Machine Learning the period finding algorithm
This work addresses a specific bottleneck in quantum algorithm design by exploring non-standard unitaries for period finding, though it appears incremental as it builds on known methods without broad SOTA impact.
The paper tackles the problem of identifying alternative unitary matrices for the period-finding algorithm in quantum computing, beyond the standard inverse quantum Fourier transform, and finds that multiple such matrices exist and can be learned using differentiable programming and gradient descent.
We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that that this is not the only unitary matrix appropriate for the period finding algorithm, There exist several unitary matrices that can affect out the same transformation and they are significantly different from each other as well. These unitary matrices can be learned by an algorithm. Neural networks can be applied to differentiate such unitary matrices from randomly generated ones indicating that these unitaries do have characteristic features that cannot otherwise be discerned easily.