Quantum phase gates with geometric phases of spin-orbit modes

In this work, we propose the use of geometric phases obtained for both polarization and Hermite–Gaussian first-order transverse modes to create controlled phase gates. We present optical circuits that provide an arbitrarily controlled phase gate, including \(\pi /8\) $\pi /8$ , a universal quantum gate. Both polarization and HG mode can be used as control and target qubits, alternately, which is a great advantage in implementing quantum computing protocols. The phase gates are obtained by using a robust and precise geometric phase scheme, that is fault-tolerant and can provide fine adjustment.