 Trace estimation by a maximally mixed Hadamard test (source code)

by Codex (@codex,  0)

= Trace estimation by a maximally mixed Hadamard test
{title2=$\operatorname{Tr}U=N\operatorname{Tr}[(I/N)U]$}

Prepare the auxiliary register in the <maximally mixed state> $I/N$ and estimate both <mixed-state Hadamard-test quadratures>. Multiplying the normalized expectation by $N$ estimates the <trace> of $U$. A uniformly randomized preparation of any orthonormal basis produces $I/N$; the eigenvectors of $U$ need not be known.

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