Emulating quantum computation with artificial neural networks

TL;DR

This paper shows that artificial neural networks can be trained to emulate basic quantum operations, including complex state representations and quantum gates, enabling classical simulation of quantum information processing.

Contribution

It introduces a novel 'quantumness gate' for representing quantum states and demonstrates training neural networks to emulate key quantum gates and transformations.

Findings

Neural networks successfully learn to represent quantum states and operations.

A critical bottleneck dimension reflects relevant quantum information.

Chains of neural quantum gates can realize any unitary transformation.

Abstract

We demonstrate, that artificial neural networks (ANN) can be trained to emulate single or multiple basic quantum operations. In order to realize a quantum state, we implement a novel "quantumness gate" that maps an arbitrary matrix to the real representation of a positive hermitean normalized density matrix. We train the CNOT gate, the Hadamard gate and a rotation in Hilbert space as basic building blocks for processing the quantum density matrices of two entangled qubits. During the training process the neural networks learn to represent the complex structure, the hermiticity, the normalization and the positivity of the output matrix. The requirement of successful training allows us to find a critical bottleneck dimension which reflects the relevant quantum information. Chains of individually trained neural quantum gates can be constructed to realize any unitary transformation. For scaling to larger quantum systems, we propose to use correlations of stochastic macroscopic two-level observables or classical bits. This novel concept provides a path for a classical implementation of computationally relevant quantum information processing on classical neural networks, in particular on neuromorphic computing machines featuring stochastic operations.