying logic, such as the temporal evolution of quantum states and the effect of quantum amplitudes on the probability of basis quantum states. To fill this research gap, we propose QuantumEyes, an interactive visual analytics system to enhance the interpretability of quantum circuits through both global and local levels. For the global-level analysis, we present three coupled visualizations to delineate the changes of quantum states and the underlying reasons: a Probability Summary View to overview the probability evolution of quantum states; a State Evolution View to enable an in-depth analysis of the influence of quantum gates on the quantum states; a Gate Explanation View to show the individual qubit states and facilitate a better understanding of the effect of quantum gates. For the local-level analysis, we design a novel geometrical visualization Dandelion Chart to explicitly reveal how the quantum amplitudes affect the probability of the quantum state. We thoroughly evaluated QuantumEyes as well as the novel QuantumEyes integrated into it through two case studies on different types of quantum algorithms and in-depth expert interviews with 12 domain experts. The results demonstrate the effectiveness and usability of our approach in enhancing the interpretability of quantum circuits.

In this extended abstract, we have introduced a highly memory-efficient state vector simulation of quantum circuits premised on data compression, harnessing the capabilities of both CPUs and GPUs. We have elucidated the inherent challenges in architecting this system, while concurrently proposing our tailored solutions. Moreover, we have delineated our preliminary implementation and deliberated upon the potential for integration with other GPU-oriented simulators. In forthcoming research, we aim to present a more comprehensive set of results, bolstering the assertion of the efficacy and performance of our approach.

In the near-term noisy intermediate-scale quantum (NISQ) era, high noise will significantly reduce the fidelity of quantum computing. Besides, the noise on quantum devices is not stable. This leads to a challenging problem: At run-time, is there a way to efficiently achieve a consistent high-fidelity quantum system on unstable devices? To study this problem, we take quantum learning (a.k.a., variational quantum algorithm) as a vehicle, such as combinatorial optimization and machine learning. A straightforward approach is to optimize a Circuit with a parameter-shift approach on the target quantum device before using it; however, the optimization has an extremely high time cost, which is not practical at run-time. To address the pressing issue, in this paper, we proposed a novel quantum pulse-based noise adaptation framework, namely QuPAD. In the proposed framework, first, we identify that the CNOT gate is the fidelity bottleneck of the conventional VQC, and we employ a more robust parameterized multi-quit gate (i.e., Rzx gate) to replace the CNOT gate. Second, by benchmarking the Rzx gate with different parameters, we build a fitting function for each coupling qubit pair, such that the deviation between the theoretic output of the Rzx gate and its on-device output under a given pulse amplitude and duration can be efficiently predicted. On top of this, an evolutionary algorithm is devised to identify the pulse amplitude and duration of each Rzx gate (i.e., calibration) and find the quantum circuits with high fidelity. Experiments show that the runtime on quantum devices of QuPAD with 8-10 qubits is less than 15 minutes, which is up to 270x faster than the parameter-shift approach. In addition, compared to the vanilla VQC as a baseline, QuPAD can achieve 59.33% accuracy gain on a classification task, and average 66.34% closer to ground state energy for molecular simulation.

Quantum circuit cutting has emerged as a promising method for simulating large quantum circuits using a collection of small quantum machines. Running low-qubit "circuit fragments" not only overcomes the size limitation of near-term hardware, but it also increases the fidelity of the simulation. However, reconstructing measurement statistics requires computational resources - both classical and quantum - that grow exponentially with the number of cuts. In this manuscript, we introduce the concept of a golden cutting point, which identifies unnecessary basis components during reconstruction and avoids related down-stream computation. We propose a hypothesis-testing scheme for identifying golden cutting points, and provide robustness results in the case of the test failing with low probability. Lastly, we demonstrate the applicability of our method on Qiskit's Aer simulator and observe a reduced wall time from identifying and avoiding obsolete measurements.

The rapid advancement of quantum hardware brings a host of research opportunities and the potential for quantum advantages across numerous fields. In this landscape, quantum circuit simulations serve as an indispensable tool by emulating quantum behavior on classical computers. They offer easy access, noise-free environments, and real-time observation of quantum states. However, the sustainability aspect of quantum circuit simulation is yet to be explored. In this paper, we introduce for the first time the concept of environmental impact from quantum circuit simulation. We present a preliminary model to compute the CO2e emissions derived from quantum circuit simulations. Our results indicate that large quantum circuit simulations (43 qubits) could lead to CO2e emissions 48 times greater than training a transformer machine learning model.

