In #compchem applications of #quantumcomputing, IBM is currently using QSD (quantum sample diagonalization) as their workhorse. In some sense this is just encoding a wave function and then observing the frequency distribution afterwards. Why is that interesting? - ThreadSky

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qmechanic.bsky.social • 84 days ago

In #compchem applications of #quantumcomputing, IBM is currently using QSD (quantum sample diagonalization) as their workhorse. In some sense this is just encoding a wave function and then observing the frequency distribution afterwards. Why is that interesting?

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qmechanic.bsky.social•84 days ago

In my opinion, the trick is in the exponential parametrization (dUCC or whatever form you prefer), that is not-trivially mapped to a linear parameterization (akin to a frequency distribution). While in principle it may offer a more compact access to the wave function there are some caveats:

qmechanic.bsky.social•84 days ago

1.) The parameterization is not in general exact. It may be, but the number of parameters will grow as the number of free parameters in the FullCI wave function. This is bad news, but we may still hope for getting a good approximation with fewer parameters.

qmechanic.bsky.social•84 days ago

2.) The number of samples required to resolve some components with small absolute amplitudes scales as the inverse of the absolute amplitude squared. To resolve abs amplitudes with 1e-3, one thus needs a million samples.

qmechanic.bsky.social•84 days ago

3.) Even if the two points above turned out not to be so bad, it would still be necessary to save the result of the measurments in classical memory and perform a diagonalization - and the scale here is with the number of components of the target state (in worst case exponential)

qmechanic.bsky.social•84 days ago

4.) Could we truncate the number of observed components to the ones with some significant frequency? Yes, but that approximately corresponds to being able to classically cut those components in the same way - eliminating any advantage of the quantum hardware

qmechanic.bsky.social•84 days ago

4 - addendum: There is a slight chance that interfering terms may save the day, but I have not yet observed in practice that it makes any sense.

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