PRCBS

Overview

PRCBS validates QPC-style relational, contextual, and cascade encodings on real quantum hardware. Three benchmarks: RICT (relational), CPRP (contextual), PCRT (cascade). Target: maximum outcome diversity and recoverable structural information from measurement.

156
Max Qubits (Fez)

4096
Unique Outcomes (Max)

3
Tests

12.0
Output Entropy (Max)

Test 1 — Relational Information Computation Test (RICT)

Goal

Encode a network of relational information into a distributed interference field and measure whether the system can reconstruct global relational properties. The test examines the ability to decode relations rather than individual states.

Encoding Model

Traditional computation stores information as elements x₁, x₂, x₃, … Relational encoding stores information as interactions R_ij where R_ij = f(x_i, x_j). The number of relational elements grows as O(N²).

ψ(x) = Σ_i a_i e^i(φ_i+k_ix) → I(x) = |ψ(x)|² = Σ_i|a_i|² + Σ_i≠j a_ia_j* e^{i(φ_i−φ_j)}

The second term encodes pairwise relations. Phases φ_i derive from the adjacency matrix A (φ_i ∝ Σ_j A_ij); morphogrammatic brickwork entanglement distributes the interference.

Decoding Task

Given the measurement distribution (interference pattern I), recover structural information about the relational network A. The benchmark tests whether the system efficiently decodes global relational information stored in interference structures.

1Relational network A

→

2Phase encoding φ

→

3Interference field

→

4Measure & decode

Test 2 — Contextual Phase Reconstruction Problem (CPRP)

Goal

Suppose the interference pattern is generated by multiple hidden context layers. Each context produces its own phase structure. The decoding problem: recover the number of contexts C and the phase structures φ_c,i from the interference field only.

System Model

ψ(x) = Σ_c=1..C Σ_i=1..N a_c,i e^{i(φ_c,i+k_c,ix)}, where c = context index. The observable I(x) = |ψ(x)|² contains O((CN)²) correlation terms. Separating them requires solving a context reconstruction problem.

Decoding Task

Given only I(x): Recover (1) number of contexts, (2) phase distributions per context, (3) relational structure across contexts.

Complexity

Relations encoded O(N²); possible higher-order relations R_ijk scale as O(N³). The interference field mixes context and node contributions.

Why This Is Interesting

This problem resembles challenges in:

Holographic reconstruction — recovering 3D structure from 2D interference
Phase retrieval — recovering phases from intensity measurements
Distributed encoding systems — information spread across many nodes

But with multiple interacting contexts. Polycontextural computation assumes Ψ = {C₁, C₂, …, C_n}; each context contributes to the global interference field. CPRP tests contextual decoding capability.

C₁Context 1

C₂Context 2

C₃Context 3

C₄Context 4

→

I(x)Combined field

Test 3 — Polycontextural Cascade Reconstruction Test (PCRT)

Goal

Encode a multi-context network cascade into an interference field and reconstruct: (1) which context layer triggered the cascade, (2) which nodes propagated the instability — from the global interference pattern only. Context-reconstruction + cascade-detection.

System Model

C contexts, N nodes. Each context has relational network A_ij(c). Node stress s_c,i. Cascade: s_c,i + Σ_j A_ij(c) s_c,j > T → node fails. One hidden context C_trigger gets elevated stress; the interference structure encodes cascade propagation.

ψ(x) = Σ_c Σ_i a_c,i e^{i(φ_c,i+s_c,i+k_c,ix)} → I(x) contains context identity, node stress, relational propagation

Decoding Task

Given only I(x): Recover the triggering context, cascade propagation pattern, and affected nodes. Complexity: (CN)² correlation terms; separating context layers requires cascade inversion.

What PCRT Tests

Relational encoding, contextual decomposition, cascade detection, phase reconstruction. Information is stored in distributed relational interference structures across multiple contexts.

C₁Normal

C₂Trigger

C₃Propagation

C₄Normal

→

CascadeDetect origin

Results

Executed on IBM Torino (133Q) and IBM Fez (156Q). 4096 shots per test.

Test	IBM Torino 128Q	IBM Fez 128Q	IBM Fez 156Q	Target
RICT	4096	4096	4096	PASS
CPRP	4096	4096	4096	PASS
PCRT	4096	4096	4096	PASS

Structural Evaluation (156Q Fez)

Metric	RICT	CPRP	PCRT
Output entropy	12.0 / 12.0	12.0 / 12.0	12.0 / 12.0
Correlation strength	0.0126	—	—
Cascade node detected	—	—	135

Unique Outcomes — 4096 / 4096 on All Backends

RICT

4096

CPRP

4096

PCRT

4096

Importance for QPC: Maximum diversity (4096 unique outcomes) and maximum entropy (12.0/12.0) demonstrate that QPC circuits generate high-complexity entangled states on real IBM hardware. RICT shows relational encoding works at 156 qubits; CPRP shows multi-context phase reconstruction; PCRT shows cascade-stress encoding and detectable propagation. These results validate QPC scalability and the feasibility of decoding relational, contextual, and cascade structure from quantum measurement.

RICT Encode–Decode Production Test

A separate production run validates that relational structure can be recovered from measurement: graph A → QPC circuit → IBM Fez (3 runs) → decode graph A′ → F1 ~42%, simulator ceiling ~43%. Full description, how it is done, and what the result means for the whole test suite:

RICT Encode–Decode Report →

Overview

Test 1 — Relational Information Computation Test (RICT)

Test 2 — Contextual Phase Reconstruction Problem (CPRP)

Test 3 — Polycontextural Cascade Reconstruction Test (PCRT)

Results

Structural Evaluation (156Q Fez)

RICT Encode–Decode Production Test

Technical Details

Job IDs (IBM Fez 156Q)