Here we extend the exploration of significantly super-Chandrasekhar magnetised white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetised polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetised axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3 + 1 formalism of numerical relativity, implemented in the open source XNS code. We construct equilibrium sequences by varying different physical quantities in turn, and highlight the plausible existence of super-Chandrasekhar white dwarfs, with masses in the range of 2 − 3 solar mass, with central (deep interior) magnetic fields of the order of 10 14 G and differential rotation with surface time periods of about 1 − 10 seconds. We note that such white dwarfs are candidates for the progenitors of peculiar, overluminous type Ia supernovae, to which observational evidence ascribes mass in the range 2.1 − 2.8 solar mass. We also present some interesting results related to the structure of such white dwarfs, especially the existence of polar hollows in special cases.

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We consider methods for implementing smooth functions f (A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has advantages of simplicity and resource consumption in some cases. Our construction uses the linear combination of unitaries method with Chebyshev polynomial approximations. The query complexity we obtain is log C   ( ) where ò is the approximation precision, and C>0 is an upper bound on the magnitudes of the derivatives of the function f over the domain of interest. The success probability depends on the 1-norm of the Taylor series coefficients of f, the sparsity d of the matrix, and inversely on the smallest singular value of the target matrix f (A).

Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor γ > 1 of the Shannon entropy of probability distributions and the von Neumann entropy of mixed quantum states. Our main results are: