Unconditionally teleported quantum gates between remote solid-state qubit registers

TL;DR

This work demonstrates unconditional non-local quantum gate teleportation between remote solid-state qubits by integrating photonic entanglement, local NV-center logic, and real-time feed-forward. It achieves a teleported C-NOT between remote $^{13}$C data qubits across two NV-node registers and benchmarks the network with a distributed 4-qubit GHZ state, all without post-selection. The approach combines two nuclear-spin control schemes, robust remote-entanglement generation via DC Stark tuning, and meticulous phase-tracking to preserve coherence during networking, enabling scalable distributed quantum processing in solid-state platforms. Together, these results establish a foundational capability for modular, networked quantum information processing with potential pathways to larger resource states, improved link efficiencies, and integration into quantum-network software stacks.

Abstract

Quantum networks connecting quantum processing nodes via photonic links enable distributed and modular quantum computation. In this framework, quantum gates between remote qubits can be realized using quantum teleportation protocols. The essential requirements for such non-local gates are remote entanglement, local quantum logic within each processor, and classical communication between nodes to perform operations based on measurement outcomes. Here, we demonstrate an unconditional Controlled-NOT quantum gate between remote diamond-based qubit devices. The control and target qubits are Carbon-13 nuclear spins, while NV electron spins enable local logic, readout, and remote entanglement generation. We benchmark the system by creating a Greenberger-Horne-Zeilinger state, showing genuine 4-partite entanglement shared between nodes. Using deterministic logic, single-shot readout, and real-time feed-forward, we implement non-local gates without post-selection. These results demonstrate a key capability for solid-state quantum networks, enabling exploration of distributed quantum computing and testing of complex network protocols on fully integrated systems.

Figures (8)

• Figure 1: Experiment and resources overview. a) C-NOT quantum gate teleportation: we use two separated nodes based on NV-center defects in diamond. Each node is composed of two qubits: one communication qubit (in purple), obtained via controlling the electron spin of the NV, and one data qubit (in yellow), made by controlling a single $^{13}$C nuclear spin. To realize a non-local C-NOT gate between the data qubits, a teleportation protocol is used, including the generation of remote entanglement, local operations and feed-forward operations. b) Concept of the control setup for the two-qubit register on each node, separated by 2m of optical fibers. The qubits are manipulated via MicroWaves (in GHz range), and additionally RadioFrequency (MHz) waves for Alice's data qubit, sent along a gold stripline. Preparation, readout and entanglement generation require optical control via red (637nm) and yellow (575nm) lasers, whose outputs are combined in a single excitation optical path. A DC voltage is applied to use the Stark effect for tuning the emitted photon frequency of the two nodes.
• Figure 2: Data qubit preparation. a) Data qubit initialization sequence. $\pm Z$ initialization with the electron spin qubit in $\ket{0}$ deterministically enables the initialization in one of the two eigenstates. The initialization gate is completed when the electron spin qubit is optically reset to the state $\ket{0}$. Initialization on the equatorial plane is obtained by adding an unconditional gate for Alice along a tailored combination of $\hat{x}$ and $\hat{y}$ axes when initialized in $\ket{0}$, or using a conditional gates and a phase gate with an arbitrary angle $\theta$ for Bob. b) Readout of the data qubit. The state of the data qubit is mapped on the communication qubit and then optically read out. c) Measured fidelity with the ideal state for a set of unbiased initial states along the Bloch sphere.
• Figure 3: Network activity characterization. a) Remote entanglement generation and entangled state fidelity. At each node, a single attempt includes a reset pulse to initialize the communication qubit in $\ket{0}$, a MW $\alpha$-pulse, which brings the qubit in an unbalanced superposition state; a short (1ns) optical $\pi$-pulse that excites the population in the $\ket{0}$ state to the excited state, enabling spontaneous emission of a single photon; a MW $\pi$-pulse played at a time $\tau$ after the $\alpha$-pulse and $\tau$ before the next reset pulse in the subsequent attempt, hence a distance $\tau-t$ from the end of a single attempt. The total duration of a single attempt is 8.392$\mu$s (details in the Methods section), which is repeated $N$ times. Lower panel shows measured and simulated correlations. b) Characterization of the nuclear spin dephasing during entanglement attempts. During each entanglement attempt, the nuclear spin gains a deterministic phase, which we correct based on the number of repetitions $N$ before entanglement is heralded. Additional stochastic phases, e.g. due to the spin reset, cause decoherence. The plot shows the state fidelity of the nuclear spin state, initialized in a superposition state, for different numbers of entanglement attempts. The dashed grey line represents the chosen timeout for entanglement generation N$_{max}$=50.
• Figure 4: Realization of a remote 4-qubit GHZ state. a) Circuit diagram. The data qubits are initialized using the sequence in Fig. \ref{['fig:fig2']}a. After heralding entanglement, a rephase gate is played on Bob's data qubit. Subsequently, a set of local operations completes the generation of the GHZ state. Dashed gates represent gates that are not individually executed, but are compiled in the readout sequence. To measure the correlators in b), we first measure the electron spin state, using single-qubit gates for the measurement basis selection and a non-destructive optical readout (highlighted in magenta). Every outcome is accepted. If the outcome is $\ket{1}$, a $\pi$-pulse flips the state to ensure the assisted-readout always starts with the communication qubit in $\ket{0}$. During the readout of the electron spin qubit, the data qubit picks up another phase $\theta'$ depending on the measurement outcome, whose rephasing is also compiled in the subsequent assisted-readout. b) GHZ correlator results and corresponding simulated values.
• Figure 5: Non-local C-NOT gate. a) Circuit diagram using native NV gates. The gates in purple compile a local C-NOT gate. For Alice, the unconditional gates on the data qubit are performed before entanglement and after the mid-circuit readout for synchronization purposes. The feed-forward operation (dashed gates) is compiled in the readout sequence. The magenta mid-circuit measurement indicates a non-destructive readout. b) Measured classical truth-table. The initial states on the data qubit are the eigenstates and we report the non-local two-qubit state fidelity. As expected, we see a bit-flip in Bob's state when Alice's input state is $\ket{1}$. c) Simulated classical truth table. d) Generation of an entangled state via the non-local C-NOT gate. We prepare the data qubits in $\ket{X}_A$ and $\ket{1}_B$, to obtain the entangled state $\Psi^+$. The histogram shows the correlator expectation values together with their simulated values.