Simulating Large Quantum Circuits on a Small Quantum Computer

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters $K$ and $d$ of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most $d$ with at most $K$ qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any $(K,d)$-clustered quantum circuit on a $d$-qubit machine in time roughly $2^{O(K)}$, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems -- such as large molecules -- that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH$_2$ molecule while running on a physical quantum device with half the number of required qubits.Comment: Codes are available at https://github.com/TianyiPeng/Partiton_VQ

Contrastive Clustering

In this paper, we propose a one-stage online clustering method called Contrastive Clustering (CC) which explicitly performs the instance- and cluster-level contrastive learning. To be specific, for a given dataset, the positive and negative instance pairs are constructed through data augmentations and then projected into a feature space. Therein, the instance- and cluster-level contrastive learning are respectively conducted in the row and column space by maximizing the similarities of positive pairs while minimizing those of negative ones. Our key observation is that the rows of the feature matrix could be regarded as soft labels of instances, and accordingly the columns could be further regarded as cluster representations. By simultaneously optimizing the instance- and cluster-level contrastive loss, the model jointly learns representations and cluster assignments in an end-to-end manner. Extensive experimental results show that CC remarkably outperforms 17 competitive clustering methods on six challenging image benchmarks. In particular, CC achieves an NMI of 0.705 (0.431) on the CIFAR-10 (CIFAR-100) dataset, which is an up to 19\% (39\%) performance improvement compared with the best baseline

Cross-modal Active Complementary Learning with Self-refining Correspondence

Recently, image-text matching has attracted more and more attention from academia and industry, which is fundamental to understanding the latent correspondence across visual and textual modalities. However, most existing methods implicitly assume the training pairs are well-aligned while ignoring the ubiquitous annotation noise, a.k.a noisy correspondence (NC), thereby inevitably leading to a performance drop. Although some methods attempt to address such noise, they still face two challenging problems: excessive memorizing/overfitting and unreliable correction for NC, especially under high noise. To address the two problems, we propose a generalized Cross-modal Robust Complementary Learning framework (CRCL), which benefits from a novel Active Complementary Loss (ACL) and an efficient Self-refining Correspondence Correction (SCC) to improve the robustness of existing methods. Specifically, ACL exploits active and complementary learning losses to reduce the risk of providing erroneous supervision, leading to theoretically and experimentally demonstrated robustness against NC. SCC utilizes multiple self-refining processes with momentum correction to enlarge the receptive field for correcting correspondences, thereby alleviating error accumulation and achieving accurate and stable corrections. We carry out extensive experiments on three image-text benchmarks, i.e., Flickr30K, MS-COCO, and CC152K, to verify the superior robustness of our CRCL against synthetic and real-world noisy correspondences.Comment: This paper is accepted by NeurIPS 202

A quantum-inspired tensor network method for constrained combinatorial optimization problems

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum inspired algorithm for general locally constrained combinatorial optimization problems by encoding the constraints directly into a tensor network state. The optimal solution can be efficiently solved by borrowing the imaginary time evolution from a quantum many-body system. We demonstrate our algorithm with the open-pit mining problem numerically. Our computational results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems

Near-Optimal Entrywise Anomaly Detection for Low-Rank Matrices with Sub-Exponential Noise

We study the problem of identifying anomalies in a low-rank matrix observed with sub-exponential noise, motivated by applications in retail and inventory management. State of the art approaches to anomaly detection in low-rank matrices apparently fall short, since they require that non-anomalous entries be observed with vanishingly small noise (which is not the case in our problem, and indeed in many applications). So motivated, we propose a conceptually simple entrywise approach to anomaly detection in low-rank matrices. Our approach accommodates a general class of probabilistic anomaly models. We extend recent work on entrywise error guarantees for matrix completion, establishing such guarantees for sub-exponential matrices, where in addition to missing entries, a fraction of entries are corrupted by (an also unknown) anomaly model. Viewing the anomaly detection as a classification task, to the best of our knowledge, we are the first to achieve the min-max optimal detection rate (up to log factors). Using data from a massive consumer goods retailer, we show that our approach provides significant improvements over incumbent approaches to anomaly detection

Adaptive Meta-learner via Gradient Similarity for Few-shot Text Classification

Few-shot text classification aims to classify the text under the few-shot scenario. Most of the previous methods adopt optimization-based meta learning to obtain task distribution. However, due to the neglect of matching between the few amount of samples and complicated models, as well as the distinction between useful and useless task features, these methods suffer from the overfitting issue. To address this issue, we propose a novel Adaptive Meta-learner via Gradient Similarity (AMGS) method to improve the model generalization ability to a new task. Specifically, the proposed AMGS alleviates the overfitting based on two aspects: (i) acquiring the potential semantic representation of samples and improving model generalization through the self-supervised auxiliary task in the inner loop, (ii) leveraging the adaptive meta-learner via gradient similarity to add constraints on the gradient obtained by base-learner in the outer loop. Moreover, we make a systematic analysis of the influence of regularization on the entire framework. Experimental results on several benchmarks demonstrate that the proposed AMGS consistently improves few-shot text classification performance compared with the state-of-the-art optimization-based meta-learning approaches.Comment: COLING 202