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QI: Fachverband Quanteninformation

QI 8: Quantum Computing Theory I

QI 8.7: Vortrag

Montag, 10. März 2025, 18:45–19:00, HS IV

Why we should expect that quantum computers cannot factor efficiently — •Liam McGuinness — University of Ulm, Ulm, Germany

Quantum information science currently poses a troubling contradiction. It can be summarized as:

1) To factor efficiently, quantum computers must perform exponentially precise energy estimation.

2) Exponentially precise energy estimation is impossible according to the Heisenberg time-energy uncertainty principle.

It is surprising that such a dramatic contradiction exists between two accepted predictions of quantum mechanics, and yet this contradiction is not widely discussed. It is even more surprising when one notes it is not a minor discrepancy -- the two statements differ by an exponential margin. Not only that, whether 1) or 2) is correct is of fundamental importance to the realisation of most quantum technologies. If 2) is correct, then quantum computers are much less powerful than expected.

This talk surveys the available experimental evidence regarding this contradiction. I highlight that all current evidence agrees with 2). I also give clear theoretical reasons why only 2) is consistent with quantum mechanics. In short there are strong reasons to expect that quantum computers cannot factor efficiently.

Keywords: Shor's algorithm; Quantum computing; Quantum metrology; Heisenberg uncertainty principle