arXiv subjects

Yuxuan Du

Publications and source records attributed to Yuxuan Du.

At least 73 records · Page 4Linked to original sources

arXiv2022

Quantum Differentially Private Sparse Regression Learning

The eligibility of various advanced quantum algorithms will be questioned if they can not guarantee privacy. To fill this knowledge gap, here we devise an efficient quantum differentially private (QDP) Lasso estimator to solve sparse regression tasks. Concretely, given $N$ $d$-dimensional data points with $N\ll d$, we first prove that the optimal classical and quantum non-private Lasso requires $Ω(N+d)$ and $Ω(\sqrt{N}+\sqrt{d})$ runtime, respectively. We next prove that the runtime cost of QDP Lasso is \textit{dimension independent}, i.e., $O(N^{5/2})$, which implies that the QDP Lasso can be faster than both the optimal classical and quantum non-private Lasso. Last, we exhibit that the QDP Lasso attains a near-optimal utility bound $\tilde{O}(N^{-2/3})$ with privacy guarantees and discuss the chance to realize it on near-term quantum chips with advantages.

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arXiv2022

QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines

The design of fast algorithms for combinatorial optimization greatly contributes to a plethora of domains such as logistics, finance, and chemistry. Quantum approximate optimization algorithms (QAOAs), which utilize the power of quantum machines and inherit the spirit of adiabatic evolution, are novel approaches to tackle combinatorial problems with potential runtime speedups. However, hurdled by the limited quantum resources nowadays, QAOAs are infeasible to manipulate large-scale problems. To address this issue, here we revisit the MaxCut problem via the divide-and-conquer heuristic: seek the solutions of subgraphs in parallel and then merge these solutions to obtain the global solution. Due to the $\mathbb{Z}_2$ symmetry in MaxCut, we prove that the merging process can be further cast into a new MaxCut problem and thus be addressed by QAOAs or other MaxCut solvers. With this regard, we propose QAOA-in-QAOA ($\text{QAOA}^2$) to solve arbitrary large-scale MaxCut problems using small quantum machines. We also prove that the approximation ratio of $\text{QAOA}^2$ is lower bounded by 1/2. Experiment results illustrate that under different graph settings, $\text{QAOA}^2$ attains a competitive or even better performance over the best known classical algorithms when the node count is around 2000. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale combinatorial optimization problems.

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arXiv2022

Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However, there are several caveats to current protocols, which are low optimality, high inference time, limited scalability, and lack of universality. To compensate for these defects, here we devise an efficient and practical quantum compiler assisted by advanced deep reinforcement learning (RL) techniques, i.e., data generation, deep Q-learning, and AQ* search. In this way, our protocol is compatible with various quantum machines and can be used to compile multi-qubit operators. We systematically evaluate the performance of our proposal in compiling quantum operators with both inverse-closed and inverse-free universal basis sets. In the task of single-qubit operator compiling, our proposal outperforms other RL-based quantum compilers in the measure of compiling sequence length and inference time. Meanwhile, the output solution is near-optimal, guaranteed by the Solovay-Kitaev theorem. Notably, for the inverse-free universal basis set, the achieved sequence length complexity is comparable with the inverse-based setting and dramatically advances previous methods. These empirical results contribute to improving the inverse-free Solovay-Kitaev theorem. In addition, for the first time, we demonstrate how to leverage RL-based quantum compilers to accomplish two-qubit operator compiling. The achieved results open an avenue for integrating RL with quantum compiling to unify efficiency and practicality and thus facilitate the exploration of quantum advantages.

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arXiv2022

Unentangled quantum reinforcement learning agents in the OpenAI Gym

Classical reinforcement learning (RL) has generated excellent results in different regions; however, its sample inefficiency remains a critical issue. In this paper, we provide concrete numerical evidence that the sample efficiency (the speed of convergence) of quantum RL could be better than that of classical RL, and for achieving comparable learning performance, quantum RL could use much (at least one order of magnitude) fewer trainable parameters than classical RL. Specifically, we employ the popular benchmarking environments of RL in the OpenAI Gym, and show that our quantum RL agent converges faster than classical fully-connected neural networks (FCNs) in the tasks of CartPole and Acrobot under the same optimization process. We also successfully train the first quantum RL agent that can complete the task of LunarLander in the OpenAI Gym. Our quantum RL agent only requires a single-qubit-based variational quantum circuit without entangling gates, followed by a classical neural network (NN) to post-process the measurement output. Finally, we could accomplish the aforementioned tasks on the real IBM quantum machines. To the best of our knowledge, none of the earlier quantum RL agents could do that.

