High-fidelity linear optical quantum computing with polarization encoding

We show that the KLM scheme [Knill, Laflamme, and Milburn, Nature 409, 46 (2001)] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of error of order ${10}^{-6}$ conditional on the gate being successful) can be implemented using polarization encoding. The detector efficiency determines the overall success probability of the gate but does not affect its fidelity. This can be applied to the efficient construction of optical cluster states with very high fidelity for quantum computing.

Figure 1

Quantum circuit that applies the HV beamsplitter.

Figure 2

Probability of detected failure $p_f$ and probability of error $p_e$ introduced by a “successful” gate in the KLM scheme ($\eta =0.8$, $\lambda \tau \sim {10}^{-7}$).

Figure 3

Probability of detected failure $p_f$ using polarization encoding ($\eta =0.8$, $\lambda \tau \sim {10}^{-7}$).

Figure 4

Probability of error $p_{nde}$ introduced by the gate when no failure was detected and using polarization encoding ($\eta =0.8$, $\lambda \tau \sim {10}^{-7}$).

Figure 5

Optical setup required to implement a CSIGN between two photons using a four-photon entangled ancilla state. The two input modes A and B are combined through beamsplitters with modes 1 and 4 of the entangled ancilla $\mid t_1^{\prime }⟩$, respectively. After the beamsplitters, the number of vertically and horizontally polarized photons in each mode is measured. When the gate succeeds, modes 2 and 3 carry the state of the input modes with a CSIGN gate applied to them, up to phase shifts.

Figure 6

Generation of a polarization GHZ state from two Bell pairs using a polarization beamsplitter and photodetection. A detector failure will introduce an error only in mode 2, which in that case will contain no photons.

Figure 7

The two modes of two pairs of GHZ states constructed according to the scheme in Fig. 6 that may have an error, are sent through the setup shown above. The polarization beamsplitters reflect vertically polarized photons. The operation is successful when exactly one photon is registered by each detector. Then, the state of the remaining four modes of the two GHZ pairs can be transformed into $\mid t_1^{\prime }⟩$ using phase shifters and polarization rotators.