#31: July 17th- July 23rd
#31: July 17th- July 23rd




  • Amazon Braket release v1.7.3
  • Quil Rust implementation release: v0.5.0


Sample Complexity of Learning Quantum Circuits

Haoyuan Cai,Qi Ye,Dong-Ling DengJul 21 2021 quant-phcs.LGmath-phmath.MP arXiv:2107.09078v1

Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to learn a quantum circuit with at most ncnc gates and each gate acting on a constant number of qubits, the sample complexity is bounded by O~(nc+1)O~(nc+1). In particular, we explicitly construct a family of variational quantum circuits with O(nc+1)O(nc+1) elementary gates arranged in a fixed pattern, which can represent all physical quantum circuits consisting of at most ncnc elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and experiment.

A quantum algorithm for training wide and deep classical neural networks

Alexander Zlokapa,Hartmut Neven,Seth LloydJul 21 2021 quant-phcs.LG arXiv:2107.09200v1

Given the success of deep learning in classical machine learning, quantum algorithms for traditional neural network architectures may provide one of the most promising settings for quantum machine learning. Considering a fully-connected feedforward neural network, we show that conditions amenable to classical trainability via gradient descent coincide with those necessary for efficiently solving quantum linear systems. We propose a quantum algorithm to approximately train a wide and deep neural network up to O(1/n)O(1/n) error for a training set of size nn by performing sparse matrix inversion in O(logn)O(log⁡n) time. To achieve an end-to-end exponential speedup over gradient descent, the data distribution must permit efficient state preparation and readout. We numerically demonstrate that the MNIST image dataset satisfies such conditions; moreover, the quantum algorithm matches the accuracy of the fully-connected network. Beyond the proven architecture, we provide empirical evidence for O(logn)O(log⁡n) training of a convolutional neural network with pooling.

Fast suppression of classification error in variational quantum circuits

Bingzhi Zhang,Quntao ZhuangJul 19 2021 quant-phcond-mat.other arXiv:2107.08026v1

Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical post-processing — maximum-likelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decay exponentially with the circuit depth, when the VQC architecture is extensive — the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, non-extensive VQCs such as quantum convolutional neural networks are sub-optimal and fail to achieve the Helstrom limit. To achieve the best performance for a given VQC, the optimal classical post-processing is crucial even for a binary classification problem. To simplify VQCs for near-term implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.

QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits

Hanrui Wang,Yongshan Ding,Jiaqi Gu,Yujun Lin,David Z. Pan,Frederic T. Chong,Song HanJul 23 2021 quant-phcs.ARcs.LG arXiv:2107.10845v1

Quantum noise is the key challenge in Noisy Intermediate-Scale Quantum (NISQ) computers. Limited research efforts have explored a higher level of optimization by making the quantum circuit resilient to noise. We propose and experimentally implement QuantumNAS, the first comprehensive framework for noise-adaptive co-search of variational circuit and qubit mapping. Variational quantum circuits are a promising approach for constructing quantum neural networks for machine learning and variational ansatzes for quantum simulation. However, finding the best variational circuit and its optimal parameters is challenging in a high-dimensional Hilbert space. We propose to decouple the parameter training and circuit search by introducing a novel gate-sharing SuperCircuit. The SuperCircuit is trained by sampling and updating the SubCircuits in it and provides an accurate estimation of SubCircuit performance trained from scratch. Then we perform an evolutionary co-search of SubCircuit and its qubit mapping. The SubCircuit performance is estimated with parameters inherited from SuperCircuit and simulated with real device noise models. Finally, we perform iterative gate pruning and finetuning to further remove the redundant gates in a fine-grained manner. Extensively evaluated with 12 QML and VQE benchmarks on 10 quantum computers, QuantumNAS significantly outperforms noise-unaware search, human and random baselines. For QML tasks, QuantumNAS is the first to demonstrate over 95% 2-class, 85% 4-class, and 32% 10-class classification accuracy on real quantum computers. It also achieves the lowest eigenvalue for VQE tasks on H2, H2O, LiH, CH4, BeH2 compared with UCCSD baselines. We also open-source QuantumEngine (https://github.com/mit-han-lab/pytorch-quantum) for fast training of parameterized quantum circuits to facilitate future research.

Quantum Bayesian Neural Networks

Noah Berner,Vincent Fortuin,Jonas LandmanJul 21 2021 quant-ph arXiv:2107.09599v1

Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from posterior distributions than on point estimation, thus it might be more forgiving in the face of additional quantum noise. We propose a quantum algorithm for Bayesian neural network inference, drawing on recent advances in quantum deep learning, and simulate its empirical performance on several tasks. We find that already for small numbers of qubits, our algorithm approximates the true posterior well, while it does not require any repeated computations and thus fully realizes the quantum speedups.

