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arXiv:1508.05966 · New Journal of Physics

Serialized quantum error correction protocol for high-bandwidth quantum repeaters

Andrew N. Glaudell, Edo Waks A, Jacob M. Taylor

Published Sep 2, 2016• 28 citations
arXivHTMLPDF

Abstract

Advances in single-photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code (QECC). Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long-range entangled bit generation with rates approaching 10 8 entangled bits per second may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with as few matter qubits as possible. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in entangled bit rates at large distances using this serial protocol and various QECCs. In particular, at a total distance of 500 km with fiber loss rates of 0.3 dB km −1 , logical gate failure probabilities of 10 −5 , photon creation and measurement error rates of 10 −5 , and a gate speed of 80 ps, we find the maximum single repeater chain entangled bit rates of 51 Hz at a 20 m node spacing and 190 000 Hz at a 43 m node spacing for the and QECCs respectively as compared to a bare success rate of 1 × 10 −140 Hz for single photon transmission.

DOI
10.1088/1367-2630/18/9/093008

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Advances in single-photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code (QECC). Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long-range entangled bit generation with rates approaching 10 8 entangled bits per second may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with as few matter qubits as possible. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in entangled bit rates at large distances using this serial protocol and various QECCs. In particular, at a total distance of 500 km with fiber loss rates of 0.3 dB km −1 , logical gate failure probabilities of 10 −5 , photon creation and measurement error rates of 10 −5 , and a gate speed of 80 ps, we find the maximum single repeater chain entangled bit rates of 51 Hz at a 20 m node spacing and 190 000 Hz at a 43 m node spacing for the and QECCs respectively as compared to a bare success rate of 1 × 10 −140 Hz for single photon transmission.
Fiber-based classical communication is all-optical and uses light pulses reamplified and reshaped every 50-100 km in classical repeaters. Most compatible with this would be a quantum communication system which is also all-optical with quantum processing units placed in similar intervals. However, existing all-optical quantum communication protocols either require complicated quantum error correction steps for logical-qubit recoveries at every few kilometers or, over larger quantum repeater segments, they would at least depend on sharing complex multi-photon entangled states. Here we propose an all-optical memory-based quantum repeater for long-distance quantum communication, with quantum memories at each repeater station realized in the form of fiber loops combined with suitable quantum error correction codes for photon-loss protection. By sending only single-photon states through the fibers connecting the stations, such repeaters can operate in the classical infrastructure's long-segment regime. We analyze the performance of our scheme for the Gottesman-Kitaev-Preskill code, including a concatenation with the Steane code, as well as the single-photon quantum parity code for total distances up to 10000 km.
Quantum communication between two distant parties will serve as a cornerstone of the future quantum internet. However, generating enough entangled Bell pairs over long distances is a critical bottleneck. Although photons are ideal carriers of quantum information, overcoming photon loss and the exponential attenuation of signals remains a major challenge. We propose an all-photonic quantum repeater architecture that enables quantum communication over 1,000 km with an equidistant repeater spacing of 9 km. This repeater spacing is enabled by elementary entangled Bell pairs protected through the concatenation of continuous-variable and discrete-variable quantum error correction codes, namely, the bosonic Gottesman-Kitaev-Preskill (GKP) code and the [[7,1,3]] Steane code, whose combination yields a synergistic improvement in robustness against photon loss. This architecture incorporates a new ranking criterion and a multi-reflection mirror-based optical cavity as a free-space photonic memory module, which we model in terms of its length and mirror-reflection efficiency. Additionally, we propose two heuristic construction methods for the elementary entangled Bell pairs. One method introduces up to two-qubit correlated errors within each logical qubit but requires a large number of GKP qubits, while the other allows up to three-qubit correlated errors within each logical qubit but requires fewer GKP qubits. To more accurately capture realistic physical conditions during photonic resource preparation, we include switching-induced imperfections in our simulations, in addition to other standard optical imperfections. In the presence of these imperfections, our realization requires only a few thousand GKP qubits per repeater station per protocol run, a resource requirement significantly smaller than the corresponding resource requirements of prior third-generation all-photonic repeater proposals.
