Figure 1

Cluster computing with POVMs. (a) A four-qubit “box” cluster, one of the largest clusters achievable experimentally with optical qubits [2, 3, 4, 5, 6, 7]. By measuring the input cluster qubits and implementing the correct Pauli error correction, one achieves output equivalent to the circuit shown. Note: $\{X,Y,Z\}$: standard Pauli operators; $H$: Hadamard operator $(X+Z)/\sqrt{2}$; $Z_{(\beta )}$: $\exp (iZ\beta /2)$; $\alpha$ (on a cluster qubit): measurement in $|{\alpha }_{\pm }⟩=|0⟩\pm \exp (i\alpha )|1⟩$. (b) A larger computation, and equivalent circuit, achievable via implementing POVMs on each input qubit of the same box cluster. Cluster qubits with dashed outlines represent “virtual” qubits simulated by performing POVMs $\{E{\}}_{\alpha }$ and $\{E{\}}_{\beta }$. (c) The computation we perform experimentally. By performing the POVM $\{E_m\}$ on the input qubit to our two-qubit cluster, we realize a three-qubit linear cluster computation, which in turn corresponds to a circuit for arbitrary pure state preparation via successive rotations of $|+⟩$ around the $z$ and $x$ axes.Reuse & Permissions

Figure 2

Experimental implementation of cluster-state computing with a POVM. (a) A source [17] produces maximally-entangled photon pairs coupled into single-mode fiber (SMF). (b) The POVM is based on an optical interferometer constructed using calcite beam-displacers (BDs), which couple the polarization of the photon to the path, thereby enlarging the state space for the generalized measurement. Details are given in the text. (c) Schematic of the cluster-state quantum computer. Photon-1 is measured in the POVM. Two Pockels cells (PCs), each fired dependent on the measurement outcome, actively perform the required correction of Pauli errors. A 50 m SMF serves to delay Photon-2, allowing time to trigger the PCs. The computational output is analyzed using quantum state tomography. Note: DM: dichroic mirror; IF: blocking and interference filter; PBS: polarizing beam splitter; H(Q)WP: half (quarter) wave plate; SPCM: fiber-coupled single-photon counting module.Reuse & Permissions

Figure 3

Experimentally reconstructed density matrix ${\rho }_{S_1{S}_2}$ of our 2-photon cluster state: real part (left) and imaginary part (right). The fidelity with the ideal state $|{\Phi }^{-}⟩$ is $F=0.980\pm 0.001$; the tangle is $T=0.926\pm 0.002$ and the purity, $\mathrm{Tr}({\rho }^2)$, is $P=0.963\pm 0.002$ [20, 21].Reuse & Permissions

Figure 4

Expected and measured fidelity of computational output. (a) The expected output fidelity based on the measured cluster state, ${\rho }_{S_1{S}_2}$, assuming perfect POVM operation and feedforward. (b) The measured output fidelity with the target outputs; the mean is $F=0.9832\pm 0.0002$. (c) The deviation from unity of the fidelity between the expected and measured states $1-F({\rho }_e,{\rho }_m)$; the mean is $(1-F)=(1.16\pm 0.05)\times {10}^{-3}$. This shows our POVM and feedforward to be operating with very high fidelity.Reuse & Permissions