Fig. 5: Energy difference as a function of the number of CNOT gates in the circuits of newly formed ansätze. | npj Quantum Information

Fig. 5: Energy difference as a function of the number of CNOT gates in the circuits of newly formed ansätze.

From: Unleashed from constrained optimization: quantum computing for quantum chemistry employing generator coordinate inspired method

Fig. 5

For ADAPT-VQE, such ansatz is the product of operators that prepare the VQE state \(\vert {\psi }_{VQE}\rangle\). For ADAPT-GCIM, the newly formed ansätze are the newly selected Givens rotation operator and the product of Givens rotation operators. All circuits are generated from the order-1 trottered fermionic operators by Qiskit. The reduced counts are obtained using qiskit.transpile with optimization level 3, which includes canceling back-to-back CNOT gates, commutative cancellation, and unitary synthesis. Our estimations to ADAPT-VQE match with the corresponding calculations in ref. 61. A further discussion on the calculation of the number of CNOT gates is in the Supplementary Information (Section V).

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