RICT Encode–Decode Production Test

Take a random graph A, encode it into phases and entanglement, run the circuit on IBM Fez, collect shots, then reconstruct an estimated graph A′ from the measured correlations. Compare A′ to A on edge precision, recall and F1 — always against an explicit chance baseline.

The question is whether the relational structure is recoverable, not whether the output looks complicated. Complexity on its own proves nothing: a maximally random output has maximum entropy and carries no information at all. What matters is whether the specific graph that went in can be read back out, and whether it can be told apart from a graph that did not go in.

Three safeguards, all applied here. Every number is quoted against the score random guessing would achieve at the same number of predicted edges. The reconstruction threshold is derived from the measured data alone and never consults the true graph, so nothing is tuned on the answer. And a decoy control runs the identical circuit on a different graph B and scores it against A: a genuine decoder must recover B and fall to chance on A. That is what happens, which rules out the result being an artifact of gate placement or of the hardware's noise.

In holography, a 3D scene is encoded into an interference pattern (a “flat” recording). When you shine light through it, you recover the full 3D structure. Here we do something similar: the graph (the “scene” of relationships) is encoded into the quantum state; the measurement gives us a kind of interference pattern. Decoding is recovering the relationship structure from that pattern. So the test shows that QPC can, in principle, support tasks where you store rich structural information in a distributed way and reconstruct it later—useful for imaging, compressed sensing, or any setting where the full structure is encoded in a mixed or lower-dimensional signal.

Many real problems are about relationships rather than single items: who influences whom, which suppliers feed which factories, which nodes in a network depend on each other. You often don’t see the links directly—you see aggregate or noisy data. Encoding/decoding here means: we put a network of links into the quantum process, run it, and then try to recover that network from the outcomes. The test proves that recovery is possible on real hardware, exactly at small scale and well above chance at larger scale. So it’s relevant for supply chains, social or contact networks, infrastructure dependencies, or any domain where “who is connected to whom” must be inferred from indirect or noisy measurements.

Sometimes you have many signals (sensors, agents, variables) and you want to know which ones are really linked—not just correlated by chance. The quantum run encodes relationship structure; the measurement outcomes give us correlations. Decoding is turning those correlations back into an estimated structure (who is linked to whom). So the test is a proof of concept for tasks where you have to infer structure from correlation data—e.g. sensor networks, fault propagation, financial or biological networks—when that structure was “hidden” inside a quantum or high-dimensional process.

Bottom line: Encoding = putting a relationship graph into the computation. Decoding = reading that graph back from the results. The test shows this works on real quantum hardware. The same idea applies to any real-world task where you need to store or recover who is connected to whom from limited or noisy data.

• 1. Generate a random graph A at density 0.25, and an independent decoy graph B for the control.
• 2. Compile each graph into a proprietary RICT-style QPC circuit (encoding details under NDA), reading out in a basis in which the encoded structure is measurable.
• 3. Transpile for ibm_fez with fractional gates, so each coupling compiles to one native two-qubit rotation. Run 3 times and merge counts. Dynamical decoupling (XY4) and measurement twirling are applied on submission.
• 4. Compute the connected correlator ⟨Z_iZ_j⟩ − ⟨Z_i⟩⟨Z_j⟩. Subtracting the single-qubit terms is essential: an uncentered joint probability is dominated by per-qubit bias rather than by pairwise structure.
• 5. Reconstruct A′ by splitting the measured correlations into a strong and a weak class and keeping the strong one, cutting where the two separate best. This reads only the measurement — not the true graph, and not even its edge count — so the number of predicted edges follows the data.
• 6. Compare every number to chance: because the threshold fixes how many edges are predicted, the null model is “pick that many pairs at random”, whose true-positive count is hypergeometric.
• 7. Score the decoy arm against both A and B. Recovery of B with chance-level performance on A is the evidence that the decoder reads the encoded graph specifically.

