In blind quantum computing (BQC), a user with a simple client device can perform a quantum computation on a remote quantum server such that the server cannot gain knowledge about the computation. Here, we numerically investigate hardware requirements for verifiable BQC using an ion trap as server and a distant measurement-only client. While the client has no direct access to quantum-computing resources, it can remotely execute quantum programs on the server by measuring photons emitted by the trapped ion. We introduce a numerical model for trapped-ion quantum devices in NetSquid, a discrete-event simulator for quantum networks. Using this, we determine the minimal hardware requirements on a per-parameter basis to perform the verifiable BQC protocol. We benchmark these for a five-qubit linear graph state, with which any single-qubit rotation can be performed, where client and server are separated by 50 km. Current state-of-the-art ion traps satisfy the minimal requirements on a per-parameter basis, but all current imperfections combined make it impossible to perform the blind computation securely over 50 km using existing technology. Using a genetic algorithm, we determine the set of hardware parameters that minimises the total improvements required, finding directions along which to improve hardware to reach our threshold error probability that would enable experimental demonstration. In this way, we lay a path for the near-term experimental progress required to realise the implementation of verifiable BQC over a 50 km distance.@en

Rare-earth ion-doped crystals are of great interest for quantum memories, a central component in future quantum repeaters. To assess the promise of 1 % Tm ³⁺-doped yttrium gallium garnet (Tm:YGG), we report measurements of optical coherence and energy-level lifetimes of its ³H 6 ↔ 3 H ₄ transition at a temperature of around 500 mK and various magnetic fields. Using spectral hole burning (SHB), we find hyperfine ground-level (Zeeman level) lifetimes of several minutes at magnetic fields of less than 1000 G. We also measure coherence time exceeding one millisecond using two-pulse photon echoes. Three-pulse photon echo and SHB measurements reveal that due to spectral diffusion, the effective coherence time reduces to a few µs over a timescale of around two hundred seconds. Finally, temporal and frequency-multiplexed storage of optical pulses using the atomic frequency comb protocol is demonstrated. Our results suggest Tm:YGG to be promising for multiplexed photonic quantum memory for quantum repeaters.

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We perform a numerical study of the distribution of entanglement on a real-world fiber grid connecting the German cities of Bonn and Berlin. The connection is realized using a chain of processing-node quantum repeaters spanning roughly 900 kilometers. Their placement is constrained by the fiber grid we consider, resulting in asymmetric links. We investigate how minimal hardware requirements depend on the target application, as well as on the number of repeaters in the chain. We find that requirements for blind quantum computing are markedly different than those for quantum key distribution, with the required coherence time being around two and a half times larger for the former. Further, we observe a trade-off regarding how target secret-key rates are achieved when using different numbers of repeaters: comparatively low-quality entangled states generated at a high rate are preferred for higher numbers of repeaters, whereas comparatively high-quality states generated at a lower rate are favored for lower numbers of repeaters. To obtain our results we employ an extensive simulation framework implemented using NetSquid, a discrete-event simulator for quantum networks. These are combined with an optimization methodology based on genetic algorithms to determine minimal hardware requirements.@en

In this work, we fabricate a multimode quantum memory out of a thulium-doped crystal and demonstrate storage of laser pulses of up to 100 µsec. A significant step forward for creating quantum memories with long optical storage times.

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The forthcoming quantum Internet is poised to allow new applications not possible with the conventional Internet. The ability for both quantum and conventional networking equipment to coexist on the same fiber network would facilitate the deployment and adoption of coming quantum technology. Most quantum networking tasks, like quantum repeaters and the connection of quantum processors, require nodes for multi-qubit quantum measurements (often Bell-State measurements), and their real-world coexistence with the conventional Internet has yet to be shown. Here we field deploy a Measurement-Device Independent Quantum Key Distribution (MDI-QKD) system, containing a Bell-State measurement node, over the same fiber connection as multiple standard Internet Protocol (IP) data networks, between three nearby cities in the Netherlands. We demonstrate over 10 Gb/s classical data communication rates simultaneously with our next-generation QKD system, and estimate 200 GB/s of classical data transmission would be easily achievable without significantly affecting QKD performance. Moreover, as the system ran autonomously for two weeks, this shows an important step towards the coexistence and integration of quantum networking into the existing telecommunication infrastructure.

