Publication

Nonstabilizerness of neural quantum states

2025

Abstract

We introduce a methodology to estimate nonstabilizerness or “magic,” a key resource for quantum complexity, with neural quantum states (NQS). Our framework relies on two schemes based on Monte Carlo sampling to quantify nonstabilizerness via stabilizer Rényi entropy (SRE) in arbitrary variational wave functions. When combined with NQS, this approach is effective for systems with strong correlations and in dimensions larger than one, unlike tensor network methods. First, we study the magic content in an ensemble of random NQS, demonstrating that neural network parametrizations of the wave function capture finite nonstabilizerness besides large entanglement. Second, we investigate the nonstabilizerness in the ground state of the J1-J2 Heisenberg model. In one dimension, we find that the SRE vanishes at the Majumdar-Ghosh point J2 = J1/2, consistent with a stabilizer ground state. In two dimensions, a dip in the SRE is observed near maximum frustration around J2/J1 ≈ 0.6, suggesting a valence bond solid between the two antiferromagnetic phases.

Official source

https://infoscience.epfl.ch/entities/publication/a791840c-a8d9-4384-b7f3-87fa80cbf44d

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a791840c-a8d9-4384-b7f3-87fa80cbf44d

About this result

Related concepts (32)

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Rectifier (neural networks)

In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the positive part of its argument: where x is the input to a neuron. This is also known as a ramp function and is analogous to half-wave rectification in electrical engineering. This activation function was introduced by Kunihiko Fukushima in 1969 in the context of visual feature extraction in hierarchical neural networks.

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