Results below are raw counts. Readout mitigation was computed alongside and left the reconstruction unchanged, since it rescales correlations without reordering them. Operator scripts and CLI flags are not published — request the reproduction package under NDA.

The same circuit was run encoding an independent decoy graph B, then scored against the target A. It carries the same gate count, the same routing burden and the same noise environment. Any effect that leaked structure through gate placement rather than through the encoding would track B, not A.

At every size the decoder recovers whichever graph was actually encoded and drops to chance against a graph that was not. The recovered structure is therefore the encoded structure.

Validated offline before any hardware time was spent. Across independently generated graphs in noiseless simulation the method reconstructs the graph exactly, and it continues to do so down to a quarter of the shot budget — so the result is not a fortunate single instance and is not balanced on the edge of its sampling statistics.

The threshold is doing no hidden work: deriving it from the measured correlations alone scores within a point of the best threshold obtainable with hindsight. A result that depends on hindsight tuning is not a result.

In noiseless simulation this method reconstructs a 20-node graph exactly, so the 14-point shortfall on hardware is not a modelling limit. The cause is visible in the table above, and the three sizes line up with it in order: accuracy falls as the routing multiplier rises, and nothing else in the setup changes.

Most pairs that need to interact are not physically adjacent on a fixed qubit lattice, so they must be transported into place, and every transport step is another opportunity for error. It is the multiplier rather than the number of couplings that governs the result: at 12 nodes, where the encoding needs only 33 operations for 12 couplings, the graph comes back perfectly.

Ordinary random noise does not account for the gap, and there is a sharp way to see it. A calibrated stochastic model — depolarising plus readout error — tracks the hardware closely for the configuration we run, predicting 88.7% against 85.71% measured. Weaken the encoded signal and the same model predicts 99.0%, while the hardware delivers 84.48%. A model that is accurate to three points in one regime and wrong by fifteen in the other is not merely imprecise; it is missing a channel that specifically punishes a weak signal.

That channel is coherent error: small systematic rotations which add structured correlation rather than washing correlation out. Its footprint on this device was measured independently and is strong enough to matter. The practical consequence is counter-intuitive and worth stating plainly — configurations that look better in simulation because they use a subtler signal are worse in reality, since a subtle signal is precisely what coherent error overwhelms first. Two such candidates were promoted by simulation and both lost on hardware.

It converts a vague “more qubits would help” into a specific requirement. Nothing here needs more qubits, more shots, or a better decoder. It needs couplings that do not have to be routed. Hardware in which the interacting elements are directly connected would remove the 5× multiplier at 20 nodes, and the method already demonstrates — on this same device, at 12 nodes — what it returns when that multiplier is small: the exact graph.

PQST-64 shows high-entropy polycontextural sampling output (64Q, high uniqueness). QPC Crash Detection shows cascade detection on 128Q Torino. PRCBS (RICT, CPRP, PCRT) shows maximum diversity and entropy at 128Q–156Q on Torino and Fez. All three run on real hardware.

This test answers the question the others do not: can we get the structure back? It reconstructs a 12-node graph exactly, a 16-node graph at 88.52% and a 20-node graph at 85.71% against chance baselines of 18–28%, with a decoy control at every size confirming that the graph recovered is the graph encoded. That makes it the load-bearing evidence that QPC relational encoding is not merely complex but decodable on current hardware.

High output diversity — many unique outcomes, high entropy — is not evidence that structure was preserved. A uniform random distribution maximises both while carrying no information at all. Only a decode against a chance baseline, with a control that rules out artifacts, can establish that structure survived. Uniqueness counts should be read as a description of the output, never as a measure of recoverable content.

The RICT encode–decode test runs on the same stack as the rest of the suite, uses the same relational encoding, and now supports one specific claim we are prepared to defend: relational structure put into a QPC circuit on current IBM hardware can be read back out — exactly, at a scale where couplings need little routing, and well above chance at larger scale — and identified as the structure that was put in.