Abstract:

Preparing arbitrary quantum states is a fundamental primitive for quantum algorithms. Existing exact state-preparation algorithms require substantially more two-qubit gates than the information-theoretic lower bound. In this work, we investigate approximate quantum state preparation using variational hardwareefficient circuits. We optimize several entangling topologies for Haar-random target states and evaluate the fidelity as a function of the number of CNOT gates. Surprisingly, we observe a sharp transition from poor approximation to high-fidelity state preparation when the CNOT count approaches the lower bound. Moreover, a brickwork topology consistently outperforms chain and ring circuits under the same CNOT budget. We further show that a reduced 2-parameter local rotation performs almost identically to the 3-parameter full Euler rotation for brickwork circuits. These observations suggest that approximate variational state preparation can nearly attain the information-theoretic minimum entangling complexity while using hardware-efficient circuits.