Hybrid Quantum Repeater Chains with Semiconductor Quantum Dots and Group-IV-Vacancy Color Centers in Diamond

TL;DR

The paper addresses the challenge of scalable long-distance entanglement distribution by proposing a hybrid quantum repeater that pairs quantum-dot photon-pair sources with group-IV-vacancy diamond memories. It introduces a detailed spin–photon interface model, incorporating polarization, field-induced level splitting, and cross-talk, and identifies practical mitigations such as frequency filtering and optimized magnetic-field orientation. It then analyzes a full repeater chain with elementary links, entanglement distillation, and swapping, showing that networks with thousands of memories can achieve secret-key rates on the order of hundreds of bits per second over $1{,}000$ km. The work highlights the potential of this hybrid platform for next-generation quantum networks and discusses pathways to robustness and scalability, including compatibility with error-correction approaches and realistic device constraints.

Abstract

We propose and analyze a hybrid quantum repeater architecture that combines two leading hardware platforms: quantum dots (QDs) as bright, deterministic sources of entangled photon pairs and group-IV-vacancy centers in diamond as efficient, heralded quantum memories. This combination leverages high-rate entanglement generation together with long-lived storage, enabling scalable entanglement distribution over long distances. A key challenge is the large bandwidth mismatch between QD photons and the narrow optical transitions of the memories. We combine a comprehensive model of the spin-photon interface, including full spin-photon coupling dynamics, and explore mitigation strategies such as frequency filtering and optimized magnetic-field orientation. Our results show that with optimized designs, photon-to-memory transfer can be achieved with high efficiency and fidelity, supporting the feasibility of such hybrid systems. Finally, we analyze a full repeater chain using experimentally achievable parameters and find that a network with thousands of memories across several repeater nodes could achieve a secret-key rate of 500 bit/s over 1,000 km, demonstrating the strong potential of this approach for next-generation quantum networks.

Figures (12)

