Fig. 3.

A polarization-sensitive spatial light modulator as a single-photon CNOT gate. a Quantum circuit of a CNOT gate and b the corresponding operator represented in the logical basis ${\left\{∣0⟩,∣1⟩\right\}}_{\mathrm{control}}\otimes {\left\{∣0⟩,∣1⟩\right\}}_{\mathrm{target}}$. c Physical realization of a CNOT gate in polarization-parity space with a spatial light modulator (SLM). The SLM imparts a phase step π between the two halves of the plane along either x or y and thus acts as a parity flipper when the control qubit (polarization) is on. d The corresponding operator represented in the $\left\{∣\mathrm{V}⟩,∣\mathrm{H}⟩\right\}$ _control $\otimes {\left\{∣\mathrm{e}⟩,∣\mathrm{o}⟩\right\}}_{\mathrm{target}}$ basis