I have a parameterized circuit that includes a certain number of rotation gates, each parameterized by an angle. By sampling over these angles, I can obtain various unitaries. What are the unitaries that I cannot reach? And among those, which ones are the farthest (by some suitable norm like fidelity) from their best approximations achievable with the parameterized circuit?
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1$\begingroup$ Please clarify (1) what kind of circuits you are building and (2) what value you assign to the parameters. I believe this information is necessary to get a proper answer. $\endgroup$– Daniele CuomoCommented May 11 at 13:41
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$\begingroup$ @Daniele Cuomo It is one of the circuits considered here - Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms. F.e., Circuit 2, Figure 2 in there. The circuits includes $2n\ell$ rotations, where $n$ is the number of qubits and $\ell$ is the number of concatenated blocks. Therefore, the circuit is parameterized with $2n\ell$ angles (let's say, each one $\in [-\pi,\pi]$). $\endgroup$– trurlCommented May 11 at 17:49
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