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Paper 1
Examples of minimal-memory, non-catastrophic quantum convolutional encoders
Mark M. Wilde, Monireh Houshmand, Saied Hosseini-Khayat
- Year
- 2010
- Journal
- arXiv preprint
- DOI
- arXiv:1011.5535
- arXiv
- 1011.5535
One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present a technique that finds quantum convolutional encoders with such desirable properties for several example quantum convolutional codes (an exposition of our technique in full generality will appear elsewhere). We first show how to encode the well-studied Forney-Grassl-Guha (FGG) code with an encoder that exploits just one memory qubit (the former Grassl-Roetteler encoder requires 15 memory qubits). We then show how our technique can find an online decoder corresponding to this encoder, and we also detail the operation of our technique on a different example of a quantum convolutional code. Finally, the reduction in memory for the FGG encoder makes it feasible to simulate the performance of a quantum turbo code employing it, and we present the results of such simulations.
Open paperPaper 2
Entanglement in XYZ model on a spin-star system: Anisotropy vs. field-induced dynamics
Jithin G. Krishnan, Harikrishnan K. J., Amit Kumar Pal
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2307.15949
- arXiv
- 2307.15949
We consider a star-network of $n=n_0+n_p$ spin-$\frac{1}{2}$ particles, where interaction between $n_0$ central spins and $n_p$ peripheral spins are of the XYZ-type. In the limit $n_0/n_p\ll 1$, we show that for odd $n$, the ground state is doubly degenerate, while for even $n$, the energy gap becomes negligible when $n$ is large, inducing an \emph{effective} double degeneracy. In the same limit, we show that for vanishing $xy$-anisotropy $γ$, bipartite entanglement on the peripheral spins computed using either a partial trace-based, or a measurement-based approach exhibits a logarithmic growth with $n_p$, where the sizes of the partitions are typically $\sim n_p/2$. This feature disappears for $γ\neq 0$, which we refer to as the \emph{anisotropy effect}. Interestingly, when the system is taken out of equilibrium by the introduction of a magnetic field of constant strength on all spins, the time-averaged bipartite entanglement on the periphery at the long-time limit exhibits a logarithmic growth with $n_p$ irrespective of the value of $γ$. We further study the $n_0/n_p\gg 1$ and $n_0/n_p\rightarrow 1$ limits of the model, and show that the behaviour of bipartite peripheral entanglement is qualitatively different from that of the $n_0/n_p\ll 1$ limit.
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