Quantum-inspired algorithms in practice

Abstract

We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical methods for problems involving low-rank matrices, but with complexity bounds that exhibit a hefty polynomial overhead compared to quantum algorithms. This raised the question of whether these methods were actually useful in practice. We conduct a theoretical analysis aimed at identifying their computational bottlenecks, then implement and benchmark the algorithms on a variety of problems, including applications to portfolio optimization and movie recommendations. On the one hand, our analysis reveals that the performance of these algorithms is better than the theoretical complexity bounds would suggest. On the other hand, their performance as seen in our implementation degrades noticeably as the rank and condition number of the input matrix are increased. Overall, our results indicate that quantum-inspired algorithms can perform well in practice provided that stringent conditions are met: low rank, low condition number, and very large dimension of the input matrix. By contrast, practical datasets are often sparse and high-rank, precisely the type that can be handled by quantum algorithms.

Commercial applications of quantum computing

“…Not all combinatorics problems require quantum computers. There are combinatorics problems that are comparatively easy for humans as well as classical computers and sufficiently large and coherent quantum computers to solve (i.e., trying every sequence of 2 2 , 2 3 , and 2 4 combinations). There are combinatorics problems that are challenging for humans to solve, but easy for classical computers as well as for sufficiently large and coherent quantum computers to solve (i.e., trying every combination on a gym lock).…”

“…2 Creative Destruction Lab, Toronto, Canada. 3 Dept. of Physics & Astronomy, University of Waterloo, Waterloo, Canada.…”

“…We have seen a large number of quantum companies, via their work with emerging quantum computing technology, develop "quantum-inspired" algorithms that enable them to solve important practical problems on classical computers. 3 As new algorithms are discovered, the boundary between quantum and classical can shift. Quantum algorithms can inspire insight into new classical solutions.…”

Genome assembly using quantum and quantum-inspired annealing

“…However, the ability of realistic quantum annealing devices to demonstrate computation speedups is still a subject of debates 29 – 34 . An interesting outcome of these debates is the appearance of a new generation of quantum-inspired (digital annealing) algorithms, which are essentially classical but appear as a result of analysing quantum systems 35 – 37 . Results on the comparison between available quantum annealers and quantum-inspired algorithms on realistic optimization problems have been obtained 37 .…”

A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time

“…It has recently been shown by Tang [26] that the data-structure required for efficient qRAMbased inner product estimation would also enable such inner products to be estimated classically, with only a polynomial slow-down relative to quantum, and her method has been employed to de-quantize a number of quantum machine learning algorithms [26][27][28] based on such data-structures. However, in practice, polynomial factors can make a difference, and an analysis of a number of such quantum-inspired classical algorithms [29] concludes that care is needed when assessing their performance relative to the quantum algorithms from which they were inspired. More importantly, in this current work, the quantum states produced using qRAM access are subsequently mapped onto a larger Hilbert space before their inner products are evaluated.…”