Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines

Pilati, Sebastiano; Pieri, P.

doi:10.1103/physreve.101.063308

Cited by 12 publications

(10 citation statements)

References 72 publications

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“…While they have been demonstrated to work well in a number of problems so far [58,67,72,99], when it comes to learning the ground state of frustrated spin systems, such as the J 1 −J 2 model, holomorphic architectures for neural network quantum states exhibit certain deficiencies: first, the holomorphic constraint correlates the phase and amplitude gradients of the variational wavefunction parameters, which means that an update to the network parameters will cause a change in both the amplitude and the phase of the output. Therefore, fine-tuning of, e.g., only the phases is not possible using a holomorphic ansatz.…”

Section: Resultsmentioning

confidence: 99%

“…Our results raise the natural question as to why neural quantum states approximate much better the ground states of other models, e.g., Ising, Heisenberg, Bose-Hubbard, etc. [58,67,72,99]. We currently believe that, for these models, even when the variational ansatz is expressive enough to capture the true ground state, independently initialized simulations still end up in distinct landscape minima characterized by different values of the network parameters.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, much like the MNIST data set of handwritten digits in the ML community [59], the ground state search of the frustrated J 1 − J 2 model has recently turned into a test bed for ideas attempting to push the boundaries of neural-network-based variational approaches [60][61][62][63][64][65]. Such studies currently receive considerable attention for both equilibrium [66][67][68][69][70][71][72] and non-equilibrium [73][74][75][76][77][78][79] problems.…”

Section: Introductionmentioning

confidence: 99%

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Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

2021

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Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate systematically the performance of a class of universal variational wave-functions based on artificial neural networks, by considering the frustrated spin-1/21/2J_1-J_2J1−J2 Heisenberg model on the square lattice. Focusing on neural network architectures without physics-informed input, we argue in favor of using an ansatz consisting of two decoupled real-valued networks, one for the amplitude and the other for the phase of the variational wavefunction. By introducing concrete mitigation strategies against inherent numerical instabilities in the stochastic reconfiguration algorithm we obtain a variational energy comparable to that reported recently with neural networks that incorporate knowledge about the physical system. Through a detailed analysis of the individual components of the algorithm, we conclude that the rugged nature of the energy landscape constitutes the major obstacle in finding a satisfactory approximation to the ground state wavefunction, and prevents learning the correct sign structure. In particular, we show that in the present setup the neural network expressivity and Monte Carlo sampling are not primary limiting factors.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

2021

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“…In the last few years, the study of quantum systems has taken advantage of the increasing interest in and the developments of machine learning techniques to face both theoretical and experimental challenges, which has led to the emergence of the broad field of quantum machine learning [1][2][3][4][5]. Some successful examples of the use of machine learning include, among others, the detection and classification of quantum phases [6][7][8][9][10][11][12][13], the prediction of the ground state energy and other characteristic quantities of quantum systems [14][15][16][17], and the enhanced control and readout in experimental setups [18][19][20][21]. Additionally, many efforts are devoted to developing machine learning algorithms that exploit quantum resources, aiming to find a quantum advantage in performing tasks.…”

Section: Introductionmentioning

confidence: 99%

Quantum Reservoir Computing for Speckle Disorder Potentials

Mujal

2022

Condensed Matter

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Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it is shown to be enhanced when two-qubit correlations are employed.

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“…1(a) for a depiction of an RBM. Together with RBMs [2,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], other network structures such as a feed-forward [34][35][36][37][38], recurrent [39,40] and convolutional neural networks [41][42][43][44][45][46][47][48][49][50][51][52] have also been intensively studied. The significant interest in the field is attributed to the fact that these networks could offer possibility to fight against the curse of dimensionality in many-body quantum systems.…”

mentioning

confidence: 99%

Ground state search by local and sequential updates of neural network quantum states

Zhang¹,

Xu²,

Wu³

et al. 2022

Preprint

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Neural network quantum states are a promising tool to analyze complex quantum systems given their representative power. It can however be difficult to optimize efficiently and effectively the parameters of this type of ansatz. Here we propose a local optimization procedure which, when integrated with stochastic reconfiguration, outperforms previously used global optimization approaches. Specifically, we analyze both the ground state energy and the correlations for the non-integrable tilted Ising model with restricted Boltzmann machines. We find that sequential local updates can lead to faster convergence to states which have energy and correlations closer to those of the ground state, depending on the size of the portion of the neural network which is locally updated. To show the generality of the approach we apply it to both 1D and 2D non-integrable spin systems.

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Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines

Cited by 12 publications

References 72 publications

Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape

Quantum Reservoir Computing for Speckle Disorder Potentials

Ground state search by local and sequential updates of neural network quantum states

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