Generation of entangled ancilla states for use in linear optics quantum computing

Quantum logic operations can be performed using linear optical elements, additional photons (ancilla photons), and postselection based on measurements made on the ancilla. Here we describe a method for generating the required entangled state of $n$ ancilla photons using elementary logic gates and postselection. This approach is capable of generating the ancilla states required for either the original proposal by Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001)] or those required for the more general high-fidelity approach [J. D. Franson, M. M. Donegan, M. J. Fitch, B. C. Jacobs, and T. B. Pittman, Phys. Rev. Lett. 89, 137901 (2002)]. We also show that the entangled ancilla photons could be generated using a series of quantum wells coupled with tunnel junctions.

Figure 1

Ancilla registers $x$ and $y$ used in the quantum teleportation of qubit $q$. Each mode initially contains zero or one photon, while the total number of photons in $x$ and $y$ has a fixed value $n$ ($n=5$ for the example shown here). The index $j$ in the entangled state of Eq. (1) corresponds to the number of photons in $x$. Similar ancilla registers $x^{\prime }$ and $y^{\prime }$ are used to teleport a second qubit $q^{\prime }$ during logic operations.

Figure 2

The first step in the generation of the entangled ancilla state is the transfer of a single photon into each mode of registers $y$ and $y^{\prime }$.

Figure 3

Coherent transfer of a single photon from register $y$ to the appropriate mode of register $x$ with probability $P_1$.

Figure 4

Conditional transfer of a photon from one mode of register $y$ to the corresponding mode of register $x$. This process only takes place if the first mode in register $x$ contains a photon, in which case it creates a superposition of states in which the second photon would be found in register $x$ with probability $P_2$.

Figure 5

Interferometer arrangement used to implement the conditional photon transfer of Fig. 4. A photon initially present in path $a$ will be transferred to path $f$ with probability amplitude $2iRT$ if $\varphi =0°$, while it will exit with certainty in path $e$ if $\varphi =180°$.

Figure 6

Generation of a photonic ancilla state by first generating the corresponding entangled state of $n$ electrons in a series of quantum dots labeled $D_1$ through $D_6$. The $B$ gates are used to control the height of a tunneling barrier between the quantum dots, while the $U$ gates are used to control the energies of the quantized states within each dot. A typical set of bit values is also shown below each quantum dot.