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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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The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap.
Lihm JM, Kiese D, Lee SB, Kugler FB
- Year
- 2026
- Journal
- Proceedings of the National Academy of Sciences of the United States of America
- DOI
- 10.1073/pnas.2525308123
- arXiv
- -
We present the finite-difference parquet method that greatly improves the applicability and accuracy of two-particle correlation approaches to interacting electron systems. This method incorporates the nonperturbative local physics from a reference solution and builds all parquet diagrams while circumventing potentially divergent irreducible vertices. Its unbiased treatment of different fluctuations is crucial for reproducing the strong-coupling pseudogap in the underdoped Hubbard model, consistent with diagrammatic Monte Carlo calculations. We reveal a strong-coupling spin-fluctuation mechanism of the pseudogap with decisive vertex corrections that encode the enhanced, energy-dependent scattering amplitude between electrons and antiferromagnetic spin fluctuations.
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