Research notebook

QSVT Linear Solvers

Research code exploring quantum singular value transformation for linear-system solving.

Overview

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About this project

![CI](https://github.com/MonitSharma/qsvt-linear-solvers/actions/workflows/ci.yml) ![License: MIT](LICENSE)

A from-scratch, end-to-end quantum linear-system solver built on the Quantum Singular Value Transformation (QSVT) — and actually run on real quantum hardware from two different vendors.

Solving A x = b is the inner loop of almost everything in scientific computing: structural mechanics, fluid dynamics, circuit simulation, optimization, machine learning. This project implements a quantum algorithm for that problem the modern way (QSVT, the successor to HHL), verifies it against ordinary linear algebra, and then compiles the same circuit down to Quantinuum Helios and IBM Quantum processors to see whether today's hardware can reproduce the answer.

It can.

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Results

Results at a glance

5 result figures

The main result: the same linear system is recovered on an ideal simulator, IBM Kingston, and Quantinuum Helios. The figures also show the inverse-polynomial approximation used by QSVT.