How nonlocal are the entanglements in Conway's game of cellular automata, if they're entanglements with symmetry; conservation but emergence? TIL about the effect of two Hadamard gates upon a zero.
> In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.
> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.
> The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on 2^{n} amplitudes can be implemented as a quantum circuit consisting of only O(n^2) Hadamard gates and controlled phase shift gates, where n is the number of qubits.[2] This can be compared with the classical discrete Fourier transform, which takes O(n*(2^n)) gates (where n is the number of bits), which is exponentially more than O(n^2).
Quantum discord: https://en.wikipedia.org/wiki/Quantum_discord :
> In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.
From "Convolution Is Fancy Multiplication" https://news.ycombinator.com/item?id=25194658 :
> FWIW, (bounded) Conway's Game of Life can be efficiently implemented as a convolution of the board state: https://gist.github.com/mikelane/89c580b7764f04cf73b32bf4e94...
Conway's Game is a 2D convolution; without complex phase or constructive superposition.
Convolution theorem: https://en.wikipedia.org/wiki/Convolution_theorem :
> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.
From Quantum Fourier transform: https://en.wikipedia.org/wiki/Quantum_Fourier_transform :
> The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices. The discrete Fourier transform on 2^{n} amplitudes can be implemented as a quantum circuit consisting of only O(n^2) Hadamard gates and controlled phase shift gates, where n is the number of qubits.[2] This can be compared with the classical discrete Fourier transform, which takes O(n*(2^n)) gates (where n is the number of bits), which is exponentially more than O(n^2).