Experimental demonstration of entanglement pumping with bosonic logical qubits

Entanglement is crucial for quantum networks and computation, yet maintaining high-fidelity entangled quantum states is hindered by decoherence and resource-intensive purification methods. Here, we experimentally demonstrate entanglement pumping, utilizing bosonic quantum error correction (QEC) codes as long-coherence-time storage qubits. By repetitively generating entanglement with short-coherence-time qubits and injecting it into error-detectable logical qubits, our approach effectively preserves entanglement. Through error-detection to discard error states and entanglement pumping to mitigate errors within the code space, we extend the existence time of entanglement by nearly 50% compared to the case without entanglement pumping. This entanglement pumping scheme can additionally serve as an erasure detection protocol for the dual-rail code. This work highlights the potential of bosonic logical qubits for scalable quantum networks and introduces a novel paradigm for efficient entanglement management.

💡 Research Summary

Entanglement is a vital resource for quantum networks and computation, yet its practical use is limited by decoherence, noisy channels, and imperfect operations. Traditional entanglement purification consumes many low‑fidelity pairs to distill a high‑fidelity one, which is resource‑intensive and experimentally demanding. In this work, the authors demonstrate a more efficient approach called entanglement pumping (EP) combined with bosonic quantum error‑correction (QEC) codes realized in superconducting 3D cavities. The experimental platform consists of three high‑Q coaxial cavities (S₁, S₂, S₃) and four transmon qubits (I₁, I₂, Y₁, Y₂). The two “communication” transmons (Y₁, Y₂) have short coherence times but can be rapidly entangled via the bus cavity S₂. The two “storage” cavities (S₁, S₃) serve as long‑lived bosonic logical qubits encoded with the lowest‑order binomial code (|0⟩ₗ = (|0⟩+|4⟩)/√2, |1⟩ₗ = |2⟩).

The protocol proceeds as follows: first, Y₁ and Y₂ are prepared in a Bell state (|ge⟩+|eg⟩)/√2 using echoed cavity‑induced phase (CIP) gates that cancel dispersive shifts from the storage cavities. This entanglement is swapped into the storage cavities, creating an initial photonic Bell state (|01⟩+|10⟩)/√2 with a fidelity of ~91 %. The communication qubits are then re‑entangled repeatedly, and each new entangled pair is used to perform bilateral CNOT‑like operations on the storage qubits followed by post‑selection on the |gg⟩ outcome. This constitutes one round of EP.

When EP is applied without any waiting time (τ = 0), accumulated gate errors cause the fidelity to saturate around 87 % after several rounds. Introducing a deliberate wait (τ = 10 µs) that allows decoherence in the storage cavities reveals the power of EP: the fidelity, starting from ~72 %, climbs with each round and stabilizes near 86 %. Thus EP can actively replenish lost entanglement when local decoherence is significant.

In parallel, the authors implement error detection (ED) by measuring the parity of the binomial code. A single‑photon loss flips the parity and is detected; the corresponding logical pair is discarded. Combining EP with ED yields a further improvement: the “existence time” of entanglement—defined as the interval over which fidelity remains above 0.5 or negativity stays positive—is extended by roughly 50 % compared with using ED alone.

The paper also points out that the EP circuit is mathematically equivalent to an erasure‑detection protocol for a dual‑rail encoding of the two‑cavity state. By applying bilateral CNOTs (or parity‑mapping gates) to a dual‑rail qubit together with the entangled communication qubits, an erasure (photon loss) manifests as a distinguishable measurement pattern on the communication qubits, allowing immediate detection.

A technical highlight is the echoed CIP gate used to re‑entangle Y₁ and Y₂ even when the storage cavities contain multiple photons. Two CIP operations separated by Xπ flips cancel unwanted dispersive phases, and by fine‑tuning the gate duration the authors achieve the required phase condition (Φ₁+Φ₂−Φ₃ = π/2), producing a high‑fidelity Bell state on the communication qubits (~93 %).

Overall, the experiment demonstrates that bosonic logical qubits, when paired with entanglement pumping, can maintain high‑quality entanglement with far fewer physical resources than conventional purification. The approach reduces the number of required entangled pairs, mitigates decoherence through continuous pumping, and integrates naturally with error‑detecting bosonic codes. While the success probability per EP round drops with successive iterations, the authors argue that with state‑of‑the‑art transmons and cavities, fidelities exceeding 99 % and near‑deterministic success become realistic. This work therefore provides a practical roadmap for scalable quantum networks and distributed quantum computing, where long‑lived, high‑fidelity entanglement is essential.