Tuna-9 hardware · Feb 2026 · 4096 shots
A quantum walk shows interference that defies classical intuition. QAOA MaxCut reveals the limits of noisy hardware. And a 9-qubit GHZ state proves genuine entanglement across the entire chip.
A photon rippling through nine coupled resonators
Each qubit on Tuna-9 is a tiny superconducting resonator vibrating at about 5 GHz. They're connected by tunable couplers — physical links that let energy flow between neighbors. We trap a single microwave photon in qubit 0, then watch what happens as we repeatedly pulse the chip.
Waves cancel at the neighbors, reinforce further out
We pulse and couple again. Now something happens that has no classical analog. The photon's quantum amplitude is traveling along all paths simultaneously. To reach q4 (two hops away), the wave can go q0→q1→q4 or q0→q2→q4 — two paths that arrive in phase and reinforce each other.
But at q1 and q2 (the nearest neighbors), the outgoing wave and the reflected wave from the second pulse arrive with opposite phases. They partially cancel out. This is exactly like noise-canceling headphones: two signals, perfectly out of sync, producing silence.
The result: nearest neighbors (6.4%) are less excited than qubits two hops away (20%). If this were a classical random walk — like a ball bouncing randomly between connected rooms — the neighbors would always be most excited. The inversion is purely quantum.
Node brightness = probability of finding the photon there
The dip at d=1 is destructive interference. A classical walk would show monotonic decay.
Classical random walk
Energy decays monotonically with distance. Always.
Quantum walk (this experiment)
d=1 dips below d=2. Destructive interference at the nearest neighbors.
When noise wins
Hardware
0.502
approx ratio
Emulator
0.691
approx ratio
Random
0.500
baseline
CZ gates
24
circuit depth
The idea: Run QAOA MaxCut on Tuna-9's own connectivity graph. The chip tries to solve a problem about its own topology. The graph is bipartite, so the maximum cut is 12 (every edge). On the noiseless emulator, p=1 QAOA finds the optimal partition 11.1% of the time. On hardware: 0.3%.
Hardware result: indistinguishable from random
With 24 two-qubit gates across 12 edges, the circuit is too deep for Tuna-9's current error rates. Each CZ gate introduces ~3-5% error, compounding exponentially. The emulator shows the algorithm works perfectly — this is a noise problem, not an algorithm problem.
Next steps: error mitigation (ZNE, readout correction), fewer layers (p=1 with restricted edges), or simply waiting for better hardware fidelity. Multiple runs with different qubit subsets could also help identify which edges contribute most noise.
Genuine entanglement across the whole chip
Fidelity lower bound
56.7%
F > 50% = genuine entanglement
Entanglement certified
The GHZ state (|000000000〉 + |111111111〉)/√2 requires all 9 qubits to be coherently entangled. A fidelity above 50% proves the state cannot be produced by any separable (unentangled) process. At 56.7%, Tuna-9 clears this threshold — 8 CNOT gates along a spanning tree is within the chip's noise budget.
The quantum walk (2-3 CZ layers) shows clear quantum signatures. The GHZ (8 CNOTs) proves full-chip entanglement.
QAOA with 24 CZ gates produces random output. There's a sharp threshold between "quantum" and "noise" on this hardware.
The walk's non-classical spreading pattern — nearest neighbors less excited than distant qubits — is clearly visible on real hardware.