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A classical computer does not allow to calculate a discrete cosine transform on AE points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and… (More)

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

Two orthonormal bases B and B ′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |b|b ′ | 2 = 1/d holds for all b ∈ B and b ′ ∈ B ′. The size of any set containing pairwise mutually unbiased bases of C d cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d + 1 mutually unbiased bases are… (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)

- R F Werner, G Alber, +9 authors R Horodecki
- 2000

This text is part of a volume entitled " Quantum information — an introduction to basic theoretical concepts and experiments " , to be published in Springer Tracts in Modern Physics. Authors will be From the foundations of quantum theory to quantum technology-an introduction Mixed-state entanglement and quantum communication Joint index Joint list of… (More)

Clifford codes are a class of quantum error control codes that form a natural generalization of stabilizer codes. These codes were introduced in 1996 by Knill, but only a single Clifford code was known, which is not already a stabilizer code. We derive a necessary and sufficient condition that allows to decide when a Clifford code is a stabilizer code, and… (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)

- BY PRADEEP, KIRAN SARVEPALLI, ANDREAS KLAPPENECKER, MARTIN RÖTTELER, P. K. 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 bit-and 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… (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)

- Salah A. Aly, Markus Grassl, Andreas Klappenecker, Martin Rötteler, Pradeep Kiran Sarvepalli
- 2007 10th Canadian Workshop on Information Theory…
- 2007

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to construct classical convolutional codes from block codes, in particular BCH codes. These codes have the property that… (More)

- Andreas Klappenecker, Martin Rötteler
- IEEE Transactions on Information Theory
- 2005

Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill that yields nice error bases, and a combinatorial construction by Werner that yields shift-and-multiply bases. An open problem posed by Schlingemann and Werner relates these two… (More)