Routing Qubits on Noisy Networks

TL;DR

This work tackles the problem of robust quantum routing in networks engineered for ideal transfer by analyzing a Lily Graph CTQW router. It models qubit routing as a single-excitation dynamics problem with input qubits encoded on two nodes and multiple outputs, and examines resilience to static and dynamical phase and weight noise using von Mises, Gaussian and Ornstein-Uhlenbeck processes. The key finding is that high routing fidelity persists near a common routing time, with the first fidelity peak typically occurring around the routing moment, especially for moderate numbers of outputs; phase noise mainly alters peak heights while weight noise largely reduces peak magnitude, making weight fluctuations the dominant degradation mechanism for larger port counts. The results demonstrate practical guidance for designing scalable, noisy quantum routers and naturally extend to long-range routing and qudit routing, highlighting the universality of the routing time and the crucial role of chirality.

Abstract

Robust quantum routing is essential for scalable quantum technologies. This paper investigates the resilience of routing protocols in network architectures designed for perfect, high-fidelity transfer of both classical and quantum information under ideal conditions. We encode information in the position of a quantum walker on a graph, modelling the routing of a generic qubit state from a single input to multiple (orthogonal) outputs. We analyse and assess routing performance in various regimes, evaluating their robustness against static and dynamical noise.

Figures (6)

• Figure 1: (a)-- The input nodes ($\ket{1}$ and $\ket{2}$) are green and magenta labelled, the chiral layer ($\{\ket{k_j}\}$), composed of $2$ nodes, is blue labelled, the routing layer ($\ket{l}$ and $\ket{r}$) composed of $n$ vertices is yellow labelled and the $n$ outputs ($\ket{f}$ and $\ket{o}$) are orange labelled. Here for simplicity the structure present 3 outputs, but in general the number of outputs can be arbitrary high, as theoretically presented in Eq.\ref{['eq:out_adjacency']}. (b)-- Reduced Lily Network. Exploiting the symmetry of the structure, it is possible to define a reduced network, in which the vertices associated with the same quantum probability are grouped together. The colour palette reproduce the one presented in Fig.\ref{['fig:Lily Graph']}. The mathematical definition of each node is presented in Eq.\ref{['eq:Symmetry Basis']}.
• Figure 2: Effect of static Phase Noise -- (a) Average quantum fidelity as a function of time, for different values of the concentration parameter $k$ and for $n=2$ outputs. To facilitate the comparison with the dynamical noise, we label the curves with the effective Gaussian variance $\sigma^2=\frac{1}{k}$. The continuous gray curve is the unperturbed unitary case and the vertical grey lines mark its first peaks, located at $t=\pi$ and $t=3\pi$. (b) Scaling of the maximum of the average fidelity as a function of the effective Gaussian standard deviation $\sigma=\sqrt{\frac{1}{k}}$, for different number of outputs.
• Figure 3: Effect of the OU dynamic Phase Noise-- (a) Average quantum fidelity as a function of time, for $n=2$ outputs and for different values of the noise parameters $\theta$ and $\Sigma$. The parameter $\theta$ is kept fixed at the value of $1$ while $\Sigma=0.4$ (green), $\Sigma=0.8$ (blue) and $\Sigma=1$ (red). The curves are labelled with the effective Gaussian variance ($\sigma^2=\frac{\Sigma^2}{2\theta}$). The continuous gray curve is the unperturbed unitary case and the vertical grey lines mark its first peaks, located at $t=\pi$ and $t=3\pi$. (b) Scaling of the maximum of the average fidelity as a function of the standard deviation $\sigma=\sqrt{\frac{\Sigma^2}{2\theta}}$ of the effective Gaussian distribution for different numbers of outputs.
• Figure 4: Effect of static noise on the weights --(a) Fidelity over time averaged with respect to the initial state, for different values of the variance $\sigma^2$. The continuous gray curve is the unperturbed unitary case and the vertical grey lines mark its first peaks, located at $t=\pi$ and $t=3\pi$. (b) Reduction in the peak Fidelity as the standard deviation of the weight Gaussian distribution is raised.
• Figure 5: Effect of dynamical noise on the weights --(a) Average routing fidelity as a function of time, for different values of the noise parameters $\theta$ and $\Sigma$. The parameter $\theta$ is kept fixed at the value of $1$ while $\Sigma=0.1$ (green), $\Sigma=0.2$ (blue) and $\Sigma=0.3$ (red). The curves are labelled with the effective Gaussian variance ($\sigma^2=\frac{\Sigma^2}{2\theta}$). The continuous gray curve is the unperturbed unitary case and the vertical grey lines mark its first peaks, located at $t=\pi$ and $t=3\pi$. (b) Scaling of the maximum of the fidelity as a function of the standard deviation $\sigma=\sqrt{\frac{\Sigma^2}{2\theta}}$ of the effective Gaussian distribution.