Recently, we have been witnessing the scale-up of superconducting quantum computers; however, the noise of quantum bits (qubits) is still an obstacle for real-world applications to leveraging the power of quantum computing. Although there exist error mitigation or error-aware designs for quantum applications, the inherent fluctuation of noise (a.k.a., instability) can easily collapse the performance of error-aware designs. What's worse, users can even not be aware of the performance degradation caused by the change in noise. To address both issues, in this paper we use Quantum Neural Network (QNN) as a vehicle to present a novel compression-aided framework, namely QuCAD, which will adapt a trained QNN to fluctuating quantum noise. In addition, with the historical calibration (noise) data, our framework will build a model repository offline, which will significantly reduce the optimization time in the online adaption process. Emulation results on an earthquake detection dataset show that QuCAD can achieve 14.91% accuracy gain on average in 146 days over a noise-aware training approach. For the execution on a 7-qubit IBM quantum processor, IBM-Jakarta, QuCAD can consistently achieve 12.52% accuracy gain on earthquake detection.

Quantum circuit cutting has been proposed to help execute large quantum circuits using only small and noisy machines. Intuitively, cutting a qubit wire can be thought of as classically passing information of a quantum state along each element in a basis set. As the number of cuts increase, the number of quantum degrees of freedom needed to be passed through scales exponentially. We propose a simple reduction scheme to lower the classical and quantum resources required to perform a cut. Particularly, we recognize that for some cuts, certain basis element might pass "no information" through the qubit wire and can effectively be neglected. We empirically demonstrate our method on circuit simulators as well as IBM quantum hardware, and we observed up to 33 percent reduction in wall time without loss of accuracy., Comment: 7 pages, 5 figures, submitted to 37th IEEE International Parallel & Distributed Processing Symposium

Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely-used visualization for showing quantum states, which leverages angles to represent quantum amplitudes. However, it cannot support the visualization of quantum entanglement and superposition, the two essential properties of quantum computing. To address this issue, we propose VENUS, a novel visualization for quantum state representation. By explicitly correlating 2D geometric shapes based on the math foundation of quantum computing characteristics, VENUS effectively represents quantum amplitudes of both the single qubit and two qubits for quantum entanglement. Also, we use multiple coordinated semicircles to naturally encode probability distribution, making the quantum superposition intuitive to analyze. We conducted two well-designed case studies and an in-depth expert interview to evaluate the usefulness and effectiveness of VENUS. The result shows that VENUS can effectively facilitate the exploration of quantum states for the single qubit and two qubits.

In recent years, there have been quite a few attempts to apply intelligent techniques to financial trading, i.e., constructing automatic and intelligent trading framework based on historical stock price. Due to the unpredictable, uncertainty and volatile nature of financial market, researchers have also resorted to deep learning to construct the intelligent trading framework. In this paper, we propose to use CNN as the core functionality of such framework, because it is able to learn the spatial dependency (i.e., between rows and columns) of the input data. However, different with existing deep learning-based trading frameworks, we develop novel normalization process to prepare the stock data. In particular, we first empirically observe that the stock data is intrinsically heterogeneous and bursty, and then validate the heterogeneity and burst nature of stock data from a statistical perspective. Next, we design the data normalization method in a way such that the data heterogeneity is preserved and bursty events are suppressed. We verify out developed CNN-based trading framework plus our new normalization method on 29 stocks. Experiment results show that our approach can outperform other comparing approaches.

Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting -- a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the limited quantum resource at hand -- is used to mitigate these problems. However, classical postprocessing involved in circuit cutting generally grows exponentially with the number of cuts and quantum counts. This article introduces the notion of approximate circuit reconstruction. Using a sampling-based method like Markov Chain Monte Carlo (MCMC), we probabilistically select bit strings of high probability upon reconstruction. This avoids excessive calculations when reconstructing the full probability distribution. Our results show that such a sampling-based postprocessing method holds great potential for fast and reliable circuit reconstruction in the NISQ era and beyond.

Quantum computing has attracted considerable public attention due to its exponential speedup over classical computing. Despite its advantages, today's quantum computers intrinsically suffer from noise and are error-prone. To guarantee the high fidelity of the execution result of a quantum algorithm, it is crucial to inform users of the noises of the used quantum computer and the compiled physical circuits. However, an intuitive and systematic way to make users aware of the quantum computing noise is still missing. In this paper, we fill the gap by proposing a novel visualization approach to achieve noise-aware quantum computing. It provides a holistic picture of the noise of quantum computing through multiple interactively coordinated views: a Computer Evolution View with a circuit-like design overviews the temporal evolution of the noises of different quantum computers, a Circuit Filtering View facilitates quick filtering of multiple compiled physical circuits for the same quantum algorithm, and a Circuit Comparison View with a coupled bar chart enables detailed comparison of the filtered compiled circuits. We extensively evaluate the performance of VACSEN through two case studies on quantum algorithms of different scales and an in-depth interviews with 12 quantum computing users. The results demonstrate the effectiveness and usability of VACSEN in achieving noise-aware quantum computing.