We present a quantum repeater protocol for distributing entanglement over long distances, where a dedicated communication stage enables trial rates not limited by the travel time between repeater nodes. To accomplish this, each node contains several qubits that can couple to one single-photon emitter. Photons from the emitters in neighboring nodes generate heralded entanglement between qubits in these nodes. The protocol leaves the emitters disentangled from the rest of the system immediately after emitting the photons, thus allowing them to be reused to entangle other qubits without waiting for the repeater link round-trip time. This time multiplexing increases the protocol trial rate by up to an order of magnitude. The protocol is then combined with conventional deterministic entanglement swapping and heralded entanglement purification to extend the entanglement distance and reduce the entanglement error, respectively. We perform a complete protocol analysis by considering all relevant error sources, such as initialization, two-qubit gate, and qubit measurement errors, as well as the exponential decoherence of the qubits with time. The latter is particularly important since we analyze the protocol performance for a broad range of experimental parameters and obtain secret key rates ranging from 1 to 1000 Hz at a distance of 1000 km. Our results suggest that it is important to reach a qubit memory coherence time of around 1 s, and two-qubit gate and measurement errors on the order of 10 − 3 to obtain reasonable secret key rates over distances longer than achievable with direct transmission. While this work focuses on optimizing secret key rates, the protocol can also be used for Einstein-Podolsky-Rosen pair generation and is thus also relevant for, e.g., distributed quantum computing.
To realize long-distance quantum communication, it is crucial to design quantum repeater architectures that can deal with transmission losses and operational errors. Code concatenation of photonic graph codes is a promising way to achieve this; however, existing concatenated codes that can correct both transmission losses and operational errors are extremely hardware-demanding. We propose a one-way quantum repeater architecture based on concatenated ring graph codes and linear optical Bell-state measurements. We construct a scheme to generate the concatenated ring graph codes using quantum emitters, where the number of matter qubits scales linearly with concatenation depth. Furthermore, we devise a measurement strategy at each repeater station with a simple experimental setup where photons are measured in the order that they are created and show that entanglement swapping is fault-tolerant to both transmission losses and operational errors. This allows for long-distance quantum communication (>104> 10^4>104 km) at a kHZ rate even in the presence of single qubit error rates ε>10−3ε> 10^{-3}ε>10−3.
Quantum repeaters constitute a promising platform for enabling long-distance quantum communication and may ultimately serve as the backbone of a secure quantum internet, a scalable quantum network, or a distributed quantum computer. An efficient approach to encoding qubits within an error correcting code is provided by bosonic codes, in which even a single oscillator mode can function as a sufficiently large physical system. In this work, we initially investigate the bosonic Gottesman Kitaev Preskill (GKP) code as a promising platform for loss correcting quantum repeaters, compatible with room temperature implementation, and analyse how loss and other noise sources propagate through the circuit using Heisenberg evolution. We analyse three quantum repeater protocols in which transmission loss is suppressed at the cost of logical errors, identifying a relay-like teleamplifier as the optimal scheme. This enables long distance quantum communication via densely packed nodes without higher-level encoding, and we evaluate the resulting secure key rates exploiting analog syndrome information. Furthermore, we propose a concatenated Bell-state measurement (CBSM) scheme with a modified parity encoding based on GKP qubits, CV measurement with teleamplifier and a clipping method that corrects transmission loss without introducing logical errors. This significantly enhances the possible secure key distance. We find that GKP based repeaters can achieve performance comparable to approaches relying on photonic qubits, while requiring orders of magnitude fewer qubits. Our parity encoded GKP repeater protocol achieves a substantially higher secret key rate than existing GKP based repeater schemes while maintaining a comparable resource overhead.
One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.