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- Markus Grassl, Thomas Beth, Martin Rötteler, EQIS, No-Cloning Bound
- 2008

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-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters [[n,n − 2d + 2, d]]q exist for all 3 ≤ n ≤ q and 1 ≤ d ≤ n/2+1. We… (More)

- Matthew Amy, Dmitri Maslov, Michele Mosca, Martin Rötteler
- IEEE Transactions on Computer-Aided Design of…
- 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 force algorithms. As an illustration of our method, we implemented this algorithm and found factorizations of commonly used quantum logical operations into elementary gates in… (More)

- Andreas Klappenecker, Martin Rötteler
- International Conference on Finite Fields and…
- 2003

Two orthonormal bases B andB′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |〈b|b〉| = 1/d holds for all b ∈ B and b′ ∈ B′. The size of any set containing pairwise mutually unbiased bases of C cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to… (More)

- Markus Grassl, Martin Rötteler
- 2006 IEEE International Symposium on Information…
- 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 index which has a non-catastrophic encoding circuit. Our work generalizes the conditions for non-catastrophic encoders derived in a paper by Oliver and Tillich… (More)

- Markus Grassl, Martin Rötteler
- Encyclopedia of Complexity and Systems Science
- 2008

e?cient fault-tolerant quantum computing arxiv fault-tolerant quantum computing crcnetbase an introduction to quantum error correction and fault quantum error correction and fault tolerant quantum computing fault tolerance in quantum computation eceu fault-tolerant quantum computation world scientific fault -tolerant quantum computation versus realistic… (More)

We present a family of non-abelian groups for which the hidden subgroup problem can be solved efficiently on a quantum computer. supported by DFG grant GRK 209/3-98

- BY PRADEEP KIRAN, Andreas Klappenecker, Martin Rötteler, Pradeep Kiran Sarvepalli
- 2009

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-flip errors. An example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit and phase… (More)

- Sean Hallgren, Cristopher Moore, Martin Rötteler, Alexander Russell, Pranab Sen
- J. ACM
- 2006

It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the resulting algorithms is the use of quantum coset states, which encode the hidden subgroup. An open question has been how hard… (More)

- Markus Grassl, Martin Rötteler, 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 dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit has O(n(n− k)) gates. The running time of the classical… (More)

- Andreas Klappenecker, Martin Rötteler
- 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 of small degree, and all nice error bases with abelian index groups. We show that in general an index group of a nice error basis is necessarily solvable.