Quantum computing is a new technology that is expected to revolutionize the computation paradigm in the next few years. Qubits exploit the quantum physics proprieties to increase the parallelism and speed of computation. Unfortunately, besides being intrinsically noisy, qubits have also been shown to be highly susceptible to external sources of faults, such as ionizing radiation. The latest discoveries highlight a much higher radiation sensitivity of qubits than traditional transistors and identify a much more complex fault model than bit-flip. We propose a framework to identify the quantum circuits sensitivity to radiation-induced faults and the probability for a fault in a qubit to propagate to the output. Based on the latest studies and radiation experiments performed on real quantum machines, we model the transient faults in a qubit as a phase shift with a parametrized magnitude. Additionally, our framework can inject multiple qubit faults, tuning the phase shift magnitude based on the proximity of the qubit to the particle strike location. As we show in the paper, the proposed fault injector is highly flexible, and it can be used on both quantum circuit simulators and real quantum machines. We report the finding of more than 285M injections on the Qiskit simulator and 53K injections on real IBM machines. We consider three quantum algorithms and identify the faults and qubits that are more likely to impact the output. We also consider the fault propagation dependence on the circuit scale, showing that the reliability profile for some quantum algorithms is scale-dependent, with increased impact from radiation-induced faults as we increase the number of qubits. Finally, we also consider multi qubits faults, showing that they are much more critical than single faults. The fault injector and the data presented in this paper are available in a public repository to allow further analysis., Comment: 13 pages, 11 figures. To be published in the 52nd Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN'22)

Soft errors have become one of the major concerns for HPC applications, as those errors can result in seriously corrupted outcomes, such as silent data corruptions (SDCs). Prior studies on error resilience have studied the robustness of HPC applications. However, it is still difficult for program developers to identify potential vulnerability to soft errors. In this paper, we present Visilence, a novel visualization tool to visually analyze error vulnerability based on the control-flow graph generated from HPC applications. Visilence efficiently visualizes the affected program states under injected errors and presents the visual analysis of the most vulnerable parts of an application. We demonstrate the effectiveness of Visilence through a case study.

Cloud systems are becoming increasingly powerful and complex. It is highly challenging to identify anomalous execution behaviors and pinpoint problems by examining the overwhelming intermediate results/states in complex application workflows. Domain scientists urgently need a friendly and functional interface to understand the quality of the computing services and the performance of their applications in real time. To meet these needs, we explore data generated by job schedulers and investigate general performance metrics (e.g., utilization of CPU, memory and disk I/O). Specifically, we propose an interactive visual analytics approach, BatchLens, to provide both providers and users of cloud service with an intuitive and effective way to explore the status of system batch jobs and help them conduct root-cause analysis of anomalous behaviors in batch jobs. We demonstrate the effectiveness of BatchLens through a case study on the public Alibaba bench workload trace datasets.

Quantum computing is one of the most promising technology advances of the latest years. Once only a conceptual idea to solve physics simulations, quantum computation is today a reality, with numerous machines able to execute quantum algorithms. One of the hardest challenges in quantum computing is reliability. Qubits are highly sensitive to noise, which can make the output useless. Moreover, lately it has been shown that superconducting qubits are extremely susceptible to external sources of faults, such as ionizing radiation. When adopted in large scale, radiation-induced errors are expected to become a serious challenge for qubits reliability. In this paper, we propose an evaluation of the impact of transient faults in the execution of quantum circuits. Inspired by the Architectural and Program Vulnerability Factors, widely adopted to characterize the reliability of classical computing architectures and algorithms, we propose the Quantum Vulnerability Factor (QVF) as a metric to measure the impact that the corruption of a qubit has on the circuit output probability distribution. First, we model faults based on the latest studies on real machines and recently performed radiation experiments. Then, we design a quantum fault injector, built over Qiskit, and characterize the propagation of faults in quantum circuits. We report the finding of more than 15,000,000 fault injections, evaluating the reliability of three quantum circuits and identifying the faults and qubits that are more likely than others to impact the output. With our results, we give guidelines on how to map the qubits in the real quantum computer to reduce the output error and to reduce the probability of having a radiation-induced corruption to modify the output. Finally, we compare the simulation results with experiments on physical quantum computers.

State change comparison of multiple data items is often necessary in multiple application domains, such as medical science, financial engineering, sociology, biological science, etc. Slope graphs and grouped bar charts have been widely used to show a "before-and-after" story of different data states and indicate their changes. However, they visualize state changes as either slope or difference of bars, which has been proved less effective for quantitative comparison. Also, both visual designs suffer from visual clutter issues with an increasing number of data items. In this paper, we propose Intercept Graph, a novel visual design to facilitate effective interactive comparison of state changes. Specifically, a radial design is proposed to visualize the starting and ending states of each data item and the line segment length explicitly encodes the "state change". By interactively adjusting the radius of the inner circular axis, Intercept Graph can smoothly filter the large state changes and magnify the difference between similar state changes, mitigating the visual clutter issues and enhancing the effective comparison of state changes. We conducted a case study through comparing Intercept Graph with slope graphs and grouped bar charts on real datasets to demonstrate the effectiveness of Intercept Graph.

