19 citations · 24 across the 5 of their papers we have counts for
7 papers
Stabilizer operators and Barnes-Wall lattices
Vadym Kliuchnikov, Sebastian Schönnenbeck
We give a simple description of rectangular matrices that can be implemented by a post-selected stabilizer circuit. Given a matrix with entries in dyadic cyclotomic number fields $…
Multi-qubit circuit synthesis and Hermitian lattices
Vadym Kliuchnikov, Sebastian Schönnenbeck
We present new optimal and heuristic algorithms for exact synthesis of multi-qubit unitaries and isometries. For example, our algorithms find Clifford and T circuits for unitaries…
Automorphic Forms on Feit's Hermitian Lattices
Neil Dummigan, Sebastian Schönnenbeck
We consider the genus of classes of unimodular Hermitian lattices of rank over the Eisenstein integers. This set is the domain for a certain space of algebraic modular fo…
Computing -unit groups of orders
Sebastian Schönnenbeck
Based on the general strategy described by Borel and Serre and the Voronoi algorithm for computing unit groups of orders we present an algorithm for finding presentations of -un…
Simultaneous computation of Hecke operators
Sebastian Schönnenbeck
We present a method to compute two Hecke operators acting on a space of algebraic modular forms simultaneously based on an idea of Eichler's. We show that in certain cases this met…
Resolutions for unit groups of orders
Sebastian Schönnenbeck
We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible -c…
Computing in arithmetic groups with Voronoi's algorithm
Oliver Braun, Renaud Coulangeon, Gabriele Nebe +1
We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi)simple algebra over Q. Our method is based on a generalis…