Qu&Co comments on this publication:

Quantum computers are envisioned to have significantly higher computational capabilities compared to their classical counterparts, especially for optimization and machine learning problems that involve a large classical data set. However, existing quantum algorithms use the trivial methods of turning large classical datasets into either quantum oracles or quantum states which are so expensive that negate any possible quantum advantage. Such quantum algorithms focus at problems in which classical runtime scales rapidly with the input size, perhaps exponentially. To be able to achieve quantum speedup with algorithms like Grover search, a “quantum RAM” is proposed, which is a large classical memory that can be queried in superposition. Although quantum RAMs do not yet exist and creating one might encounter the same challenges that quantum computer hardware faces, it has the potential to provide significant speedup to applications like the k-means clustering, logistical regression, zero-sum games and boosting.

This paper introduces hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. Then a data reduction technique is used to construct a weighted subset of X called a coreset that yields approximately the same loss for each model. The coreset can be constructed either by a classical computer or by the combination of classical – quantum computer by utilization of quantum measurements.

The main message of this work is that in order to avoid losing quantum speedup for ‘big-data’ applications, techniques such as data reduction are required, so that the time for loading and storing the data set is limited. Also, non-fault tolerant quantum algorithms should be designed in a way that does not require an excessive amount of gates, so that the algorithm can run before qubits lose their coherence and invalidate the result. The goal of the paper is to draw attention to problems that arise from such actions like testing for quantum advantage when data reduction is used, explore general data reduction techniques and investigate new hybrid classical-quantum algorithms.