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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 paper

Paper 2

Simulation of quantum computation with magic states via Jordan-Wigner transformations

Michael Zurel, Lawrence Z. Cohen, Robert Raussendorf

Year
2023
Journal
arXiv preprint
DOI
arXiv:2307.16034
arXiv
2307.16034

Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the magic state model. It is based on generalized Jordan-Wigner transformations, and it has a close connection to the probability representation of universal quantum computation based on the $Λ$ polytopes. For each number of qubits, it defines a polytope contained in the $Λ$ polytope with some shared vertices. It leads to an efficient classical simulation algorithm for magic state quantum circuits for which the input state is positively represented, and it outperforms previous representations in terms of the states that can be positively represented.

Open paper