Deep learning and data-driven approaches have shown great potential in scientific domains. The promise of data-driven techniques relies on the availability of a large volume of high-quality training datasets. Due to the high cost of obtaining data through expensive physical experiments, instruments, and simulations, data augmentation techniques for scientific applications have emerged as a new direction for obtaining scientific data recently. However, existing data augmentation techniques originating from computer vision, yield physically unacceptable data samples that are not helpful for the domain problems that we are interested in. In this paper, we develop new data augmentation techniques based on convolutional neural networks. Specifically, our generative models leverage different physics knowledge (such as governing equations, observable perception, and physics phenomena) to improve the quality of the synthetic data. To validate the effectiveness of our data augmentation techniques, we apply them to solve a subsurface seismic full-waveform inversion using simulated CO$_2$ leakage data. Our interest is to invert for subsurface velocity models associated with very small CO$_2$ leakage. We validate the performance of our methods using comprehensive numerical tests. Via comparison and analysis, we show that data-driven seismic imaging can be significantly enhanced by using our data augmentation techniques. Particularly, the imaging quality has been improved by 15% in test scenarios of general-sized leakage and 17% in small-sized leakage when using an augmented training set obtained with our techniques., Comment: 15 pages, 15 figures, accepted by IEEE Transactions on Geoscience and Remote Sensing, available as early access

In recent years, the increasing complexity in scientific simulations and emerging demands for training heavy artificial intelligence models require massive and fast data accesses, which urges high-performance computing (HPC) platforms to equip with more advanced storage infrastructures such as solid-state disks (SSDs). While SSDs offer high-performance I/O, the reliability challenges faced by the HPC applications under the SSD-related failures remains unclear, in particular for failures resulting in data corruptions. The goal of this paper is to understand the impact of SSD-related faults on the behaviors of complex HPC applications. To this end, we propose FFIS, a FUSE-based fault injection framework that systematically introduces storage faults into the application layer to model the errors originated from SSDs. FFIS is able to plant different I/O related faults into the data returned from underlying file systems, which enables the investigation on the error resilience characteristics of the scientific file format. We demonstrate the use of FFIS with three representative real HPC applications, showing how each application reacts to the data corruptions, and provide insights on the error resilience of the widely adopted HDF5 file format for the HPC applications., Comment: 12 pages, 9 figures, 4 tables, accepted by IEEE Cluster'21

In the past decade, remarkable progress has been achieved in deep learning related systems and applications. In the post Moore's Law era, however, the limit of semiconductor fabrication technology along with the increasing data size have slowed down the development of learning algorithms. In parallel, the fast development of quantum computing has pushed it to the new ear. Google illustrates quantum supremacy by completing a specific task (random sampling problem), in 200 seconds, which is impracticable for the largest classical computers. Due to the limitless potential, quantum based learning is an area of interest, in hopes that certain systems might offer a quantum speedup. In this work, we propose a novel architecture QuClassi, a quantum neural network for both binary and multi-class classification. Powered by a quantum differentiation function along with a hybrid quantum-classic design, QuClassi encodes the data with a reduced number of qubits and generates the quantum circuit, pushing it to the quantum platform for the best states, iteratively. We conduct intensive experiments on both the simulator and IBM-Q quantum platform. The evaluation results demonstrate that QuClassi is able to outperform the state-of-the-art quantum-based solutions, Tensorflow-Quantum and QuantumFlow by up to 53.75% and 203.00% for binary and multi-class classifications. When comparing to traditional deep neural networks, QuClassi achieves a comparable performance with 97.37% fewer parameters.

Significant experimental progress has been made recently for observing long-sought supersolid-like states in Bose-Einstein condensates, where spatial translational symmetry is spontaneously broken by anisotropic interactions to form a stripe order. Meanwhile, the superfluid stripe ground state was also observed by applying a weak optical lattice that forces the symmetry breaking. Despite of the similarity of the ground states, here we show that these two symmetry breaking mechanisms can be distinguished by their collective excitation spectra. In contrast to gapless Goldstone modes of the \textit{spontaneous} stripe state, we propose that the excitation spectra of the \textit{forced} stripe phase can provide direct experimental evidence for the long-sought gapped pseudo-Goldstone modes. We characterize the pseudo-Goldstone mode of such lattice-induced stripe phase through its excitation spectrum and static structure factor. Our work may pave the way for exploring spontaneous and forced/approximate symmetry breaking mechanisms in different physical systems., Comment: 5 pages, 4 figures, and 4 page Supplementary Materials