Deterministic Generation of Loss-Tolerant Photonic Cluster States with a Single Quantum Emitter

A photonic cluster state with a tree-type entanglement structure constitutes an efficient resource for quantum error correction of photon loss. But the generation of a tree cluster state with an arbitrary size is notoriously difficult. Here, we propose a protocol to deterministically generate photonic tree states of arbitrary size by using only a single quantum emitter. Photonic entanglement is established through both emission and rescattering from the same emitter, enabling fast and resource-efficient entanglement generation. The same protocol can also be extended to generate more general tree-type entangled states.

Figure 1

(a) The schematic setup to generate a photonic tree cluster state with an arbitrary size. The inset shows the energy-level structure of the quantum emitter. (b),(c) The left-hand panels illustrate the effects of the $E$ gate (b) and the cz gate (c) applied on the joint emitter-photon quantum state. The right-hand panels show the pulse sequences required to implement the $E$ gate (b) and the cz gate (c). The color of each block in the pulse sequence is used to indicate the optical transition [also color labeled in (a)] to which the rotation pulse is applied.

Figure 2

Graph representation of the procedure for generating a tree with branching parameters $b_0=b_1=b_2=2$.

Figure 3

(a) The effective error probability of the logic qubit encoded by the tree as a function of the tree size (the total number of photons in the tree). We assume a single-photon loss probability of $ϵ=0.1$ in this calculation. The blue circles represent the case where $t_{\mathrm{coh}}\to \infty$, and the orange squares represent the case where $t_{\mathrm{coh}}/t_{\mathrm{ph}}={10}^4$. (b) The optimized value of ${ϵ}_{\mathrm{eff}}$ as a function of single-photon loss probability and coherence-time-bandwidth product.