The first generation of practical quantum computers, known as noisy intermediate-scale quantum processors, will offer a quantum computational advantage by being able to sample from a probability distribution that is intractable for classical devices. But how can the results of the quantum computation be checked? Writing in Nature Physics, Jacques Carolan and colleagues report a neural network-inspired algorithm that can do the exact opposite of sampling in an efficient way. The protocol, dubbed variational quantum unsampling, was shown to work on a photonic quantum processor.
The probability distribution to be sampled comes from the output of a quantum circuit that is fed a known initial state. In sampling algorithms, the unitary operation implemented by the quantum circuit is known and one is interested in the output or final state. In the unsampling algorithm, the task is to learn as much as possible about the unitary operation given a polynomial number of outputs and the known initial state. Carolan and colleagues showed how to do this using a variational approach that solves an optimization problem by efficiently exploring the associated Hilbert space. This protocol is hardware independent and can be used not only for verifying quantum computation, but also for characterizing unknown physical processes.
Carolan, J. et al. Variational quantum unsampling on a quantum photonic processor. Nat. Phys. https://doi.org/10.1038/s41567-019-0747-6 (2020)
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Georgescu, I. Variational unsampling. Nat Rev Phys 2, 72 (2020). https://doi.org/10.1038/s42254-020-0147-y