Deep Reinforcement Learning for Quantum State Preparation with Weak Nonlinear Measurements

Riccardo Porotti,Antoine Essig,Benjamin Huard,Florian MarquardtJul 20 2021 quant-ph arXiv:2107.08816v1

Quantum control has been of increasing interest in recent years, e.g. for tasks like state initialization and stabilization. Feedback-based strategies are particularly powerful, but also hard to find, due to the exponentially increased search space. Deep reinforcement learning holds great promise in this regard. It may provide new answers to difficult questions, such as whether nonlinear measurements can compensate for linear, constrained control. Here we show that reinforcement learning can successfully discover such feedback strategies, without prior knowledge. We illustrate this for state preparation in a cavity subject to quantum-non-demolition detection of photon number, with a simple linear drive as control. Fock states can be produced and stabilized at very high fidelity. It is even possible to reach superposition states, provided the measurement rates for different Fock states can be controlled as well.

Variational Quantum Linear Solver with Dynamic Ansatz

Hrushikesh Patil,Yulun Wang,Predrag KrsticJul 20 2021 quant-ph arXiv:2107.08606v1

Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational Quantum Linear Solver for a system of linear algebraic equations. In this improved algorithm, the number of layers in the hardware efficient ansatz circuit is evolved, starting from a small and gradually increasing until convergence of the solution is reached. We demonstrate the algorithm advantage in comparison to the standard, static ansatz by utilizing fewer quantum resources and with a smaller quantum depth on average, in presence and absence of quantum noise, and in cases when the number of qubits or condition number of the system matrix are increased. The numbers of iterations and layers can be altered by a switching parameter. The performance of the algorithm in using quantum resources is quantified by a newly defined metric.

Qsun: an open-source platform towards practical quantum machine learning applications

Chuong Nguyen Quoc,Le Bin Ho,Lan Nguyen Tran,Hung Q. NguyenJul 23 2021 quant-ph arXiv:2107.10541v1

Currently, quantum hardware is restrained by noises and qubit numbers. Thus, a quantum virtual machine that simulates operations of a quantum computer on classical computers is a vital tool for developing and testing quantum algorithms before deploying them on real quantum computers. Various variational quantum algorithms have been proposed and tested on quantum virtual machines to bypass the limitations of quantum hardware. Our goal is to exploit further the variational quantum algorithms towards practical applications of quantum machine learning using state-of-the-art quantum computers. In this paper, we first introduce our quantum virtual machine named Qsun, whose operation is underlined by quantum state wavefunctions. The platform provides native tools supporting variational quantum algorithms. Especially using the parameter-shift rule, we implement quantum differentiable programming essential for gradient-based optimization. We then report two tests representative for quantum machine learning: quantum linear regression and quantum neural network.

Quantum Pattern Recognition in Photonic Circuits

Rui Wang,Carlos Hernani-Morales,José D. Martín-Guerrero,Enrique Solano,Francisco Albarrán-ArriagadaJul 22 2021 quant-phcond-mat.mes-hall arXiv:2107.09961v1

We propose a machine learning method to characterize photonic states via a simple optical circuit and the data processing of photon number distributions as photonic patterns. The input states consist of two coherent states used as references and a two-mode unknown state to be studied. We successfully trained a supervised learning algorithm to predict the degree of entanglement in the two-mode state and to perform the full tomography of one photonic mode, obtaining good accuracy and an rr-factor performance of our algorithm r>0.75r>0.75.

Quantum Deep Learning: Sampling Neural Nets with a Quantum Annealer

Catherine F. Higham,Adrian BedfordJul 20 2021 quant-phcs.LG arXiv:2107.08710v1

We demonstrate the feasibility of framing a classically learned deep neural network as an energy based model that can be processed on a one-step quantum annealer in order to exploit fast sampling times. We propose approaches to overcome two hurdles for high resolution image classification on a quantum processing unit (QPU): the required number and binary nature of the model states. With this novel method we successfully transfer a convolutional neural network to the QPU and show the potential for classification speedup of at least one order of magnitude.

An unsupervised feature learning for quantum-classical convolutional network with applications to fault detection

Tong Dou,Zhenwei Zhou,Kaiwei Wang,Shilu Yan,Wei CuiJul 20 2021 quant-ph arXiv:2107.08171v1

Combining the advantages of quantum computing and neural networks, quantum neural networks (QNNs) have gained considerable attention recently. However, because of the lack of quantum resource, it is costly to train QNNs. In this work, we presented a simple unsupervised method for quantum-classical convolutional networks to learn a hierarchy of quantum feature extractors. Each level of the resulting feature extractors consist of multiple quanvolution filters, followed by a pooling layer. The main contribution of the proposed approach is to use the KK-means clustering to maximize the difference of quantum properties in quantum circuit ansatz. One experiment on the bearing fault detection task shows the effectiveness of the proposed method.

Turbulence-immune computational ghost imaging based on a multi-scale generative adversarial network

Hao Zhang,Deyang DuanJul 19 2021 eess.IVquant-ph arXiv:2107.07870v1Scite!0

There is a consensus that turbulence-free images cannot be obtained by conventional computational ghost imaging (CGI) because the CGI is only a classic simulation, which does not satisfy the conditions of turbulence-free imaging. In this article, we first report a turbulence-immune CGI method based on a multi-scale generative adversarial network (MsGAN). Here, the conventional CGI framework is not changed, but the conventional CGI coincidence measurement algorithm is optimized by an MsGAN. Thus, the satisfactory turbulence-free ghost image can be reconstructed by training the network, and the visual effect can be significantly improved.

Categories: Week-in-QML


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