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.
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.
Quantum communication can enable new features that are provably impossible with classical communication alone. However, the optical fibers used to send the quantum information are inherently lossy. To overcome the exponential losses over distance so-called quantum repeaters are needed to amplify the signal. As opposed to memory-based approaches, the third generation of quantum repeaters, also called one-way quantum repeaters do not require two-way communication thus enabling very high communication rates. In particular, the one-way quantum repeater based on photonic tree states proposed by Borregaard et al. (2019) realizes this task with a very modest amount of resources. Nevertheless, the method considered is susceptible to operational errors. In this work, we propose the use of code concatenation of a stabilizer code and the tree code, so that by measuring stabilizers of the stabilizer code and applying the syndrome corrections we can achieve a fault-tolerant one-way quantum repeater. In order to do so, we present a detailed protocol that uses the 5-qubit code. Moreover, we develop the first fully general simulation framework for studying the performance of tree-code based one-way quantum repeater chains, which in this thesis is used to perform an analysis of the proposed protocol. We find that the code-concatenation protocol under consideration has a similar tolerance against operational errors to the protocol proposed by Borregaard et al. (2019). Unfortunately, we are not able to draw a distinction between the tolerance of the two approaches. We do however suggest modified protocols that may provide fault tolerance. Studying these is beyond the scope of this thesis.
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.
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 km) at a kHZ rate even in the presence of single qubit error rates ε>10−3.
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.
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, a hybrid approach is proposed which combines the code concatenation technique with the other mentioned approaches. The proposed approach outperforms code concatenation in terms of both number of qubits and error threshold and also significantly reduces the resource overhead of code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.
We develop protocols for generating loss-tolerant quantum tree-codes; these are designed to safeguard information against qubit losses, with wide applications in quantum communications. Contrary to previous proposals, our method enables fast encoding and decoding, thereby reducing losses due to the lagging and photon-reordering at the repeater stations. At the hardware level, we show how to achieve this with a single quantum emitter equipped with a feedback mechanism, which we leverage to engineer entangling gates between a fed-back qubit and multiple emitted qubits in parallel. In addition, analyzing typical patterns within the error-correction decoding graphs, we find optimizations of the structure of tree-codes, which enable improved performance by also reducing the code size; these are based on the introduction of in the code, which mimic the intrinsic adaptiveness of the recovery procedure. We show numerically that these improvements together significantly enhance the loss-correction performance. Specifically, focusing on quantum repeater protocols, we show that our fast recovery scheme (decoding-encoding) allows for improved repeater rates with smaller photon numbers per code.