Quantum inverse iteration algorithm for programmable quantum simulators

A researcher at University of Exeter, Oleksandr Kyriienko,  proposes a quantum inverse iteration algorithm, which can be used to estimate ground state properties of a programmable quantum device.

The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares the approximate ground state. To apply the inverse Hamiltonian operation, the scientist writes it as a sum of unitary evolution operators using the Fourier approximation approach. This allows to reformulate the protocol as separate measurements for the overlap of initial and propagated wavefunction. The algorithm thus crucially depends on the ability to run Hamiltonian dynamics with an available quantum device, and can be used for analog quantum simulators.

He has benchmarked the performance using paradigmatic examples of quantum chemistry, corresponding to molecular hydrogen and beryllium hydride. He has also showed its use for studying the ground state properties of relevant material science models, which can be simulated with existing devices, considering an example of the Bose-Hubbard atomic simulator.

The paper has been published in Nature.

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