softwareQ Inc.

Published purpose

The project investigates the potential of quantum linear solvers such as the HHL algorithm and the Quantum Singular-Value Transform (QSVT) algorithm for achieving exponential speedup, taking into considerations challenges such as the need for quantumly-accessible Random-Access Memory (qRAM), sparsity/well-conditioning of the associated matrix, and fault-tolerant quantum computing. The primary focus is on determining realistic quantum advantages and exploring industry use cases. The Project aims to perform resource estimates for HHL-based algorithms and QSVT using the surface code and color code, addressing decoding overheads. Additionally, the project aims to develop new quantum algorithms for state preparation with novel data approximation methods. The project will also explore output/uniform amplitude amplification using QSVT, exploring analytical methods to find a polynomial approximation to the target function with a lower degree. The overall goal is to evaluate the practicality and potential applications of these quantum algorithms.