# Solving Systems of Linear Equations with a Superconducting Quantum Processor

## TL;DR

This paper demonstrates using a four-qubit superconducting quantum processor to solve a 2D linear system, showcasing potential for large-scale problem solving with quantum advantage.

## Contribution

First implementation of a quantum linear solver on a superconducting quantum processor, with process characterization and benchmarking.

## Key findings

- Achieved a process fidelity of 0.837±0.006
- Successfully solved a 2D linear system using quantum algorithms
- Showcased potential for large-scale linear system applications

## Abstract

Superconducting quantum circuits are promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm proposed by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett. \textbf{103}, 150502 (2009)], which promises an exponential speedup over classical algorithms under certain circumstances. We benchmark the solver with quantum inputs and outputs, and characterize it by non-trace-preserving quantum process tomography, which yields a process fidelity of $0.837\pm0.006$. Our results highlight the potential of superconducting quantum circuits for applications in solving large-scale linear systems, a ubiquitous task in science and engineering.