Quantum linear network coding for entanglement distribution in restricted architectures

Abstract

In this paper we propose a technique for distributing entanglement in architectures in which interactions between pairs of qubits are constrained to a fixed network G. This allows for two-qubit operations to be performed between qubits which are remote from each other in G, through gate teleportation. We demonstrate how adapting quantum linear network coding to this problem of entanglement distribution in a network of qubits can be used to solve the problem of distributing Bell states and GHZ states in parallel, when bottlenecks in G would otherwise force such entangled states to be distributed sequentially. In particular, we show that by reduction to classical network coding protocols for the k-pairs problem or multiple multicast problem in a fixed network G, one can distribute entanglement between the transmitters and receivers with a Clifford circuit whose quantum depth is some (typically small and easily computed) constant, which does not depend on the size of G, however remote the transmitters and receivers are, or the number of transmitters and receivers. These results also generalise straightforwardly to qudits of any prime dimension. We demonstrate our results using a specialised formalism, distinct from and more efficient than the stabiliser formalism, which is likely to be helpful to reason about and prototype such quantum linear network coding circuits.

Increasing the classical data throughput in quantum networks by combining quantum linear network coding with superdense coding

“…3 shows a general illustration of such a network. The first part of the proof is showing that components (b) -(g) admit a quantum linear network code that can distribute a Bell pair between each transmitter-receiver pair, for which the QLNC formalism [10] is used. To recap the QLNC formalism, to the extent which it is used here:…”

“…All transmitters and receivers are distinct nodes, and additionally there are "relay" nodes that are neither transmitters or receivers. Whilst the techniques developed by de Beaudrap and Herbert [10] are used to prove the main result below, in this paper a slightly different setting is considered: the nodes are not single qubits, but rather are small devices hosting a number of qubits and equipped with the necessary (quantum) computational power and resources to enable the desired operations in communications network. The goal is to maximise the data throughput, which for simplicity is defined:…”

“…For this reason, along with the aforementioned advantage of superdense coding over directed networks, this paper is concerned with directed networks (i.e., networks in which all of the links are unidirectional, but with parallel oppositely directed edges permitted) and also considers only the "k-pairs" setting, in which k bitstreams must be transmitted from transmitter nodes to receiver nodes (i.e., the Butterfly network shows a 2-pairs network coding problem). The possibility of combining network coding and superdense coding to increase data throughput is motivated by the observation that network coding protocols can be applied to quantum information transfer [5] and entanglement distribution [6][7][8][9][10]. The main result presented in this paper is that combining quantum linear network coding (QLNC) and superdense coding can yield a factor (2 − ) increase in data throughput compared to that which could be achieved using QLNC or superdense coding alone (for arbitrarily small > 0).…”

Quantum Monte-Carlo Integration: The Full Advantage in Minimal Circuit Depth

“…Ref. [26,27]), thus effectively facilitating the simulation of a quantum computer with lower qubit-number but higher quantumvolume on the hardware. In such a case, it will in turn be reasonable to think not only of running quantum algorithms with variationally-optimised ansätze, but also those with explicitly-constructed circuits, such as QAE, so long as they can adequately handle the inclement noise.…”

The Impact of Hardware Specifications on Reaching Quantum Advantage in the Fault Tolerant Regime

“…Error correction codes which rely on global interactions at the physical level have favourable encoding rates as a function of code distance [11] but enabling this global connectivity on large devices may be challenging, or the connectivity overheads may outweigh the benefits relative to closer-range-connectivity codes. Entanglement distribution may be a viable method of enabling distant connectivity for large scale devices with limited physical connectivity in the limit of large reserves of quantum memory [12] . Higher dimensional error correction codes can have access to a greater range of transversal gates which may considerably improve final run-times, where transversal implies that each qubit in a code block is acted on by at most a single physical gate and each code block is corrected independently when an error occurs.…”