Hadamard

This construction is advantageous because it takes the same time as an elementary Hadamard gate and the transversal, or block-wise, character of the logical gate ensures that errors do not spread between qubits of the code.

This code has an X and a Z stabilizer check for each vertex, leading to a transversal Hadamard H gate, and gauge checks associated with edges.

The CNOT, Hadamard and S gates generate the group of Clifford gates.

Parts of it appear in The Mathematician’s Mind, written by Jacques Hadamard in 1945, in Creativity: Selected Readings, edited by Philip Vernon in 1976, in Roger Penrose’s award-winning 1989 book, The Emperor’s New Mind, and it is alluded to in Jonah Lehrer’s 2012 bestseller Imagine.

In “The Psychology of Invention in the Mathematical Field,” published in 1945, Jacques Hadamard quotes a mathematician who says, “It often seems to me, especially when I am alone, that I find myself in another world. Ideas of numbers seem to live. Suddenly, questions of any kind rise before my eyes with their answers.”