Adaptive Variational Quantum Dynamics Simulations

Yao, Yongxin; Gomes, Niladri; Zhang, Feng; Wang, Cai‐Zhuang; Ho, Kai-Ming; Iadecola, Thomas; Orth, Peter P.

doi:10.1103/prxquantum.2.030307

Cited by 97 publications

(68 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Due to mild requirements on the gate noise and the circuit connectivity, variational quantum algorithms (VQAs) [4] become one of the most promising frameworks for achieving practical quantum advantages on NISQ devices. Specifically, different VQAs have been proposed for many topics, e.g., quantum chemistry [5,6,7,8,9,10,11,12,13], quantum simulations [14,15,16,17,18,19,20,21,22,23], machine learning [24,25,26,27,28,29,30,31], numerical analysis [32,33,34,35,36], and linear algebra problems [37,38,39]. Recently, various small-scale VQAs have been implemented on real quantum computers for tasks such as finding the ground state of molecules [8,11,12] and exploring promising applications in supervised learning [25], generative learning [30] and reinforcement learning [29].…”

Section: Introductionmentioning

confidence: 99%

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

Zhang¹,

Hsieh²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Zhang¹,

Hsieh²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The variational ansatz can either be chosen to have a fixed form or to be adaptively modified during the computation [25,32,33]. Here, we choose a fixed ansatz that is inspired by the Hamiltonian variational ansatz (HVA) [34,35] and that takes a layered form,…”

Section: A Choice Of Ansatzmentioning

confidence: 99%

“…In one class of VQAs, one derives an equation of motion for the variational parameters, j M ij θj (t) = V i [23][24][25], by extremizing the distance between the variational state and the exact time-evolved state at every (infinitesimally small) time step in the evolution. Here, the matrix M ij and vector V j must be obtained at every time step by performing measurements on the QPU, and the main bottleneck of the algorithm is the large number of measurements.…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression

Berthusen,

Trevisan,

Iadecola

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We demonstrate a post-quench dynamics simulation of a Heisenberg model on present-day IBM quantum hardware that extends beyond the coherence time of the device. This is achieved using a hybrid quantum-classical algorithm that propagates a state using Trotter evolution and then performs a classical optimization that effectively compresses the time-evolved state into a variational form. When iterated, this procedure enables simulations to arbitrary times with an error controlled by the compression fidelity and a fixed Trotter step size. We show how to measure the required cost function, the overlap between the time-evolved and variational states, on present-day hardware, making use of several error mitigation methods. In addition to carrying out simulations on real hardware, we investigate the performance and scaling behavior of the algorithm with noiseless and noisy classical simulations. We find the main bottleneck in going to larger system sizes to be the difficulty of carrying out the optimization of the noisy cost function.

show abstract

“…The self-consistency is performed until convergence. VQAs have been extensively employed to tackle numerous tasks, including the variational quantum eigensolvers (VQEs) [10][11][12][13][14][15][16], quantum dynamics simulation [17][18][19][20][21][22], mathematical applications [23][24][25][26][27][28][29][30][31], quantum machine learning (QML) [32][33][34][35][36][37][38][39][40], and new frontiers in quantum foundations [8,[41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

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

Quoc

Tran

et al. 2022

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

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 surpass 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 a 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 of quantum machine learning: quantum linear regression and quantum neural network.

show abstract

Adaptive Variational Quantum Dynamics Simulations

Cited by 97 publications

References 53 publications

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

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

Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression

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

Contact Info

Product

Resources

About