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I am interested in leveraging IBM's quantum computers that are currently available for public access. Specifically, I am looking for an algorithm that has been successfully implemented on a real, accessible quantum computer and demonstrates quantum supremacy. My goal is to study and replicate their work to enhance my understanding of quantum computing.

Could anyone point me to such an implementation or share relevant resources or repositories? Any guidance on how to get started with algorithms that have shown quantum supremacy on IBM's quantum devices would be greatly appreciated.

Thanks in advance for your help!

ali khosravi
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There are many algorithms you can implement, but showing quantum supremacy isn't as trivial as just running a quantum algorithm. As of my understanding, examples of quantum supremacy to date (e.g. Google's demonstration) aren't demonstrations of quantum computers solving real-world problems better or faster than classical systems. So for the purposes of gaining understanding of quantum computation, I would suggest focusing on algorithms that could have potential practical applications.

As an example, a (relatively) simple and fun algorithm you can run is the variational quantum eigensolver (VQE). Given some Hamiltonian $H$, the aim of the VQE is to minimize $\langle \psi | H | \psi \rangle$ in order to get an upper bound on the lowest eigenvalue of $H$. This can be done through parameterized quantum circuits, e.g. using $U(\theta) |\psi\rangle = |\psi(\theta)\rangle$ and optimizing $\theta$ in order to minimize the expectation value.

This algorithm has (potential) use in both chemistry and physics, but it is still some way from achieving quantum supremacy. There are a lot of resources (especially by IBM themselves) on the VQE, so it could be a fun place to start for replicating work and growing understanding.

banercat
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