Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the g...

In our companion paper [1], an information identity decomposition has been derived, which can be interpreted as a law of conservation of information flows in feedback systems. In this paper, we further investigate this decomposition result when specified to linear time-invariant(LTI) systems connected with additive white Gaussian noise(AWGN) channels. It is shown that the quantities in the deco...

Mesh generation is one of the key issues in Computational Fluid Dynamics. This paper presents an adaptive three-dimensional mesh refinement method based on the law of mass conservation. The method can be used to a governing system that includes the law of mass conservation (continuity equation) for incompressible or compressible steady flows. We show one example that demonstrates the refined me...

We propose a multisymplectic scheme to solve the coupled Klein–Gordon–Schrödinger system. The scheme preserves the multisymplectic geometry structure exactly by satisfying the discrete multisymplectic conservation law, and can simulate the original waves well in a long time. This scheme also has discrete quasi-norm conservation law. Numerical experiments demonstrate the consistency between the ...

We investigate the consequence of the energy-momentum conservation law for the holographic S-matrix from AdS/CFT correspondence. It is shown that the conservation law is not a natural consequence of conformal invariance in the large N limit. We predict a new singularity for the four point correlation function of a marginal operator. Only the two point scattering amplitude is explicitly calculat...

Using the Spencer-Goldschmidt version of the Cartan-Kähler theorem, we prove the local existence of conservation laws for analytical quasi-linear systems of two independent variables in the nilpotent and 2-cyclic case. Introduction A conservation law for a (1-1) tensor field h on a manifold M , dimM = n, is a 1-form θ which satisfies dθ = 0 and dh∗θ = 0, where h∗ is the transpose of h : h∗θ := ...