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arXiv:2210.02878 · Physical Review A

Demonstration of teleportation across a quantum network code

Hjalmar Rall, Mark Tame

Published Aug 2, 2024• 3 citations
arXivHTMLPDF

Abstract

In quantum networks an important goal is to reduce resource requirements for the transport and communication of quantum information. Quantum network coding presents a way to do this by distributing entangled states over a network that would ordinarily exhibit contention. In this work, we study measurement-based quantum network coding (MQNC), which is a protocol particularly suitable for noisy intermediate-scale quantum devices. In particular, we develop techniques to adapt MQNC to state-of-the-art superconducting processors and subsequently demonstrate successful teleportation of quantum information, giving new insight into MQNC in this context after a previous study was not able to produce a useful degree of entanglement. The teleportation in our demonstration is shown to occur with fidelity higher than could be achieved via classical means, made possible by considering qubits from a polar cap of the Bloch sphere. We also present a generalization of MQNC with a simple mapping onto the heavy-hex processor layout and a direct mapping onto a proposed logical error-corrected layout. Our work provides some useful techniques to test and successfully carry out quantum network coding.

DOI
10.1103/physreva.110.022602

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In quantum networks an important goal is to reduce resource requirements for the transport and communication of quantum information. Quantum network coding presents a way to do this by distributing entangled states over a network that would ordinarily exhibit contention. In this work, we study measurement-based quantum network coding (MQNC), which is a protocol particularly suitable for noisy intermediate-scale quantum devices. In particular, we develop techniques to adapt MQNC to state-of-the-art superconducting processors and subsequently demonstrate successful teleportation of quantum information, giving new insight into MQNC in this context after a previous study was not able to produce a useful degree of entanglement. The teleportation in our demonstration is shown to occur with fidelity higher than could be achieved via classical means, made possible by considering qubits from a polar cap of the Bloch sphere. We also present a generalization of MQNC with a simple mapping onto the heavy-hex processor layout and a direct mapping onto a proposed logical error-corrected layout. Our work provides some useful techniques to test and successfully carry out quantum network coding.
Quantum network coding has been proposed to improve resource utilization to support distributed computation but has not yet been put into practice. We investigate a particular implementation of quantum network coding using measurement-based quantum computation on IBM Q processors. We compare the performance of quantum network coding with entanglement swapping and entanglement distribution via linear cluster states. These protocols outperform quantum network coding in terms of the final Bell pair fidelities but are unsuitable for optimal resource utilization in complex networks with contention present. We demonstrate the suitability of noisy intermediate-scale quantum devices such as the IBM Q for the study of quantum networks. We also identify the factors that limit the performance of quantum network coding on these processors and provide estimates of error rates required to boost the final Bell pair fidelities to a point where they can be used for generation of genuinely random cryptographic keys, among other useful tasks. Surprisingly, the required error rates are only around a factor of 2 smaller than the current status, and we expect they will be achieved in the near future.
Quantum network coding is an effective solution for alleviating bottlenecks in quantum networks. We introduce a measurement-based quantum network coding scheme for quantum repeater networks (MQNC), and analyze its behavior based on results acquired from Monte Carlo simulation that includes various error sources over a butterfly network. By exploiting measurement-based quantum computing, operation on qubits for completing network coding proceeds in parallel. We show that such an approach offers advantages over other schemes in terms of the quantum circuit depth and therefore improves the communication fidelity without disturbing the aggregate throughput. The circuit depth of our protocol has been reduced by 56.5% compared to the quantum network coding scheme (QNC) introduced in 2012 by Satoh et al. For MQNC, we have found that the resulting entangled pairs' joint fidelity drops below 50% when the accuracy of local operations is lower than 98.9%, assuming that all initial Bell pairs across quantum repeaters have a fixed fidelity of 98%. Overall, MQNC showed substantially higher error tolerance compared to QNC and slightly better than buffer space multiplexing using step-by-step entanglement swapping, but not quite as strong as simultaneous entanglement swapping operations.
The quantum internet will give us an infrastructure able to distribute and process quantum information on a planetary scale. The core of that internet will be formed from quantum error corrected links able to distribute information over large distances all while maintaining their coherence for long periods of time. However, many of the applications at the edge of such networks may rely on raw unencoded data – not protected by error correcting codes due to the nature of how it was generated. In this presentation, we will describe an experiment in which quantum information encoded on a physical qubit can be teleported into an error-corrected logical qubit. Our demonstration shows how one can get information into and out of quantum processors and tomorrows large-scale quantum networks.
The topological surface code is a leading candidate for harnessing long-range entanglement to protect logical quantum information against errors, and teleportation of logical states is desirable for robust quantum information processing. Nevertheless, scaling up the surface code in quantum teleportation poses a formidable challenge to experiment. Here on a superconducting quantum processor with 125 qubits, we demonstrate the robust teleportation of topological rotated surface code prepared by a linear-depth unitary circuit, with code distances up to 7. We obtain the teleportation phase diagram by tuning the local entangling gates uniformly across a finite threshold. Furthermore, we show that the entangling threshold can be boosted by coherent qubit rotations that inject magic resources beyond the Clifford regime, restoring the duality symmetry of the topological phase, which serves as a guiding principle to minimize the entanglement resource. Our results shed light on simulating and leveraging topological quantum matter on quantum devices, and pave the way to the ultimate goal of distributed fault tolerant quantum computation.
Quantum teleportation is a key protocol for transmitting quantum information using entanglement and classical communication. Its reliability is constrained by both the availability and fidelity of shared entangled pairs, which are affected by stochastic generation and memory decoherence. In this work, we focus on encoded teleportation, in which quantum information is encoded using a quantum error-correcting code and transmitted as a codeword. We evaluate reliability in terms of logical error probability, considering latency-constrained settings where entanglement is accumulated over time and degrades while in memory. We develop a unified framework that captures the interaction between entanglement availability, decoherence, and coding decisions. Our results show that the benefits of longer codes depend on the availability and fidelity of entangled pairs, as acquiring additional resources introduces delays that can reduce their quality. To address this latency-reliability tradeoff, we leverage code puncturing to enable flexible encoded teleportation, allowing the effective code length to adapt across different latency regimes while preserving a common stabilizer structure. Numerical results show that encoded teleportation can provide substantial reliability gains over uncoded transmission under a common entanglement-acquisition latency constraint, and that selecting appropriate punctured codes improves performance across varying latency budgets. Overall, our results highlight the importance of resource-aware adaptation for reliable quantum networking.
Abstract Quantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.