This paper studies the effect of quantum computers on Bitcoin mining. The shift in computational paradigm towards quantum computation allows the entire search space of the golden nonce to be queried at once by exploiting quantum superpositions and entanglement. Using Grover’s algorithm, a solution can be extracted in time $O\left(\sqrt{2^{256}/t}\right)$, where t is the target value for the nonce. This is better using a square root over the classical search algorithm that requires $O(2^{256}/t)$ tries. If sufficiently large quantum computers are available for the public, mining activity in the classical sense becomes obsolete, as quantum computers always win. Without considering quantum noise, the size of the quantum computer needs to be $\approx$${10}^4$ qubits.

Matrix–matrix multiplication is of singular importance in linear algebra operations with a multitude of applications in scientific and engineering computing. Data structures for storing matrix elements are designed to minimize overhead information as well as to optimize the operation count. In this study, we utilize the notion of the compact diagonal storage method (CDM), which builds upon the previously developed diagonal storage—an orientation-independent uniform scheme to store the nonzero elements of a range of matrices. This study exploits both these storage schemes and presents efficient GPU-accelerated parallel implementations of matrix multiplication when the input matrices are banded and/or structured sparse. We exploit the data layouts in the diagonal storage schemes to expose a substantial amount of fine-grained parallelism and effectively utilize the GPU shared memory to improve the locality of data access for numerical calculations. Results from an extensive set of numerical experiments with the aforementioned types of matrices demonstrate orders-of-magnitude speedups compared with the sequential performance.

The implementation of a graph generator associated with the estimation of mathematical derivatives is described. The graph colouring instances are obtained as intersection graphs G _Π(A) of the sparsity pattern of A∈ℜ ^m×n with row partition Π. The size of the graph is dependent on the row partition; the number of vertices can be varied between the number of columns (using single block row partition Π=Π₁) and the number of nonzero entries of A (using m-block row partition Π=Π _m ). The chromatic number of the generated graph instances satisfy . A summary of colouring results on the ColSegSet problems is presented. We also show that the main idea of the graph instance generator can be extended to general undirected graphs.