Quantum repeater networks have attracted attention for the implementation of long-distance and large-scale sharing of quantum states. Recently, researchers extended classical network coding, which is a technique for throughput enhancement, into quantum information. The utility of quantum network coding (QNC) has been shown under ideal conditions, but it has not been studied previously under conditions of noise and shortage of quantum resources. We analyzed QNC on a butterfly network, which can create end-to-end Bell pairs at twice the rate of the standard quantum network repeater approach. The joint fidelity of creating two Bell pairs has a small penalty for QNC relative to entanglement swapping. It will thus be useful when we care more about throughput than fidelity. We found that the output fidelity drops below 0.5 when the initial Bell pairs have fidelity F < 0.90, even with perfect local gates. Local gate errors have a larger impact on quantum network coding than on entanglement swapping.
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of physically faulty qubits. Though these physical faults must negatively affect the computation, we can deal with them by adapting error-correction schemes. In this paper we have simulated statically placed single-fault lattices and lattices with randomly placed faults at functional qubit yields of 80%, 90%, and 95%, showing practical performance of a defective surface code by employing actual circuit constructions and realistic errors on every gate, including identity gates. We extend Stace et alʼs superplaquettes solution against dynamic losses for the surface code to handle static losses such as physically faulty qubits [1]. The single-fault analysis shows that a static loss at the periphery of the lattice has less negative effect than a static loss at the center. The randomly faulty analysis shows that 95% yield is good enough to build a large-scale quantum computer. The local gate error rate threshold is~0.3%, and a code distance of seven suppresses the residual error rate below the original error rate at = p 0.1%. 90% yield is also good enough when we discard badly fabricated quantum computation chips, while 80% yield does not show enough error suppression even when discarding 90% of the chips. We evaluated several metrics for predicting chip performance, and found that the average of the product of the number of data qubits and the cycle time of a stabilizer measurement of stabilizers gave the strongest correlation with logical error rates. Our analysis will help with selecting usable quantum computation chips from among the pool of all fabricated chips.
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.
In quantum networking, repeater hijacking menaces the security and utility of quantum applications. To deal with this problem, it is important to take a measure of the impact of quantum repeater hijacking. First, we quantify the work of each quantum repeater with regards to each quantum communication. Based on this, we show the costs for repeater hijacking detection using distributed quantum state tomography and the amount of work loss and rerouting penalties caused by hijacking. This quantitive evaluation covers both purification-entanglement swapping and quantum error correction repeater networks. Naive implementation of the checks necessary for correct network operation can be subverted by a single hijacker to bring down an entire network. Fortunately, the simple fix of randomly assigned testing can prevent such an attack.
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