New answers tagged random-quantum-circuit
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Induced measure on the set of density matrices defined through the Ginibre ensemble
Turns out this induced measure is the so called the Hilbert-Schmidt measure: https://arxiv.org/pdf/quant-ph/0012101.pdf
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How do I prove these gate identities?
For (a), and in accordance with the hint:
With controls = 00, the target qubit is not operated on (because all the gates have their controls set to 0 and so they do not affect the target).
With ...
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Induced measure on the set of density matrices defined through the Ginibre ensemble
Let $X=A+\mathrm{i}B$, with $A,B\in\mathbb{R}^{N\times M}$ whose entries are standard normal centered gaussian variables.
We thus have:
$$X^\dagger X=(A^\top-\mathrm{i}B^\top)(A+\mathrm{i}B)=A^\top A+...
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