Scientists at the Skolkovo Institute of Science and Technology (Skoltech) in Moscow, Russia have shown that quantum enhanced machine learning can be used on quantum (as opposed to classical) data. This research offers a path to help overcome a significant slowdown common to these applications - opening a ‘fertile ground to develop computational insights into quantum systems.’

Quantum computers utilise quantum mechanical effects to store and manipulate information. Quantum computing offers orders of magnitude better performance than classical computing devices used today but so far there are a limited number of suitable applications.

Quantum algorithms have been developed to enhance a range of different computational tasks; more recently this has grown to include quantum enhanced machine learning. Quantum machine learning was, in part, pioneered by Skoltech’s resident-based Laboratory for Quantum Information Processing, led by Jacob Biamonte, a coauthor of the Skoltech research paper. ‘Machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is not surprising that quantum computers might outperform classical computers on machine learning tasks,’ comments Biamonte.

The standard approach to quantum enhanced machine learning has been to apply quantum algorithms to classical data. In other words, classical data (represented by bit strings of 1’s and 0’s) must be stored or otherwise represented by a quantum processor before quantum effects can be utilised.

A team of Skoltech researchers has merged quantum enhanced machine learning with quantum enhanced simulation, applying their approach to study phase transitions in many-body quantum magnetic problems. In doing so, they train quantum neural networks using only quantum states as data. In other words, the authors circumvent the data-readin problem by feeding in quantum mechanical states of matter. Such states appear to generally require an impossible amount of memory to represent using standard (non-quantum) approaches.

The lead author of the study, Skoltech doctoral student Alexey Uvarov describes the study as “a step towards understanding the power of quantum devices for machine learning.” Researchers merged an assortment of techniques, which included applying some ideas from tensor networks and entanglement theory in the analysis of their approach.

The work uses a subroutine known as the variational quantum eigensolver (VQE) — an algorithm that iteratively finds an approximation to the ground state of a given quantum Hamiltonian. The output of this subroutine is a set of instructions to prepare a quantum state on a quantum computer.

Writing the state down explicitly, though, typically requires an exponential amount of memory, hence the properties of such a state are best examined by preparing it in hardware. The learning algorithm in the paper deals with the following problem: given a VQE state solving the ground state problem for a quantum spin model, find out which of the two phases of matter that state belongs to.

‘While we have focused our approaches on problems from condensed matter physics, such quantum enhanced algorithms equally apply to challenges faced in materials science and drug discovery,’ Biamonte notes.

The research was supported by a grant from the Russian Foundation for Basic Research.

The work is also available freely as an arXiv preprint. The paper was published in the journal Physical Review A.