There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking an ...

Quantum machine learning

Physical Review B

Journal of Statistical Mechanics: theory and experiment

The lattice dynamics of hcp crystalline $^{4}\text{H}\text{e}$ is studied at zero temperature and for two different densities (near and far from melting), using a ground-state path-integral quantum Monte Carlo technique. The complete phonon dispersion is obtained, with particular attention to the separation of optic and acoustic branches and to the identification of transverse modes. Our study also sheds light on the residual coherence affecting quasiparticle excitations in the intermediate momentum region, in between the phonon and nearly free-particle regimes.

Zero-temperature dynamics of solidH4efrom quantum Monte Carlo simulations

We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports perfect sampling and wave function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension.

From Tensor Network Quantum States to Tensorial Recurrent Neural Networks

Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent variational Monte Carlo (t-VMC). In particular, stable and accurate time propagation over long time scales has been observed in the square-lattice Heisenberg model using the Restricted Boltzmann machine architecture. However, achieving similar performance in other systems has proven to be more challenging. In this article, we focus on the two-leg Heisenberg ladder driven out of equilibrium by a pulsed excitation as a benchmark system. We demonstrate that unmitigated noise is strongly amplified by the nonlinear equations of motion for the network parameters, which by itself is sufficient to cause numerical instabilities in the time-evolution. As a consequence, the achievable accuracy of the simulated dynamics is a result of the interplay between network expressiveness and regularization required to remedy these instabilities. Inspired by machine learning practice, we propose a validation-set based diagnostic tool to help determining the optimal regularization hyperparameters for t-VMC based propagation schemes. For our benchmark, we show that stable and accurate time propagation can be achieved in regimes of sufficiently regularized variational dynamics.

/pdf/role-of-stochastic-noise-and-generalization-error-in-the-4hnmil6s2i.pdf

Role of stochastic noise and generalization error in the time propagation of neural-network quantum states

A notion of quantum natural evolution strategies is introduced, which provides a geometric synthesis of a number of known quantum/classical algorithms for performing classical black-box optimization. Recent work of Gomes et al. [2019] on combinatorial optimization using neural quantum states is pedagogically reviewed in this context, emphasizing the connection with natural evolution strategies. The algorithmic framework is illustrated for approximate combinatorial optimization problems, and a systematic strategy is found for improving the approximation ratios. In particular it is found that natural evolution strategies can achieve state-of-art approximation ratios for Max-Cut, at the expense of increased computation time.

Natural evolution strategies and quantum approximate optimization.

This corrects the article DOI: 10.1103/PhysRevLett.113.035301.

https://link.aps.org/pdf/10.1103/PhysRevLett.116.169901

Giuseppe Carleo

Papers

Zero-temperature dynamics of solidH4efrom quantum Monte Carlo simulations

From Tensor Network Quantum States to Tensorial Recurrent Neural Networks

Role of stochastic noise and generalization error in the time propagation of neural-network quantum states

Natural evolution strategies and quantum approximate optimization.

Erratum: Quench-Induced Breathing Mode of One-Dimensional Bose Gases [Phys. Rev. Lett. 113, 035301 (2014)].