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- Matthew Amy, Dmitri Maslov, Michele Mosca, Martin Roetteler
- IEEE Transactions on Computer-Aided Design ofâ€¦
- 2013

We present an algorithm for computing depth-optimal decompositions of logical operations, leveraging a meet-in-the-middle technique to provide a significant speedup over simple brute forceâ€¦ (More)

- Andreas Klappenecker, Martin Roetteler
- International Conference on Finite Fields andâ€¦
- 2003

Two orthonormal bases B and Bâ€² of a d-dimensional complex inner-product space are called mutually unbiased if and only if |ã€ˆb|bâ€²ã€‰|2 = 1/d holds for all b âˆˆ B and bâ€² âˆˆ Bâ€². The size of any setâ€¦ (More)

Recently, quantum error-correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bitand phase-flipâ€¦ (More)

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensionalâ€¦ (More)

- Markus Grassl, Martin Roetteler, Thomas Beth
- Int. J. Found. Comput. Sci.
- 2003

We present two methods for the construction of quantum circuits for quantum errorcorrecting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimensionâ€¦ (More)

- Markus Grassl, Brandon Langenberg, Martin Roetteler, Rainer Steinwandt
- PQCrypto
- 2016

We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard (AES) and analyze the quantum resources required to carry out such an attack. We consider theâ€¦ (More)

- Markus Grassl, Martin Roetteler
- 2006 IEEE International Symposium on Informationâ€¦
- 2006

We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite indexâ€¦ (More)

- Andreas Klappenecker, Martin Roetteler
- IEEE Trans. Information Theory
- 2002

Nice error bases have been introduced by Knill as a generalization of the Pauli basis. These bases are shown to be projective representations of finite groups. We classify all nice error bases ofâ€¦ (More)

- Micha L Horodecki, Pawe, +10 authors Anton Zeilinger
- 2008

We present basics of mixed-state entanglement theory. The first part of the article is devoted to mathematical characterizations of entangled states. In second part we discuss the question of usingâ€¦ (More)

As the end of the semiconductor roadmap for CMOS approaches, architectures based on nanoscale molecular devices are attracting attention. Among several alternatives, silicon nanowires and carbonâ€¦ (More)