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Update ansatz.rst
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damarkian authored Oct 31, 2024
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Expand Up @@ -143,7 +143,7 @@ An example of how to build a UCC doubles circuit ansatz for the :math:`H_2` mole
UCC with Qubit-Excitation-Based n-tuple Excitation
--------------------------------------------------

A CNOT depth-efficient quantum circuit for employing the UCC ansatz, dubbed the Qubit-Excitation-Based (QEB) n-tuple excitations for UCC, was constructed by Yordanov et al. [#f7]_ and Magoulas et al. [#f8]_, avoiding the exponential number of CNOT cascades in those developed before. [#f5]_ The quantum circuits generated have a reduction of CNOTs from :math:`(2n-1)2^{2n}` to :math:`2^{2n-1}+4n-2`.
A CNOT depth-efficient quantum circuit for employing the UCC ansatz, dubbed the Qubit-Excitation-Based (QEB) n-tuple excitations for UCC, was constructed by Yordanov et al. [#f7]_ and Magoulas et al. [#f8]_, avoiding the exponential number of CNOT cascades in those developed before. [#f5]_ The quantum circuits generated for :math:`N` qubits have a reduction of CNOTs from :math:`(2N-1)2^{2N}` to :math:`2^{2N-1}+4N-2`.

An example for the :math:`H_2` molecule is given here:

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