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arXiv:1202.4077 · Physical Review A

Long-distance entanglement generation with scalable and robust two-dimensional quantum network

Ying Li, Daniel Cavalcanti, L. C. Kwek

Published Jun 29, 2012• 7 citations
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Abstract

We present a protocol for generating entanglement over long distances in a two-dimensional quantum network based on the surface-error-correction code. This protocol requires a fixed number of quantum memories at each node of the network and tolerates error rates of up to $1.67%$ in the quantum channels. If local operations are of an error rate of ${10}^{\ensuremath{-}3}$, error rates of about $1.27%$ in the quantum channels are tolerable.

DOI
10.1103/physreva.85.062330

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We present a protocol for generating entanglement over long distances in a two-dimensional quantum network based on the surface-error-correction code. This protocol requires a fixed number of quantum memories at each node of the network and tolerates error rates of up to 1.671.67%1.67 in the quantum channels. If local operations are of an error rate of 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3, error rates of about 1.271.27%1.27 in the quantum channels are tolerable.
We consider two-dimensional networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank-2 states. By using this method and combining it with the concept of percolation, we also show that the generation of long-distance entanglement is possible with rank-3 states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application to networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol cannot generate a singlet between any two nodes. In contrast, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower.
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We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the effective probability for the quantum errors is below a certain threshold, which is achieved by a local encoding of the qubits and a global bit-flip correction. In contrast to the conventional quantum-repeater schemes, we do not need to store the qubits in quantum memory for a long time: our protocol is a one-shot process (i.e., the elementary entangled pairs are used only once) involving one-way classical communication. Furthermore, the overhead of local resources increases only logarithmically with the size of the network, making our proposal favorable to long-distance quantum communication.
Scaling fault-tolerant quantum computing beyond a single processor demands logical—logical entanglement. While surface codes excel in local error correction, creating robust, distributed entanglement remains challenging. In this work, we introduce Entanglement Ejection—a protocol for generating physical—logical entanglement from a single logical qubit. This subroutine establishes logical—logical entanglement via entanglement swapping with a physical Bell pair provided by a quantum network. Unlike common injection-based methods, our protocol is deterministic, requiring no post-selection and thereby has the potential of reducing spatio-temporal resource overhead. We show via numerical simulations under a superconducting-specific noise model that this potential resource efficiency comes at the cost of a slightly higher, yet comparable, logical error rate.
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Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations so long as the error rate is below a threshold value. The two-dimensional surface code permits relatively high fault-tolerant thresholds at the ∼ 1% level, and only requires a latticed network of qubits with nearest-neighbor interactions. I will discuss our implementation of a sub-section of the larger fabric using three transmon qubits and two linking microwave resonators. We demonstrate high-fidelity control over the sub-section surface code strand, verified via quantum prcoess tomography and randomized benchmarking experiments. Our fixed-frequency qubit approach relies on the two-qubit cross-resonance microwave driving interaction, which is now one of many microwave-based entangling gate protocols. I will also discuss the prospects to scale to surface code plaquette level experiments.