Towards Optimizing the Expected Performance of Sampling-Based Quantum-Inspired Algorithms

TL;DR

This paper analyzes and optimizes key subroutines in sampling-based quantum-inspired algorithms by generalizing data structures, leading to improved performance and tighter bounds, with implications for high-dimensional quantum machine learning tasks.

Contribution

It introduces a generalized data structure approach to optimize subroutines in quantum-inspired algorithms, improving efficiency and measurement bounds.

Findings

Optimal data structure identified for subroutines

Experimental results favor the proposed data structure

Tighter bounds on measurements for fidelity estimation

Abstract

Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks. In this work, we analyze two major subroutines in sampling-based quantum-inspired algorithms, specifically, inner product estimation and sampling from a linear combination of vectors, and discuss their possible improvements by generalizing the data structure. The idea is to consider the average behavior of the subroutines under certain assumptions regarding the data elements. This allows us to determine the optimal data structure, and the high-dimensional nature of data makes our assumptions reasonable. Experimental results from recommendation systems also highlight a consistent preference for our proposed data structure. Motivated by this observation, we tighten the upper bound on the number of required measurements for direct fidelity estimation. We expect our findings to suggest optimal implementations for various quantum and quantum-inspired machine learning algorithms that involve extremely high-dimensional operations, which has potential for many applications.