They map the Pauli group to itself under conjugation. For example,HXH†=Z. Here,H†is the Hermitian conjugate (or the adjoint) of the Hadamard gateH, andHacts as the Clifford gate.XandZare Pauli X gate and Pauli Z gate, respectively. They can be efficiently simulated using classical ...
(as found for instance in this recent paper of Arnold, David, Jerison, and my two coauthors) is the following observation: if is an eigenvector for with energy , then is an eigenvector for with the same energy , thus the original Schrödinger operator is conjugate to a (variable ...
Let be a large natural number, and let be a matrix drawn from the Gaussian Unitary Ensemble (GUE), by which we mean that is a Hermitian matrix whose upper triangular entries are iid complex gaussians with mean zero and variance one, and whose diagonal entries are iid real gaussians with ...
where denotes the conjugate transpose. For example, we can generalize the formula for a complex number to an matrix by splitting into its Hermitian and skew-Hermitian parts: where and . Then If a matrix is not explicitly known but we can compute matrix–vector products with it then the trace...
The following information is a summary of the updates that are made to the ESSL Version 6.1 documentation:ESSL Version 6.1 supports the following IBM Power Systems: IBM POWER9 servers Notes: The ESSL SMP CUDA Library is supported only on the IBM Power Systems AC922 (8335-GTC and 8335-...
Maple provides a state-of-the-art environment for algebraic computations in Physics, with emphasis on ensuring that the computational experience is as natural as possible. The theme of the Physics project for Maple 2019 has been the consolidation of the functionality introduced in previous releases,...
(AQC) can readily solve a quantum linear system problem (QLSP) with O(κ poly(log(κ/ϵ ))) runtime, where κ is the condition number, and ϵ is the target accuracy.” According to the authors, their “method is applicable to general non-Hermitian matrices, and the cost, as ...
=== PARDISO: solving a Hermitian indefinite system === Single-level factorization algorithm is turned ON Summary: ( factorization phase ) === Times: === Time spent in copying matrix to internal data structure (A to LU): 0.000000 s Time spent in factorization step (numfct) : 9888.516431 ...
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this_task_arena::isolate() function is now a fully supported feature. Also, this_task_arena::isolate() function and task_arena::execute() methods were extended to pass on the value returned by the executed functor (this feature requires C++11). The task_arena::enqueue() and task_group:...