Experimental Application of Decoherence-Free Subspaces in an Optical Quantum-Computing Algorithm

For a practical quantum computer to operate, it is essential to properly manage decoherence. One important technique for doing this is the use of “decoherence-free subspaces” (DFSs), which have recently been demonstrated. Here we present the first use of DFSs to improve the performance of a quantum algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces; we observe a reduction of the error rate from 35% to 7%, essentially its value in the absence of noise.

Figure 1

Schematic of an interferometer which implements the two-qubit Deutsch-Jozsa algorithm (a). All beam splitters are $50/50$. With beam splitters $C1$ and $C2$ in place, the standard algorithm (b) is performed. We show that an alternate encoding (c) is preferable in the presence of random collective noise on rails 2 and 3; replacing beam splitters $C1$ and $C2$ with beam splitters $D1$ and $D2$ implements this modified algorithm.

Figure 2

Experimental setup. Variable-reflectivity beam splitters are implemented using a pair of polarizing beam splitters (PBS) and a half wave plate. The “preparation” portion of the interferometer produces the same superposition as the pair of Hadamards in Fig. 1. The oracle consists of two variable beam splitters which can each be set to exchange two rails or leave them unchanged, plus two half wave plates used to induce $\pi$ phase shifts on two of the outputs. The random noise is generated by inducing turbulent airflow under rails 2 and 3 while they are spatially superposed.

Figure 3

Experimental data: Normalized intensity is a measure of the fraction of photons reaching each detector, $PD1$ through $PD4$, denoted by dotted, long dashed, solid, and short dashed lines, respectively. Data are shown for both the DFS and standard encoding, for each of the four oracles (00, 01, 10, and 11); C indicates “constant” oracles while B indicates “balanced” oracles. The bottom plot shows the same data in the presence of noise. Note that the noise has a much more significant effect in the case of the standard encoding.

Figure 4

The probability of the algorithm returning a 0 or a 1 for each of the oracles, in each encoding, with (bottom plot) and without (top plot) the addition of phase noise. The data are extracted by summing the normalized intensities from Fig. 3 for the pair of detectors indicating the constant functions (dashed line), and the balanced functions (solid line). Note that the success rate is close to unity even in the presence of noise when the DFS encoding is used.