Figure 1

(a) Our scheme to implement nondestructive CNOT gate with polarization beam splitters (PBS) in $|H⟩/|V⟩$ basis, in $|+⟩/|-⟩$ basis, and in $|R⟩/|L⟩$ basis. PBS in $|+⟩/|-⟩$ basis (PBS-2) is constructed with a PBS in $|H⟩/|V⟩$ basis and four half-wave plates (HWP); PBS in $|R⟩/|L⟩$ basis (PBS-3) is constructed with a PBS in $|H⟩/|V⟩$ basis and four quarter-wave plates (QWP). This gate works like this: four photons (control qubit, target qubit, and two auxiliary qubit) enter from the bottom; if there is a coincident count between detector $D_A$ and detector $D_B$, a successful CNOT gate operation will be made after sending 1 bit classical information and doing the corresponding single-qubit unitary operations on photon 1 and 4. Then the state of photon 1 is exactly the output of the control qubit; and the state of photon 4 is exactly the output of the target qubit. In our proof-of-principle experiment, for simplification only the coincident events between $D_A^H$ and $D_B^H$ are registered, and a HWP is added to do the corresponding ${\sigma }_z$ operation on photon 1. (b) Experimental setup to generate the required four photons. Near infrared femtosecond laser pulses ($\approx 200\mathrm{fs}$, 76 MHz, 788 nm) are converted to ultraviolet pulses through a frequency doubler LBO ($\mathrm{Li}{\mathrm{B}}_3{\mathrm{O}}_5$) crystal (not shown). Then the ultraviolet pulse transmits through the main BBO ($\beta \mathrm{\text{−}}\mathrm{Ba}{\mathrm{B}}_2{\mathrm{O}}_4$) crystal (2 mm) generating the first photon pair, then reflected back generating the second photon pair. Compensators (Comp.) which are composed of a HWP (45°) and a BBO crystal (1 mm) are added in each arm. The observed twofold coincident count rate is about $1.2\times {10}^4/\mathrm{s}$. In each arm we add a polarizer to do the disentanglement and set the initial product four-photon state to $|H{⟩}_c|+{⟩}_{a1}|H{⟩}_{a2}|H{⟩}_t$. Additional wave plates are added in path $c$ and path $t$ to prepare arbitrary polarization states.Reuse & Permissions

Figure 2

Two-photon Mach-Zehnder interference as a method to find the overlap on PBS-3. (a) Schematic diagram of the method. After perfect overlaps on PBS-1 and PBS-2 have been achieved, by adjusting polarizers and wave plates, two photons originated from the first pair will be on path 3 with polarization state of $|1R,1L{⟩}_3$ and the other two photons originated from the second pair will be on path 2 with polarization state of $|1R,1L{⟩}_2$. Consider that the probability of generating two pairs simultaneously is rarely low, so the coincident click between detector $D_A$ and detector $D_B$ maybe originate either from the two photons on path 2 or from the two photons on path 3. So the two-photon state before PBS-3 can be expressed as $1/\sqrt{2}(|1R,1L{⟩}_3+e^{i\varphi }|1R,1L{⟩}_2)$ in the case where these two possibilities interfere. Then passing through PBS-3, the state will change to $1/\sqrt{2}(|R{⟩}_A|L{⟩}_B+e^{i\varphi }|L{⟩}_A|R{⟩}_B)$. So when we move the delay mirror adjusting the phase $\varphi$, the coincident count between $D_A^H$ and $D_B^H$ will oscillate as a function of the position. (b) Experimental result of the oscillation. We can estimate the overlap position from the best fit of the envelop with Gauss function.Reuse & Permissions

Figure 3

Experimental evaluation of the CNOT gate; each data point is measured in 320 min for the first three figures. (a) In the computational basis ($|H⟩/|V⟩$). (b) In the complementary basis ($|+⟩/|-⟩$). For (c), the input control qubit is in the $|+⟩/|-⟩$ basis and the input target qubit is in the $|H⟩/|V⟩$ basis, while the output qubits are measured in the $|R⟩/|L⟩$ basis. (d)–(f) are theoretical values (for the vertical axis, probability is adopted instead of count rate) for (a), (b), and (c), respectively.Reuse & Permissions