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Long optical storage times are an essential requirement to establish high-rate entanglement distribution over large distances using memory-based quantum repeaters. Rare earth ion-doped crystals are arguably well-suited candidates for building such quantum memories. Toward this end, we investigate the 795.32 nm ³H₆ ↔ ³H₄ transition of 1% thulium-doped yttrium gallium garnet crystal (Tm³⁺:Y₃Ga₅O₁₂ : Tm³⁺:YGG). Most essentially, we find that the optical coherence time can reach 1.1 ms, and, using laser pulses, we demonstrate optical storage based on the atomic frequency comb (AFC) protocol up to 100 µs. In addition, we demonstrate multiplexed storage, including feed-forward selection, shifting, and filtering of spectral modes, as well as quantum state storage using members of non-classical photon pairs. Our results show that Tm:YGG can be a potential candidate for creating multiplexed quantum memories with long optical storage times.

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The original version of this Article contained errors in the Competing interests statement and Table 1 and incorrectly omitted the Acknowledgements section. The original Competing interests statement reported no competing interests for the authors; this has been corrected to “B.H. and F.F. are employees of ID Quantique, Geneva and ID Quantique Europe, Vienna, respectively, which have competing interests with Arqit in developing quantum communication technologies. B.T. is an employee of Thales Alenia Space, a joint Venture which invests in satellite quantum communications. B.H. is the inventor of several patents, both pending and accepted, in the field of space QKD. The authors declare that there are no other competing interests”. The original Table 1 omitted the captions. Table 1 captions read: The different steps of the protocol are described below, each item corresponding to the numbered row in the Table. 1. Alice prepares a series of quantum states, according to BB84 polarisation protocol. For each state, she chooses both the bit value and the corresponding basis. She sends the states to Bob over a quantum channel (arrow with diagonal stripes). 2. Many states are lost in the transmission. Bob tells Alice, which states have been lost (X in the table). He uses the classical discussion channel (white arrow). Alice and Bob discard all the corresponding states. The resulting series of bits is the raw key. 3. Alice tells Bob, over the classical discussion channel, which bases she used. Bob notes the cases when he and Alice used different bases (X in the table), but does not tell Alice. The remaining bits represent the sifted key for Bob. Alice cannot know, which of the states were received by Bob in the correct basis. 4. to 6. Alice and Carol follow the same protocol with a new series of states. 7. Alice performs an XOR of the two raw keys she exchanged with Bob and with Carol and sends the result to Carol, over the classical discussion channel. 8. Bob sends directly to Carol, which bits he received in the wrong basis and should not be used (X in the table). He uses a confidential classical channel, “which cannot be eavesdropped by Alice” (black arrow). 9. Carol notes the wrong bits in the XORed key. 10. Carol makes an XOR of the two sifted keys, and sends to Bob, which bits should not be used (X in the table). She also uses the same confidential classical channel, “which cannot be eavesdropped by Alice”. 11. Bob and Carol now share a common sifted key, unknown to Alice. They can process it in the standard way (error estimation, error correction, privacy amplification) to finally get a shared secret key. The main hypothesis of the protocol is that Bob and Carol share a confidential classical channel, which cannot be eavesdropped by Alice. The correct Acknowledgements read: B.H., R.A., E.D., F.F., P.G., H.H., V.M., A.P., J.A.S., A.W. and H.Z. acknowledge support from the H2020-funded research project OPENQKD, Grant agreement contract number 857156, https://openqkd.eu/. This has now been corrected in both the PDF and HTML versions of the Article.

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We argue that long optical storage times are required to establish entanglement at high rates over large distances using memory-based quantum repeaters. Triggered by this conclusion, we investigate the 795.325 nm3 H6↔H34 transition of Tm:Y3Ga5O12 (Tm:YGG). Most importantly, we find that the optical coherence time can reach 1.1 ms, and, using laser pulses, we demonstrate optical storage based on the atomic frequency comb protocol during up to 100 μs as well as a memory decay time Tm of 13.1 μs. Possibilities of how to narrow the gap between the measured value of Tm and its maximum of 275 μs are discussed. In addition, we demonstrate multiplexed storage, including with feed-forward selection, shifting and filtering of spectral modes, as well as quantum state storage using members of nonclassical photon pairs. Our results show the potential of Tm:YGG for creating multiplexed quantum memories with long optical storage times, and open the path to repeater-based quantum networks with high entanglement distribution rates.

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