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arXiv2022

DyRep: Bootstrapping Training with Dynamic Re-parameterization

Structural re-parameterization (Rep) methods achieve noticeable improvements on simple VGG-style networks. Despite the prevalence, current Rep methods simply re-parameterize all operations into an augmented network, including those that rarely contribute to the model's performance. As such, the price to pay is an expensive computational overhead to manipulate these unnecessary behaviors. To eliminate the above caveats, we aim to bootstrap the training with minimal cost by devising a dynamic re-parameterization (DyRep) method, which encodes Rep technique into the training process that dynamically evolves the network structures. Concretely, our proposal adaptively finds the operations which contribute most to the loss in the network, and applies Rep to enhance their representational capacity. Besides, to suppress the noisy and redundant operations introduced by Rep, we devise a de-parameterization technique for a more compact re-parameterization. With this regard, DyRep is more efficient than Rep since it smoothly evolves the given network instead of constructing an over-parameterized network. Experimental results demonstrate our effectiveness, e.g., DyRep improves the accuracy of ResNet-18 by $2.04\%$ on ImageNet and reduces $22\%$ runtime over the baseline. Code is available at: https://github.com/hunto/DyRep.

cs.CV↗

arXiv2022

Efficient measure for the expressivity of variational quantum algorithms

The superiority of variational quantum algorithms (VQAs) such as quantum neural networks (QNNs) and variational quantum eigen-solvers (VQEs) heavily depends on the expressivity of the employed ansatze. Namely, a simple ansatze is insufficient to capture the optimal solution, while an intricate ansatze leads to the hardness of the trainability. Despite its fundamental importance, an effective strategy of measuring the expressivity of VQAs remains largely unknown. Here, we exploit an advanced tool in statistical learning theory, i.e., covering number, to study the expressivity of VQAs. In particular, we first exhibit how the expressivity of VQAs with an arbitrary ansatze is upper bounded by the number of quantum gates and the measurement observable. We next explore the expressivity of VQAs on near-term quantum chips, where the system noise is considered. We observe an exponential decay of the expressivity with increasing circuit depth. We also utilize the achieved expressivity to analyze the generalization of QNNs and the accuracy of VQE. We numerically verify our theory employing VQAs with different levels of expressivity. Our work opens the avenue for quantitative understanding of the expressivity of VQAs.

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arXiv2022

Do We Need to Penalize Variance of Losses for Learning with Label Noise?

Algorithms which minimize the averaged loss have been widely designed for dealing with noisy labels. Intuitively, when there is a finite training sample, penalizing the variance of losses will improve the stability and generalization of the algorithms. Interestingly, we found that the variance should be increased for the problem of learning with noisy labels. Specifically, increasing the variance will boost the memorization effects and reduce the harmfulness of incorrect labels. By exploiting the label noise transition matrix, regularizers can be easily designed to reduce the variance of losses and be plugged in many existing algorithms. Empirically, the proposed method by increasing the variance of losses significantly improves the generalization ability of baselines on both synthetic and real-world datasets.

cs.LG↗

arXiv2022

Quantum circuit architecture search on a superconducting processor

Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale quantum (NISQ) machines. To address this issue, here we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search (QAS), to enhance VQAs on an 8-qubit superconducting quantum processor. In particular, we apply QAS to tailor the hardware-efficient ansatz towards classification tasks. Compared with the heuristic ansatze, the ansatz designed by QAS improves test accuracy from 31% to 98%. We further explain this superior performance by visualizing the loss landscape and analyzing effective parameters of all ansatze. Our work provides concrete guidance for developing variable ansatze to tackle various large-scale quantum learning problems with advantages.

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arXiv2021

Experimental Quantum Generative Adversarial Networks for Image Generation

Quantum machine learning is expected to be one of the first practical applications of near-term quantum devices. Pioneer theoretical works suggest that quantum generative adversarial networks (GANs) may exhibit a potential exponential advantage over classical GANs, thus attracting widespread attention. However, it remains elusive whether quantum GANs implemented on near-term quantum devices can actually solve real-world learning tasks. Here, we devise a flexible quantum GAN scheme to narrow this knowledge gap, which could accomplish image generation with arbitrarily high-dimensional features, and could also take advantage of quantum superposition to train multiple examples in parallel. For the first time, we experimentally achieve the learning and generation of real-world hand-written digit images on a superconducting quantum processor. Moreover, we utilize a gray-scale bar dataset to exhibit the competitive performance between quantum GANs and the classical GANs based on multilayer perceptron and convolutional neural network architectures, respectively, benchmarked by the Fréchet Distance score. Our work provides guidance for developing advanced quantum generative models on near-term quantum devices and opens up an avenue for exploring quantum advantages in various GAN-related learning tasks.

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arXiv2021

Towards understanding the power of quantum kernels in the NISQ era

A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To this end, a crucial open question is: does the power of quantum kernels still hold under the NISQ setting? In this study, we fill this knowledge gap by exploiting the power of quantum kernels when the quantum system noise and sample error are considered. Concretely, we first prove that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise. With the aim of preserving the superiority of quantum kernels in the NISQ era, we further devise an effective method via indefinite kernel learning. Numerical simulations accord with our theoretical results. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.

