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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.
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Spatial inversion symmetry breaking of vortex current in biased-ladder superfluid
Weijie Huang, Yao Yao
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2307.15889
- arXiv
- 2307.15889
We investigate the quench dynamics of interacting bosons on a two-leg ladder in presence of a uniform Abelian gauge field. The model hosts a variety of emergent quantum phases, and we focus on the superfluid biased-ladder phase breaking the $Z_{2}$ symmetry of two legs. We observe an asymmetric spreading of vortex current and particle density, i.e., the current behaves particle-like on the right and wave-like on the left, indicating spontaneous breaking of the spatial inversion symmetry. By decreasing the repulsion strength, it is found the particle-like current is more robust than the wave-like one. The evolution of entanglement entropy manifests logarithmic growth with time suggesting many-body localization matters.
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