Automatic quantum circuit encoding of a given arbitrary quantum state

Understand

We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $\vert \Psi \rangle$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates.

• The proposed algorithm employs as an objective function the absolute value of fidelity $F = \langle 0 \vert \hat{\mathcal{C}}^{\dagger} \vert \Psi \rangle$, which is maximized iteratively to construct an optimal quantum circuit $\hat{\mathcal{C}}$ with controlled accuracy.
• The key ingredient of the algorithm is the sequential determination of a set of optimal two-qubit unitary operators one by one via the singular value decomposition of the fidelity tensor.
• Once the optimal unitary operators are determined, including the location of qubits on which each unitary operator acts, elementary quantum gates are assigned algebraically.