Interoperability in encoded quantum repeater networks

Abstract

The future of quantum repeater networking will require interoperability between various error correcting codes. A few specific code conversions and even a generalized method are known, however, no detailed analysis of these techniques in the context of quantum networking has been performed. In this paper, we analyze a generalized procedure to create Bell pairs encoded heterogeneously between two separate codes used often in error corrected quantum repeater network designs. We begin with a physical Bell pair, then encode each qubit in a different error correcting code, using entanglement purification to increase the fidelity. We investigate three separate protocols for preparing the purified encoded Bell pair. We calculate the error probability of those schemes between the Steane [[7,1,3]] code, a distance three surface code and single physical qubits by Monte Carlo simulation under a standard Pauli error model, and estimate the resource efficiency of the procedures. A local gate error rate of 10 −3 allows us to create high-fidelity logical Bell pairs between any of our chosen codes. We find that a postselected model, where any detected parity flips in code stabilizers result in a restart of the protocol, performs the best.

Distributed Quantum Computing Utilizing Multiple Codes on Imperfect Hardware

“…Portions of this dissertation are adapted from papers under copyrights by the American Physical Society [121,123] and by the IOP Publishing [122].…”

“…This conversion works as the state injection for the deformationbased qubit and e.g. to support networking among multiple quantum computers that employ heterogeneous error correcting codes [121]. To complete universality of the deformation-based surface code, we demonstrate the arbitrary state injection in this section.…”

Large-scale quantum networks based on graphs

“…'Partially quantum' networks are considered in the so-called trusted node scenario [26], while fully quantum networks have been investigated in the context of network routing [27][28][29][30] and coding [31-33] strategies and heterogeneous network technologies [34].…”

“…Several theoretical variations have been proposed: some of them are based on entanglement distillation [12][13][14] and others are based on forward error correction [15][16][17][18]. Much experimental progress towards the realisation of a quantum repeater has been made [19][20][21][22][23][24][25].'Partially quantum' networks are considered in the so-called trusted node scenario [26], while fully quantum networks have been investigated in the context of network routing [27][28][29][30] and coding [31-33] strategies and heterogeneous network technologies [34].Here we propose a general multipartite quantum network architecture, where the long-distance links are bridged by quantum repeater stations. This idea is illustrated in figure 1 for the long-term vision of a 'world-wide quantum web'.…”

Robust entanglement distribution via quantum network coding

“…Hence intermediate devices that recover the original signal, so-called quantum repeaters, are necessary [1,2]. Many proposals for them have been made, including approaches based on repeat-until-success strategies using two-way communication [3][4][5] and forward-error correction based protocols which do not require this acknowledgment of successful transmission [6][7][8][9][10]. The requirements of quantum repeaters regarding the precision of operations are very challenging, but experiments have shown significant progress [11][12][13][14][15][16][17][18].…”