Proposal for a two-qubit quantum phase gate for quantum photonic integrated circuits

We propose a protocol for a two-qubit quantum phase gate based upon the reflection of photon pulses from a quantum dot in a cavity. Depending on the state of the quantum dot the reflected photons acquire a conditional phase shift. The key ingredient is the ultrafast control of the quantum dot energies by electric fields, which allows for tuning the exciton and biexciton successively into resonance with the cavity mode. The complete dynamics of the gate are simulated, revealing a fidelity of about 0.9. The proposed scheme uses position coding and is therefore well suited to the implementation in an integrated photonic quantum processor.

Figure 1

(a) Illustration of the $\pi$-phase gate. If and only if photon 1 enters the gate in channel $b$, photon 2 in channel $a$ will acquire a $\pi$-phase shift. (b) Schematic illustration of the relevant level structure of the QD for the three-step protocol. The frequencies $\omega$ carry indices for the exciton resonance $X$, the biexciton resonance $XX$ and for the cavity mode $C$.

Figure 2

Temporal dynamics for photons in channel $a$. (a) Evolution of the exciton population $|{\alpha }_{{}_X}{|}^2$ (black line) and the cavity ${\left|\beta \right|}^2$ [red (gray) line] for ${|a\rangle }_1{|b\rangle }_2$ as input state vs dimensionless time $gt$. The biexciton population $|{\alpha }_{{}_{XX}}{|}^2$ (dashed line) and cavity population (red solid line) corresponding to (b) ${\Psi }_{\mathrm{in}}={|a\rangle }_1{|a\rangle }_2$ and (c) ${\Psi }_{\mathrm{in}}={|b\rangle }_1{|a\rangle }_2$.

Figure 3

Performance of the phase gate. (a) Phase $\Phi$ vs dimensionless time $gt$ and (b) fidelity $F$ vs QD decay $\gamma /\kappa$ (dimensionless) for the different input states.