A case study for quantum software development: Linear systems solver

As the power of quantum computing hardware is growing, software implementations and tools for accurate resource estimation that goes beyond simple asymptotic scaling become crucial for judging the feasibility of an application. Solving linear systems of equations is one of the prime applications for which quantum algorithms with an exponential advantage over the best known classical algorithms have been developed. In this talk, we report on the implementation of state-of-the-art quantum algorithms solving partial differential equations within the Microsoft Quantum Development Kit, which provides robust simulation, debugging, and resource estimation facilities. A key point in this work has been the handling of arithmetic functions: Gate synthesis facilitates accurate resource counts and is a requisite for deployment to quantum hardware, whereas emulation by the classical simulator allows for software testing on larger systems. To this end, we have equipped the Microsoft Quantum Development Kit with a generic and efficient emulation capability for quantum oracles defined by classical functions.