What the Simulator Confirmed

1,000 steps of noise. One topology barely flinched. The other collapsed.

Theory is one thing. Running it through 1,000 circuit depths under realistic noise conditions is another.

This paper is the empirical follow-up to the Unity Pixel Framework whitepaper. The question was simple: does a tile topology actually outperform a linear chain in maintaining quantum coherence, or is that a theoretical artifact that disappears under real noise?

We ran the test. Here's what happened.

The Setup

The experiment used Fujitsu's 40-qubit quantum simulator — a high-performance distributed state-vector platform capable of realistic decoherence modeling — as part of the Fujitsu Quantum Simulator Challenge 2025–26.

Both circuits used 13 qubits. Identical noise. Identical gate counts. Identical timing. The only variable was connectivity:

• Unity Pixel tiling: 36 edges among 13 qubits. Each qubit connects to 5–6 others. Central hub + dense peripheral mesh. Any qubit can entangle directly with several others.
• Linear chain: 12 edges. Each qubit touches only its immediate neighbor. Standard nearest-neighbor topology.

The metric used was a Temporal Coherence Ratio — a measure of how similar the quantum state remains to itself over consecutive time steps. High TCR means the system is holding its quantum correlations. Low TCR means decoherence is winning.

The Results

The Unity Pixel topology outperformed the linear chain at every circuit depth tested. But the more significant finding was the shape of the gap over time.

At shallow depth, the gap is real but modest — about 6 percentage points. At 1,000 gates, the gap has widened to 14 points. The performance advantage of the tile topology isn't constant: it compounds as circuit depth increases.

This is the critical finding. The more complex the computation, the more the architecture matters. Linear chains are fine for short circuits. But if you want to run algorithms deep enough to be interesting — which is the entire point of quantum advantage — the topology has to be designed for it from the start.

Why the Gap Compounds

The mechanism is straightforward. In a linear chain, complex multi-qubit operations require SWAP gates to route information to adjacent qubits. Each SWAP is additional noise. More depth means more SWAP gates, which means noise accumulates faster than the algorithm itself.

In a Unity Pixel tile, most multi-qubit interactions can be executed directly — the qubits are already connected. Far fewer SWAPs. The circuit executes the same logical operations with less incidental noise.

The effect is multiplicative over circuit depth. At 10 gates, the difference is small. At 1,000 gates, it has been multiplying for a long time.

What the Noise Distribution Looked Like

One of the more interesting findings wasn't in the aggregate numbers — it was in the error distribution. In linear chain circuits, errors spread somewhat randomly. In Unity Pixel circuits, errors clustered into geometry-defined patterns.

This is consistent with the theoretical prediction: the tile geometry acts as a coherence filter. Rather than decoherence spreading randomly across all qubits, it gets channeled into the paths the geometry defines. The errors become more predictable — which means they're more correctable.

Random errors are hard to correct. Structured errors, once you understand the structure, are tractable. The geometry isn't just slowing decoherence — it's organizing it.

The Quasicrystal Extension

The paper also tested a quasicrystalline lattice variant — a non-periodic version of the tile that projects from a higher-dimensional crystal. The results showed something unexpected: instead of a single dominant coherence mode, the quasicrystal exhibited multiple stable entangled eigenmodes.

These secondary modes weren't noise. They were stable temporal eigenmodes — coherence organized by the lattice geometry into multiple allowed states. The system wasn't just maintaining one coherent configuration; it was supporting several simultaneously.

This aligns with predictions from Floquet theory and time-reflection physics. It suggests that quasicrystalline lattices may support a richer coherence spectrum than periodic tiles — which has implications for quantum memory and for algorithms that need to maintain multiple entangled states over time.

What It Doesn't Prove

These results are simulations. Fujitsu's platform models noise with a Lindblad master equation — realistic, but not identical to the noise profile of a specific piece of hardware. Real superconducting qubits have correlated noise, fabrication variation, crosstalk between qubits, and dozens of other factors that a uniform noise model doesn't capture.

What this does establish: the topology advantage is consistent across multiple random seeds, circuit depths, and measurement configurations. It's not a statistical artifact. Whether the 6–14 point coherence advantage survives the transition to physical hardware, and what it looks like at 100+ qubits rather than 13, is what the experimental phase needs to determine.

What It Does Suggest

Architecture decisions made early in the design of a quantum processor have compounding consequences. A topology chosen for fabrication simplicity will impose a noise tax on every algorithm you run — a tax that grows with circuit depth.

The Unity Pixel simulation results suggest that tiled, highly-connected subgraphs could substantially extend coherence lifetimes relative to linear layouts. That's not just an incremental improvement to an existing parameter — it's a different approach to where error mitigation should happen in the stack.

Not only in software, after the fact. In the geometry, from the start.