Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Communication lower bounds for distributed-memory matrix multiplication
Journal of Parallel and Distributed Computing
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
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Quantum control plays a key role in quantum technology, in particular for steering quantum systems. As problem size grows exponentially with the system size, it is necessary to deal with fast numerical algorithms and implementations. We improved an existing code for quantum control concerning two linear algebra tasks: the computation of the matrix exponential and efficient parallelisation of prefix matrix multiplication. For the matrix exponential we compare three methods: the eigendecomposition method, the Pade method and a polynomial expansion based on Chebyshev polynomials. We show that the Chebyshev method outperforms the other methods both in terms of computation time and accuracy. For the prefix problem we compare the tree-based parallel prefix scheme, which is based on a recursive approach, with a sequential multiplication scheme where only the individual matrix multiplications are parallelised. We show that this fine-grain approach outperforms the parallel prefix scheme by a factor of 2-3, depending on parallel hardware and problem size, and also leads to lesser memory requirements. Overall, the improved linear algebra implementations not only led to a considerable runtime reduction, but also allowed us to tackle problems of larger size on the same parallel compute cluster.