Efficient high-fidelity quantum computation using matter qubits and linear optics

We propose a practical, scalable, and efficient scheme for quantum computation using spatially separated matter qubits and single-photon interference effects. The qubit systems can be nitrogen-vacancy centers in diamond, Pauli-blockade quantum dots with an excess electron, or trapped ions with optical transitions, which are each placed in a cavity and subsequently entangled using a double-heralded single-photon detection scheme. The fidelity of the resulting entanglement is extremely robust against the most important errors such as detector loss, spontaneous emission, and mismatch of cavity parameters. We demonstrate how this entangling operation can be used to efficiently generate cluster states of many qubits, which, together with single-qubit operations and readout, can be used to implement universal quantum computation. Existing experimental parameters indicate that high-fidelity clusters can be generated with a moderate constant overhead.

Figure 1

In the circle: The qubit system {∣↑⟩, ∣↓⟩} with the excited state $\mid e⟩$. The $\pi$ pulse affects only the transition $\mid \downarrow ⟩\to \mid e⟩$, and the emission of a photon into the cavity mode brings the excited state back to the qubit state ∣↓⟩. Each system is placed in a leaky cavity. Emission from a pair of such cavities, via a 50:50 beam splitter (BS), is detected in detectors $D_{+}$ or $D_{-}$, and conditionally leads to entangled qubit states.

Figure 2

(Color online) (a) Probability of success $p$ vs the detector efficiency $\eta$ after both rounds of the entangling procedure, plotted for different values of the spontaneous emission rate $\gamma =\{0,0.1{\Gamma }_{\text{slow}},0.2{\Gamma }_{\text{slow}}\}$ (top to bottom). Other parameters are $g=0.3$ and $\kappa =1$. (b) Fidelity of the entangled qubit pair for imperfectly mode-matched photons. Upper curve: fidelity for nonidentical leakage rates, $x={\kappa }_1∕{\kappa }_2$, taking $g_1=g_2$. Lower curve: fidelity for nonidentical coupling parameters, $x=g_1∕g_2$, taking $g_2=0.3$ and ${\kappa }_1={\kappa }_2=1$.

Figure 3

Cluster states. (a) The qubits (circles) are entangled with their nearest horizontal neighbor via EOs (depicted by lines between the qubits), and gates between computational qubits are incorporated by the vertical lines. (b) Linear clusters can be joined together by applying the EO between qubits $A_1$ and $B_1$, and subsequently performing single-qubit operations and measurements.