Martin Roetteler

Microsoft Research, Quantum Architectures and Computation Group, Senior Researcher

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Address: Redmond, Washington, United States

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Papers

The role of attentional breadth in perceptual change detection

Psychonomic bulletin & …, 2001

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On Homogeneous Bent Functions

Lecture Notes in Computer Science, 2001

A new surprising connection between invariant theory and the theory of bent functions is establis... more A new surprising connection between invariant theory and the theory of bent functions is established. This enables us to construct Boolean function having a prescribed symmetry given by a group action. Besides the quadratic bent functions the only other known homogeneous bent functions are the six variable degree three functions constructed in [14]. We show that these bent functions arise

Computing Local Invariants of Qubit Systems

Phys Rev a, Dec 18, 1997

As an example, we consider a system of two qubits. We compute the Molien series for the correspon... more As an example, we consider a system of two qubits. We compute the Molien series for the corresponding representation which gives information about the number of linearly independent invariants. Furthermore, we present a set of polynomials which generate all invariants (at least) up to degree 23. Finally, the use of invariants to check whether two density operators are locally equivalent is demonstrated.

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Estimating a quantum state of a quantum mechanical system

Quantum Error Correction

Encyclopedia of Algorithms, 2014

Graphs, Quadratic Forms, and Quantum Codes

Computing Research Repository, 2007

We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. F... more We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Further- more we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms. We provide some simple examples to illus- trate our results.

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Quantum Information Theory - an Invitation

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Universal Simulation of Hamiltonians Using a Finite Set of Control Operations

Quantum information & computation

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Equivalence of Decoupling Schemes and Orthogonal Arrays

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Quantum Information Processing, Second Edition

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Quantum algorithms for highly non-linear Boolean functions

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Combinatorial approaches to dynamical decoupling

Improved bounded-strength decoupling schemes for local Hamiltonians

We address the task of switching off the Hamiltonian of a system by removing all internal and sys... more We address the task of switching off the Hamiltonian of a system by removing all internal and system-environment couplings. We propose dynamical decoupling schemes, that use only bounded-strength controls, for quantum many-body systems with local system Hamiltonians and local environmental couplings. To do so, we introduce the combinatorial concept of balanced-cycle orthogonal arrays (BOAs) and show how to construct them from classical error-correcting codes. The derived decoupling schemes may be useful as a primitive for more complex schemes, e.g., for Hamiltonian simulation. For the case of $n$ qubits and a $2$-local Hamiltonian, the length of the resulting decoupling scheme scales as $O(n \log n)$, improving over the previously best-known schemes that scaled quadratically with $n$. More generally, using balanced-cycle orthogonal arrays constructed from families of BCH codes, we show that bounded-strength decoupling for any $\ell$-local Hamiltonian, where $\ell \geq 2$, can be ach...

Quantum Cryptanalysis (Dagstuhl Seminar 11381)

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A quantum circuit to find discrete logarithms on binary elliptic curves in depth O(log^2 n)

Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an implementatio... more Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an implementation of Shor's algorithm which can solve the discrete logarithm problem on binary elliptic curves in quadratic depth O(n^2). In this paper we show that discrete logarithms on such curves can be found with a quantum circuit of depth O(log^2 n). As technical tools we introduce quantum circuits for GF(2^n) multiplication in depth O(log n) and for GF(2^n) inversion in depth O(log^2 n).

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