Experimental Quantum Learning of a Spectral Decomposition

TL;DR

This paper demonstrates a quantum machine learning approach that variationally diagonalizes a two-qubit unitary, showcasing potential for efficient spectral decomposition and applications in quantum simulation.

Contribution

It introduces a method for variationally learning spectral decomposition of a unitary using entanglement-enhanced quantum learning with minimal training data.

Findings

Successfully learned spectral decomposition of a 4x4 unitary

Reduced depth in dynamical quantum simulations

Showcased entanglement's role in quantum learning

Abstract

Currently available quantum hardware allows for small scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a 4x4 unitary matrix.