Speaker
Description
A central challenge in quantum machine learning (QML) is identifying physically motivated learning problems for which quantum computers exhibit advantages over classical computers. A prime candidate for such a learning task is the prediction of ground state properties of some quantum system of interest. Surprisingly, however, the prediction of ground state expectation values and classical shadows for gapped phases has been found to be solvable via classical ML algorithms. In this work, we go beyond this regime of classical learnability. We consider the problem of learning ground state properties beyond a single gapped phase of matter. Concretely, we learn ground state properties of Hamiltonian families with gaps scaling as $\Delta \in \Omega \left( \text{polylog} \left( 1/n \right) \right)$, a regime where previously developed classical learning algorithms would require superpolynomial sample complexity. Our approach is based on adiabatic state preparation and quantum Fourier coefficient extraction, a recently developed method for estimating the Fourier coefficients of parametrised quantum circuits. To use adiabatic state preparation in an efficient manner, we extend existing results in the shortcuts-to-adiabaticity literature to regimes beyond the gapped case, to cases where the gap scales inverse poly-logarithmically in $n$. To confirm there is no classical machine learning algorithm that could solve the same learning problem, we construct a task that our quantum algorithm solves efficiently, but all classical machine learning algorithms require super-polynomial resources.
| Topic | Quantum algorithms for machine learning applications |
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