Gaussian initializations help deep variational quantum circuits escape from the barren plateau

Kaining Zhang, Min-Hsiu Hsieh, Liu Liu, Dacheng Tao

Mar 18 2022 quant-ph cs.LG arXiv:2203.09376v1

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Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks. In this work, we propose an initialization strategy with theoretical guarantees for the vanishing gradient problem in general deep circuits. Specifically, we prove that under proper Gaussian initialized parameters, the norm of the gradient decays at most polynomially when the qubit number and the circuit depth increase. Our theoretical results hold for both the local and the global observable cases, where the latter was believed to have vanishing gradients even for shallow circuits. Experimental results verify our theoretical findings in the quantum simulation and quantum chemistry.

Experimental Quantum End-to-End Learning on a Superconducting Processor

Xiaoxuan Pan, Xi Cao, Weiting Wang, Ziyue Hua, Weizhou Cai, Xuegang Li, Haiyan Wang, Jiaqi Hu, Yipu Song, Dong-Ling Deng, Chang-Ling Zou, Re-Bing Wu, Luyan Sun

Mar 18 2022 quant-ph arXiv:2203.09080v1

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Machine learning can be substantially powered by a quantum computer owing to its huge Hilbert space and inherent quantum parallelism. In the pursuit of quantum advantages for machine learning with noisy intermediate-scale quantum devices, it was proposed that the learning model can be designed in an end-to-end fashion, i.e., the quantum ansatz is parameterized by directly manipulable control pulses without circuit design and compilation. Such gate-free models are hardware friendly and can fully exploit limited quantum resources. Here, we report the first experimental realization of quantum end-to-end machine learning on a superconducting processor. The trained model can achieve 98% recognition accuracy for two handwritten digits (via two qubits) and 89% for four digits (via three qubits) in the MNIST (Mixed National Institute of Standards and Technology) database. The experimental results exhibit the great potential of quantum end-to-end learning for resolving complex real-world tasks when more qubits are available.

Quantum perturbation theory using Tensor cores and a deep neural network

Joshua Finkelstein, Emanuel H. Rubensson, Susan M. Mniszewski, Christian F. A. Negre, Anders M. N. Niklasson

Mar 21 2022 physics.comp-ph quant-ph arXiv:2203.09621

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Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e. dense matrix-matrix multiplications, in mixed precision arithmetics which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

Extending the reach of quantum computing for materials science with machine learning potentials

Julian Schuhmacher, Guglielmo Mazzola, Francesco Tacchino, Olga Dmitriyeva, Tai Bui, Shanshan Huang, Ivano Tavernelli

Mar 15 2022 quant-ph cond-mat.mtrl-sci physics.chem-ph arXiv:2203.07219v1

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Solving electronic structure problems represents a promising field of application for quantum computers. Currently, much effort has been spent in devising and optimizing quantum algorithms for quantum chemistry problems featuring up to hundreds of electrons. While quantum algorithms can in principle outperform their classical equivalents, the polynomially scaling runtime, with the number of constituents, can still prevent quantum simulations of large scale systems. We propose a strategy to extend the scope of quantum computational methods to large scale simulations using a machine learning potential, trained on quantum simulation data. The challenge of applying machine learning potentials in today’s quantum setting arises from the several sources of noise affecting the quantum computations of electronic energies and forces. We investigate the trainability of a machine learning potential selecting various sources of noise: statistical, optimization and hardware noise.Finally, we construct the first machine learning potential from data computed on actual IBM Quantum processors for a hydrogen molecule. This already would allow us to perform arbitrarily long and stable molecular dynamics simulations, outperforming all current quantum approaches to molecular dynamics and structure optimization.

Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models

Anirban Mukherjee, Noah F. Berthusen, João C. Getelina, Peter P. Orth, Yong-Xin Yao

Mar 15 2022 quant-ph arXiv:2203.06745v1

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We perform a systematic study of preparing ground states of correlated egeg and t2gt2g multi-orbital impurity models using variational quantum eigensolvers (VQEs). Both fixed and adaptive wavefunction ansätze are considered and the resulting gate depths and performance with and without quantum sampling noise are analyzed. We investigate the qubit adaptive derivative-assembled pseudo-trotter (ADAPT) VQE approach in the Hartree-Fock orbital basis, as well as the Hamiltonian variational ansatz (HVA) and an adaptive variant of it in the atomic orbital basis. An operator pool composed of pairwise commutators of the Hamiltonian terms is developed to allow a fair comparison between the adaptive and the fixed HVA ansatz. Using statevector simulations, we show that the most compact ansätze are obtained in the atomic orbital representation with symmetry-based Pauli tapering in parity encoding. We further perform adaptive VQE calculations including sampling noise, and demonstrate that high-fidelity state preparation can be achieved with the Hamiltonian commutator pool. By utilizing a doubly decomposed form of the impurity Hamiltonian and a noise resilient optimizer, we show that this approach requires only a modest number of about 212212 samples per energy evaluation. We discover a dichotomy of the operator pool complexity in the presence of quantum noise, where a small pool size reduces the adaptive overhead but a larger pool size accelerates the convergence to the ground state. Finally, we measure the ground state energy of the egeg model on IBM quantum hardware using the converged qubit-ADAPT ansatz, and obtain a relative error of 0.7\% using error mitigation techniques including symmetry-filtering and zero-noise extrapolation.

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