Active Feed-Forward Improves Linear Optics Quantum Computing

Lauren I. Rugani

In one-way quantum computing, applying a feed-forward technique — in which each measurement is dependent on previous results — helps to surmount quantum measurement randomness. Researchers from the University of Vienna in Austria, Harvard University in Cambridge, Mass., and the Austrian Academy of Sciences, also in Vienna, have employed a four-qubit cluster state and three electro-optical modulators to demonstrate deterministic single- and two-qubit gate operations along with Grover’s search algorithm.

Two polarization-entangled photon pairs are generated as an ultraviolet laser pulse passes forward and backward through a nonlinear crystal and is transformed into a four-photon cluster state through an extended optical setup. A measurement made in the computational basis of the cluster state will remove a qubit, leaving a smaller cluster state, whereas measurements in a different basis process quantum information. The outcomes of the measurements define the computation, which will proceed without error only if the right result is obtained. Otherwise, a well-defined Pauli error is introduced that can be corrected by applying a feed-forward technique.

The measurement apparatus for a given basis comprises a quarter-wave plate, a half-wave plate and a polarizing beamsplitter. Qubits 1 and 2 are measured without delay, whereas measurements for qubits 3 and 4 are delayed 150 and 300 ns, respectively, in optical single-mode fibers measuring 30 and 60 m long. Three electro-optic modulators implement the active feed-forward on these two qubits, with one adapting the measurement basis of qubit 3 and two correcting Pauli errors on qubit 4.

The researchers found the output of a single-qubit computation with active feed-forward to be 0.84 ±0.08, compared with 0.55 ±0.06 for the same computation when no feed-forward is applied. Feed-forward is more complex for two-qubit gates, which are realized using horseshoe or box cluster states and implemented by measuring qubits 2 and 3 and thus transferring the two-qubit quantum state to qubits 1 and 4.

Grover’s search algorithm also can be performed on such a four-qubit box cluster. A quantum device called an oracle labels one of the four computational basis states by changing its sign. This tagged element is then found with certainty after an inversion-about-the-mean operation. Pauli errors introduced by undesired results at qubits 2 and 3 can cause the wrong element to be tagged; however, feed-forward compensates for these errors and identifies the correct element with a probability of 85 ±3%.

Nature, Jan. 4, 2007, pp. 65-69.