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arXiv2021

Accelerating variational quantum algorithms with multiple quantum processors

Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large-volume data. As such, to better exert the superiority of VQAs, it is of great significance to improve their runtime efficiency. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue. Specifically, in QUDIO, a classical central server partitions the learning problem into multiple subproblems and allocate them to multiple local nodes where each of them consists of a quantum processor and a classical optimizer. During the training procedure, all local nodes proceed parallel optimization and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in terms of the number of global iteration under the ideal scenario, while the system imperfection may incur divergent optimization. Numerical results on standard benchmarks demonstrate that QUDIO can surprisingly achieve a superlinear runtime speedup with respect to the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.

quant-ph↗

arXiv2021

The dilemma of quantum neural networks

The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bound than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that quantum neural networks (QNNs) have the ability to achieve this goal on specific datasets. With this regard, it is of great importance to understand whether these advantages are still preserved on real-world tasks. Through systematic numerical experiments, we empirically observe that current QNNs fail to provide any benefit over classical learning models. Concretely, our results deliver two key messages. First, QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. Second, the trainability of QNNs is insensitive to regularization techniques, which sharply contrasts with the classical scenario. These empirical results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.

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arXiv2020

On the learnability of quantum neural networks

We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme, which remains largely unknown due to the non-convex optimization landscape, the measurement error, and the unavoidable gate errors introduced by noisy intermediate-scale quantum (NISQ) machines. Our contributions in this paper are multi-fold. First, we derive the utility bounds of QNN towards empirical risk minimization, and show that large gate noise, few quantum measurements, and deep circuit depth will lead to the poor utility bounds. This result also applies to the variational quantum circuits with gradient-based classical optimization, and can be of independent interest. We then prove that QNN can be treated as a differentially private (DP) model. Thirdly, we show that if a concept class can be efficiently learned by QNN, then it can also be effectively learned by QNN even with gate noise. This result implies the same learnability of QNN whether it is implemented on noiseless or noisy quantum machines. We last exhibit that the quantum statistical query (QSQ) model can be effectively simulated by noisy QNN. Since the QSQ model can tackle certain tasks with runtime speedup, our result suggests that the modified QNN implemented on NISQ devices will retain the quantum advantage. Numerical simulations support the theoretical results.

quant-ph↗

arXiv2020

Quantum noise protects quantum classifiers against adversaries

Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask, can we harness the power of quantum noise that is beneficial to quantum computing? An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as `worst-case' perturbations by unknown noise sources. We show that by taking advantage of depolarisation noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy which can be extended to quantum differential privacy. For the protection of quantum data, this is the first quantum protocol that can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of classification model are absent, thus also providing a potential quantum advantage for classical data that is independent of quantum speedups. This opens the opportunity to explore other ways in which quantum noise can be used in our favour, as well as identifying other ways quantum algorithms can be helpful that is independent of quantum speedups.

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arXiv2019

A Quantum-inspired Algorithm for General Minimum Conical Hull Problems

A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexity is polynomial in size. However, big data is pushing these polynomial algorithms to their performance limits. In this paper, we propose a sublinear classical algorithm to tackle general minimum conical hull problems when the input has stored in a sample-based low-overhead data structure. The algorithm's runtime complexity is polynomial in the rank and polylogarithmic in size. The proposed algorithm achieves the exponential speedup over DCA and, therefore, provides advantages for high dimensional problems.

cs.LG↗

arXiv2019

Efficient Online Quantum Generative Adversarial Learning Algorithms with Applications

The exploration of quantum algorithms that possess quantum advantages is a central topic in quantum computation and quantum information processing. One potential candidate in this area is quantum generative adversarial learning (QuGAL), which conceptually has exponential advantages over classical adversarial networks. However, the corresponding learning algorithm remains obscured. In this paper, we propose the first quantum generative adversarial learning algorithm-- the quantum multiplicative matrix weight algorithm (QMMW)-- which enables the efficient processing of fundamental tasks. The computational complexity of QMMW is polynomially proportional to the number of training rounds and logarithmically proportional to the input size. The core concept of the proposed algorithm combines QuGAL with online learning. We exploit the implementation of QuGAL with parameterized quantum circuits, and numerical experiments for the task of entanglement test for pure state are provided to support our claims.

quant-ph↗

arXiv2018

The Expressive Power of Parameterized Quantum Circuits

Parameterized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addition, PQCs equipped with ancillary qubits for post-selection have even stronger expressive power than those without post-selection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semi-supervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical experiments using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.

quant-ph↗

arXiv2018

Bayesian Quantum Circuit

Parameterized quantum circuits (PQCs), as one of the most promising schemes to realize quantum machine learning algorithms on near-term quantum computers, have been designed to solve machine earning tasks with quantum advantages. In this paper, we explain why PQCs with different structures can achieve generative tasks in the discrete case from the perspective of probability estimation. Although different kinds of PQCs are proposed for generative tasks, the current methods often encounter the following three hurdles: (1) the mode contraction problem; (2) unexpected data are often generated with a high proportion; (3) target data cannot be sampled directly. For the purpose of tackling the above hurdles, we devise Bayesian quantum circuit (BQC) through introducing ancillary qubits to represent prior distributions. BQC advances both generative and semi-supervised quantum circuit learning tasks, where its effectiveness is validated by numerical simulations using the Rigetti Forest platform.

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