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Embodiments use quantum conditional logic in the Quantum Phase Estimation Algorithm (QPEA) to compute eigenvalues prior to inversion. Embodiments estimate the eigen-values of a unitary, U= e “, generated by a NxN Hermitian matrix A. The binary representations of the n-bit estimations of eigenvalues of A may be encoded in these states: I,)= lb, b,... b,);?, is an estimation of the i-th eigenvalue, excluding degeneracy, and. b, b,... b, is its binary representation. To perform the eigenvalue inversion, an n-qubit controlled Ry rotation with angle?,/2"*" conditioned on seeing Ib, b,... b,) is applied for each possible n-bit binary string b, b,... b,(2" values). The overall unitary is called a “uniformly controlled Ry rotation” in literature.