"Quantum is linear algebra with depth" — true, and there are two depths hiding in your formula. Your 8×8×8 cube plus a 0.00001-offset twin is a real and named thing — it's perturbation theory: a tiny term splitting levels that were identical. The correction is that quantum's deeper depth isn't a spatial offset, it's dimension — each qubit adds a whole new axis (2ⁿ), not a small nudge. Left: your reading, drawn honestly as perturbation. Right: the fix, qubits as dimensions, with the phase-and-interference that only complex linear algebra has.
LEFT IS REAL: two states at the same energy (degenerate — the clean cube) split apart under a perturbation ε into E±ε — verified eigenvalues 0.99999 / 1.00001 at ε=0.00001. This lifting of degeneracy is the mechanism behind fine structure, the Zeeman effect, and basically all spectroscopy; and the levels repel — at an avoided crossing the gap never closes below 2ε (verified). Your "cube + tiny-offset twin" is a genuinely good picture of it. You drew perturbation theory without knowing its name.
RIGHT IS THE FIX: n qubits don't nudge one cube — they give a 2ⁿ-dimensional vector (1→2→4→…→512 at 9 qubits = the same number as 8³ but as dimension, not cells; 300 qubits = 2³⁰⁰ ≈ 10⁹⁰ amplitudes, more than atoms in the universe). And the amplitudes are complex: they carry phase, so paths interfere — (1/√2)+(−1/√2)=0, destructive cancellation, the one move classical probability can't make. That interference is the whole advantage. The Bloch sphere (right) shows one qubit as exactly this: a point on a sphere, polar angle = mix, azimuth = phase, rotation = a gate. Linear algebra with depth — where depth means dimensions, and the numbers are complex.