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Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions. [ABSTRACT FROM AUTHOR]

We achieve the enhancement of the circular photogalvanic effect arising from the photoinjection of spins in topological insulator thin films by tuning the Fermi level (EF). A series of (Bi1-xSbx)2Te3 thin films were tailored so that the Fermi energy ranges above 0.34 eV to below 0.29 eV of the Dirac point, i.e., from the bulk conduction band bottom to the valence band top through the bulk in-gap surface-Dirac cone. The circular photogalvanic current, indicating a flow of spin-polarized surface-Dirac electrons, shows a pronounced peak when the EF is set near the Dirac point and is also correlated with the carrier mobility. Our observation reveals that there are substantial scatterings between the surface-Dirac and bulk state electrons in the generation process of spin-polarized photocurrent, which can be avoided by designing the electronic structure in topological insulators. [ABSTRACT FROM AUTHOR]