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Junyu Liu, Liang Jiang

A quantum version of data centers might be significant in the quantum era. In this paper, we introduce Quantum Data Center (QDC), a quantum version of existing classical data centers, with a specific emphasis on combining Quantum Random Access Memory (QRAM) and quantum networks. We argue that QDC will provide significant benefits to customers in terms of efficiency, security, and precision, and will be helpful for quantum computing, communication, and sensing. We investigate potential scientific and business opportunities along this novel research direction through hardware realization and possible specific applications. We show the possible impacts of QDCs in business and science, especially the machine learning and big data industries.

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Yunfei Wang, Yuri Alexeev, Liang Jiang, Frederic T. Chong, Junyu Liu

Quantum devices should operate in adherence to quantum physics principles. Quantum random access memory (QRAM), a fundamental component of many essential quantum algorithms for tasks such as linear algebra, data search, and machine learning, is often proposed to offer $\mathcal{O}(\log N)$ circuit depth for $\mathcal{O}(N)$ data size, given $N$ qubits. However, this claim appears to breach the principle of relativity when dealing with a large number of qubits in quantum materials interacting locally. In our study we critically explore the intrinsic bounds of rapid quantum memories based on causality, employing the relativistic quantum field theory and Lieb-Robinson bounds in quantum many-body systems. In this paper, we consider a hardware-efficient QRAM design in hybrid quantum acoustic systems. Assuming clock cycle times of approximately $10^{-3}$ seconds and a lattice spacing of about 1 micrometer, we show that QRAM can accommodate up to $\mathcal{O}(10^7)$ logical qubits in 1 dimension, $\mathcal{O}(10^{15})$ to $\mathcal{O}(10^{20})$ in various 2D architectures, and $\mathcal{O}(10^{24})$ in 3 dimensions. We contend that this causality bound broadly applies to other quantum hardware systems. Our findings highlight the impact of fundamental quantum physics constraints on the long-term performance of quantum computing applications in data science and suggest potential quantum memory designs for performance enhancement.

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Junyu Liu, Minzhao Liu, Jin-Peng Liu, Ziyu Ye, Yuri Alexeev, Jens Eisert, Liang Jiang

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $O(T^2 \times \text{polylog}(n))$, where $n$ is the size of the models and $T$ is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

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Junyu Liu, Frederik Wilde, Antonio Anna Mele, Liang Jiang, Jens Eisert

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided for example by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees of the approach and its practical functioning at hand of examples. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some noise levels could help in this perspective is expected to add a new perspective to notions of near-term variational quantum algorithms.

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Liang Jiang, Zhenyu Huang, Jia Liu, Zujie Wen, Xi Peng

Most domain adaptation methods for machine reading comprehension (MRC) use a pre-trained question-answer (QA) construction model to generate pseudo QA pairs for MRC transfer. Such a process will inevitably introduce mismatched pairs (i.e., noisy correspondence) due to i) the unavailable QA pairs in target documents, and ii) the domain shift during applying the QA construction model to the target domain. Undoubtedly, the noisy correspondence will degenerate the performance of MRC, which however is neglected by existing works. To solve such an untouched problem, we propose to construct QA pairs by additionally using the dialogue related to the documents, as well as a new domain adaptation method for MRC. Specifically, we propose Robust Domain Adaptation for Machine Reading Comprehension (RMRC) method which consists of an answer extractor (AE), a question selector (QS), and an MRC model. Specifically, RMRC filters out the irrelevant answers by estimating the correlation to the document via the AE, and extracts the questions by fusing the candidate questions in multiple rounds of dialogue chats via the QS. With the extracted QA pairs, MRC is fine-tuned and provides the feedback to optimize the QS through a novel reinforced self-training method. Thanks to the optimization of the QS, our method will greatly alleviate the noisy correspondence problem caused by the domain shift. To the best of our knowledge, this could be the first study to reveal the influence of noisy correspondence in domain adaptation MRC models and show a feasible way to achieve robustness to mismatched pairs. Extensive experiments on three datasets demonstrate the effectiveness of our method.

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Junyu Liu, Connor T. Hann, Liang Jiang

In this paper, we propose the Quantum Data Center (QDC), an architecture combining Quantum Random Access Memory (QRAM) and quantum networks. We give a precise definition of QDC, and discuss its possible realizations and extensions. We discuss applications of QDC in quantum computation, quantum communication, and quantum sensing, with a primary focus on QDC for $T$-gate resources, QDC for multi-party private quantum communication, and QDC for distributed sensing through data compression. We show that QDC will provide efficient, private, and fast services as a future version of data centers.

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Junyu Liu, Zexi Lin, Liang Jiang

We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness and \emph{barren plateau} in quantum machine learning created by quantum physicists in \cite{mcclean2018barren} for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in \cite{together}.

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Minzhao Liu, Junyu Liu, Yuri Alexeev, Liang Jiang

We develop numerical protocols for estimating the frame potential, the 2-norm distance between a given ensemble and the exact Haar randomness, using the \texttt{QTensor} platform. Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high performing using CPU and GPU parallelism. We apply the above methods to two problems: the Brown-Susskind conjecture, with local and parallel random circuits in terms of the Haar distance and the approximate $k$-design properties of the hardware efficient ans{\"a}tze in quantum machine learning, which induce the barren plateau problem. We estimate frame potentials with these ensembles up to 50 qubits and $k=5$, examine the Haar distance of the hardware-efficient ans{\"a}tze, and verify the Brown-Susskind conjecture numerically. Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.

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Junyu Liu, Khadijeh Najafi, Kunal Sharma, Francesco Tacchino, Liang Jiang, Antonio Mezzacapo

Parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.

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Ruijie Yan, Shuang Peng, Haitao Mi, Liang Jiang, Shihui Yang, Yuchi Zhang, Jiajun Li, Liangrui Peng, Yongliang Wang, Zujie Wen

Building robust and general dialogue models for spoken conversations is challenging due to the gap in distributions of spoken and written data. This paper presents our approach to build generalized models for the Knowledge-grounded Task-oriented Dialogue Modeling on Spoken Conversations Challenge of DSTC-10. In order to mitigate the discrepancies between spoken and written text, we mainly employ extensive data augmentation strategies on written data, including artificial error injection and round-trip text-speech transformation. To train robust models for spoken conversations, we improve pre-trained language models, and apply ensemble algorithms for each sub-task. Typically, for the detection task, we fine-tune \roberta and ELECTRA, and run an error-fixing ensemble algorithm. For the selection task, we adopt a two-stage framework that consists of entity tracking and knowledge ranking, and propose a multi-task learning method to learn multi-level semantic information by domain classification and entity selection. For the generation task, we adopt a cross-validation data process to improve pre-trained generative language models, followed by a consensus decoding algorithm, which can add arbitrary features like relative \rouge metric, and tune associated feature weights toward \bleu directly. Our approach ranks third on the objective evaluation and second on the final official human evaluation.

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