RICT Encode–Decode Production Test

Take a random graph A, encode it into phases and entanglement, run the circuit on IBM Heron r2 (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 metric is recoverability of the relational structure: the specific graph that went in can be read back out, and told apart from a graph that stayed out. A maximally random output has maximum entropy. Decode F1 against a chance baseline, plus the decoy control, is how this page scores that recovery.

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, beyond chance correlation. 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 (sensor networks, fault propagation, financial or biological networks) when that structure was encoded 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: the true graph and its edge count stay out of the cut, 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 sit in the NDA reproduction package.

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. The hardware result sits on a method that already reconstructs exactly in simulation.

The reconstruction threshold is derived from the measured correlations alone. That data-only split scores within a point of a hindsight-tuned split, so the published F1 is the measurement’s own cut.

In noiseless simulation this method reconstructs a 20-node graph exactly. On IBM Heron r2 the three sizes line up with the routing multiplier: accuracy falls as that multiplier rises, and nothing else in the setup changes.

Pairs that sit on native lattice edges compile cheaply. Pairs that must be transported pick up extra two-qubit operations. The multiplier, rather than the raw coupling count, governs the published F1: at 12 nodes the encoding uses 33 operations for 12 couplings, and the graph comes back perfectly.

A calibrated stochastic model (depolarising plus readout error) tracks the hardware 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%. That mismatch identifies 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. Configurations that look better in simulation because they use a subtler signal lose first under coherent error. Two such candidates were promoted by simulation; both lost on hardware.

The measured requirement is native-adjacent couplings. On this same device, at 12 nodes, with a 2.8× multiplier, the method returns the exact graph. Direct connectivity at 20 nodes would remove the 4.9× routing tax. The decoder, shot budget, and qubit count already deliver exact reconstruction when that tax is small.

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: 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. QPC relational encoding is decodable on current hardware.

High output diversity (many unique outcomes, high entropy) describes the shot histogram. Recoverable content is scored by decode F1 against a chance baseline, with a decoy control. Uniqueness counts sit beside that decode, as a description of the output.

The RICT encode–decode test runs on the same stack as the rest of the suite, uses the same relational encoding, and reads the structure back: exactly at 12 nodes, where couplings need little routing, and well above chance at 16 and 20 nodes, identified as the graph that was put in.