Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer

We report an experimental demonstration of quantum Deutsch’s algorithm using a linear-optical system. By employing photon polarization and spatial modes, we implement all balanced and constant functions for a quantum computer. The experimental system is very stable, and the experimental data are in excellent accordance with the theoretical results.

Figure 1

Quantum circuit of Deutsch’s algorithm. $H$ is the Hadamard gate.

Figure 2

(a) Optical implementation of cnot gate by employing polarization and spatial positions of photons. The dove prism (DP) is inclined at ${45}^{°}$. Red lines (heavy gray) show the left ($l$) and right ($r$) spatial modes, and green lines (light gray) show the up ($u$) and down ($d$) spatial modes. (b) Spatial positions of input and output beams on the splitting plane AB of the polarized beam splitter (PBS).

Figure 3

Experimental setup of Deutsch’s algorithm. The source is a He-Ne laser (MELLES GRIOT, 05-LHP-171) of wavelength 632.8 nm. We attenuate the coherent light into a single-photon level by using some neutral attenuators denoted by ATT. P denotes the polarizer for initial state preparation. Three half-wave plates (HWP) and two polarized beam splitters (PBS) are used in the setup. A PZT actuator is used to modulate the phase $\phi$ between $l$ and $r$ paths. The dove plate (DP) is set at ${45}^{°}$. Detectors (D${}_1$ and ${\mathrm{D}}_2$) are single-photon counting modules (SPCM-AQRH-14-FC). All the mirrors are marked as M.

Figure 4

Experimental data of Deutsch’s algorithm. Black squares show the photon counts of ${\mathrm{D}}_1$, and red triangles show the photon counts of ${\mathrm{D}}_2$. Fitting lines are also shown. By modulating the voltage of PZT from 0 to 34 V and every 1 V as a step, we record the photon counts of ${\mathrm{D}}_1$ and ${\mathrm{D}}_2$ simultaneously. (a) Identity operation of $U_f$ for constant function $f(x)=0$. (b) not operation of $U_f$ for constant function $f(x)=1$. (c) cnot operation of $U_f$ for balanced function $f(x)=x$. (d) Z-cnot operation of $U_f$ for balanced function $f(x)=\mathrm{inv}(x)$. Green dashed vertical lines are used to mark the proper points (phases) of the initial states, which can be used to perfectly discriminate the two kinds of functions.