• Figure 1: QD-G4V hybrid repeater chain protocol. a) Elementary-link establishment. The chain consists of two end nodes, Alice and Bob, and $N-1$ intermediate repeater nodes, each represented by an orange rectangle color block. QD emitters (red stars) are positioned midway between neighboring nodes and distribute entangled photons (red bell shapes) between them. In each node, G4V electron spins (dark blue) serve as interfaces for loading qubits from the incoming entangled photons, while nuclear spins (orange) provide long-term qubit storage. b) The fundamental operations of the elementary-link entanglement distillation. They involve local nucleus-nucleus cnot gates and qubit measurement and classical communications between the two nodes. c) The entanglement distillation protocol following Ref. distillation_nigmatullin2016minimally. It has four options: level-0: using directly the raw Bell pairs; level-1, -2, and -3: each distilled Bell pair is made up from 2, 4, and 6 raw ones, respectively. Single-qubit gates (not shown) are applied before the level-2 and -3 distillations. d) Entanglement swapping. It contains a cnot gate between the two nuclear spins from different memory modules in a repeater node, followed by a Hadamard gate and qubit measurements. e) The end-to-end entanglement distillation is similar to the elementary-link distillation, except that, due to its time-consuming nature, classical communication is employed for post-selection rather than as a precondition in the level-2 and level-3 operations.
• Figure 2: Optical circuits for the repeater-chain operations. a) Entanglement transfer from the photons to the nuclear spins as in the elementary-link establishment step. QDs emit frequency-distinct, polarization-entangled photon pairs, which are separated by a wavelength-division multiplexer (WDMP). Frequency filters (FFs) are used on one side or both for narrowing the bandwidth of the photon(s) in a Bell pair. Polarization-to-time-bin converters (PTBCs), implemented with polarizing beam splitters, encode polarization qubits into time-bin qubits for fiber transmission. At each repeater node, frequency converters (FCs) shift photons from telecommunication to visible wavelengths for G4V compatibility. Optical switches (S) direct photons to designated memory cells. Through controlled photon–spin interactions and subsequent photon detection, the photon qubit is mapped onto a G4V electron spin (dark blue) and then transferred to a nuclear spin (orange). Successful detection heralds photon receipt, which is confirmed via classical communication between nodes. b) and c) Optical circuit for the local nucleus-nucleus cont gates in the entanglement distillation and swapping steps, respectively. A single photon source (implemented with a separate G4V Knall2022) generates a photon, which is guided by circulators and optical switches (S). It interacts sequentially with two target G4V electron spins until heralded photon measurements confirm entanglement between them. Nucleus–nucleus cnot gates are then realized using local electron–nuclear gates.
• Figure 3: QD and G4V hardware profiles. a) Energy levels and decay paths of a quantum dot (QD). The QD includes a ground state $|0\rangle$, two approximately degenerate single-excitation states, $|\rm X\rangle$ and $|\rm X'\rangle$, and a biexcitation state, $|\rm XX\rangle$, which together give rise to two cascade decay paths. The decay times $T_{\rm X}$ and $T_{\rm XX}$ of the single- and biexcitation states correspond to linewidths $\gamma_{\rm X}$ and $\gamma_{\rm XX}$, respectively. Photons are emitted with horizontal (H) or vertical (V) polarization, depending on the decay path; the presence or absence of a prime symbol for the labels H and V denotes different photon frequencies. b) Frequency profile of photons emitted by the QD. According to the experiment presented in schimpf_quantum_2021, the photons from both $|\rm XX\rangle$, $|\rm X\rangle$ and $|\rm X'\rangle$ exhibit Lorentzian spectral profiles centered at $\omega_{\rm 0,X}$ and $\omega_{\rm 0,XX}$, with bandwidths $\gamma_{\rm XX} = 8.33$ GHz and $\gamma_{\rm X} = 4.34$ GHz, respectively. c) Fiber–cavity interface and integration of a group-IV-vacancy color center (G4V) into the sawfish nanophotonic crystal cavity bopp_sawfish_2024. The incoming photon from the fiber is in a superposition of early and late time-bin states, encoding a qubit. The cavity supports a single optical mode with resonance frequency $\omega_c$, coupling strength $\bm{g}=[g_{1A},g_{2B},g_{2A},g_{1B}]$ to the G4V, and a total loss rate $\kappa$. d) Energy levels of the G4V center (SiV or SnV), modeled as a four-level system with ground states $|1\rangle$ and $|2\rangle$ and excited states $|A\rangle$ and $|B\rangle$. The optical transitions $|1\rangle \leftrightarrow |A\rangle$ and $|2\rangle \leftrightarrow |B\rangle$ have linewidths $\gamma_{1A}$ and $\gamma_{2B}$, respectively. The cavity resonance $\omega_c$ is detuned by $\delta$ from the $|1\rangle \leftrightarrow |A\rangle$ transition. The ground-states $|1\rangle$ and $|2\rangle$ circled by the orange line make up the qubit of the G4V spin, whose splitting is denoted as $\omega_s$. e) Operational sequence for implementing the spin–photon entanglement gate via the reflection-based scheme (see App. \ref{['state_transfer']}). The protocol consists of four steps: (1) initialize the G4V spin in state $|1\rangle$; (2) scatter the early time-bin photon; (3) apply a $\pi/2$ rotation around the $y-$axis to the spin; (4) scatter the late time-bin photon. Fig. e) is adapted from bhaskar_experimental_2020.
• Figure 4: Infidelity $1-F_{\rm sp}$ and efficiency $\eta_{\rm sp}$ of the spin-spin entangled state as a function of the filtered bandwidth $\gamma\coloneqq\tilde{\gamma}_{\rm XX}$ while keeping $\gamma_{\rm X}=4.34$ GHz the same. The relevant parameters for both the SiV and SnV are shown in Tab. \ref{['tab:summary']} in App. \ref{['app:opt']}.
• Figure 5: Operational protocol and optimal secret-key rate for a QD-SiV quantum repeater chain. a) Operation timeline of the repeater chain. The red, blue, and yellow boxes represent the qubit-loading phase, one round of entanglement-distillation operation, and the entanglement swapping phase. Each chain of boxes represents an operational thread of a memory cell. b) Maximal secret-key rate ($R_{\rm sk, opt}$) as a function of total distance $L$ under certain memory cell number per module ($m$), QD photon bandwidth presented as spin Bell pair fidelity ($F_{\rm sp}$), and the photon-mediated nuclear-nuclear gate error rate $\varepsilon_{\rm n-n}$. The spin Bell pair fidelities $F_{\rm sp}=0.95$ and $0.98$ correspond to the QD photon bandwidth after the frequency filtering of $[\tilde{\gamma}_{\rm X}, \tilde{\gamma}_{\rm XX}]=[4.34, 8.17]$ GHz and $[\tilde{\gamma}_{\rm X}, \tilde{\gamma}_{\rm XX}]=[4.33, 6.50]~\text{GHz}$, respectively. Note that for the $F_{\rm sp}=0.95$ case, only one photon in a Bell pair is filtered ($\tilde{\gamma}_{\rm X}=\gamma_{\rm X}=4.34~\text{GHz}$). The optimal values of $N$, $n_{\rm loa}$, $n_{\rm dis,n}$, and $n_{\rm dis,e}$, which give the maximal secret-key rate, can be found in App. \ref{['app:opt_m_N']}.