Deterministic Quantum Computation With One Photonic Qubit

We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high dimension matrix, being limited by the resolution of the modulator panel, and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices, and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our set-up is 1080$\times$1920, which is able to represent a system with approximately 21 qubits.