ψ · 易 · the Hadamard gate

Six qubits

The hexagram as a computational basis state

Apply Hadamard to |Kun⟩, watch the uniform superposition of the 64 hexagrams appear, and measure to collapse it.

⚠ Disclaimer

This is a mathematical identity between transforms and states: the computational basis of 6 qubits is the 64 hexagrams, and the site's Walsh transform is the Hadamard gate H⊗6. Nothing quantum is claimed about the oracle; the commercial “quantum I Ching” is in the applicability register as rejected.

A hexagram is a state of the computational basis of 6 qubits: |Kun⟩ = |000000⟩, |Qian⟩ = |111111⟩. The site's Walsh transform is literally the Hadamard gate applied to the 6 lines (H⊗6, already verified as a matrix in the Fourier-over-the-cube experiment). Applying it to |Kun⟩ produces the uniform superposition of the 64 hexagrams, each with amplitude 1/8: the state that contains the whole book. On measuring, it collapses to a uniform hexagram.

state |Kun⟩ = |000000⟩ · a single amplitude

1/8

amplitude of each hexagram

1/64

probability on measuring

H⊗6

H⊗6 = the Walsh transform

unitary

preserves norms (H·Hᵀ = I)

The arithmetic is exact: (1/√2)^6 = 1/8, so the 64 amplitudes of H⊗6|Kun⟩ are 1/8 and the probabilities 0.015625 = 1/64. The transformation is unitary (it preserves the total norm at 1), which is exactly what distinguishes a quantum evolution from any other transform. Everything else about qubits and the I Ching that is not this formal identity is metaphor, and none is claimed here.