I am trying to construct a circuit which makes the following encoding $$O_H \left| i \right> \left| j \right> \left| z \right> = \left| i \right> \left| j \right> \left| z \oplus H_{ij} \right>$$ where $H \in \mathbb{C}^{N \times N}$ is a Hessian matrix and $n = \log_2(N)$ the number of qubits in the first two registers. The third register has sufficient qubits for the encoding up to a desired error.

Is there a way to do that?



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