Abstract
We’ve seen that the space of unitary operators is gigantic. Now I want to discuss how to move through it. I’ve already hinted that we don’t make big complexity jumps, but instead move in little steps called gates. A sequence of gates is called a circuit although it has nothing to do with periodicity. It’s just a name.
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Notes
- 1.
The usual inner-product metric is both left and right invariant. It is called bi-invariant.
- 2.
See Dowling, Nielsen https://arxiv.org/pdf/quant-ph/0701004.pdf.
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Susskind, L. (2020). Exploring \(SU\left( 2^K\right) \). In: Three Lectures on Complexity and Black Holes. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-45109-7_7
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DOI: https://doi.org/10.1007/978-3-030-45109-7_7
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