Quantum supremacy and quantum advantage benchmarks typically rely on random circuit sampling (RCS): circuits built by applying random single- and two-qubit gates according to a fixed layout. The computational hardness of simulating such circuits classically is used to argue that the quantum device performs a task beyond practical classical reach.
Quantum Polycontextural Computing (QPC) introduces a different principle: computation is organised around logical contextures that coexist and interact. Contexts determine phase mappings, entanglement patterns, and gate choices. The question arises whether context-driven circuit generation—without resorting to full randomness—can produce circuits that are equally or more demanding than standard RCS, while remaining interpretable within polycontextural logic.
PQST-64 (Polycontextural Quantum Sampling Test, 64-qubit variant) is designed to test this. It uses a deterministic, context-dependent recipe: each cycle applies a global superposition layer, a contextual phase layer (phases derived from context and qubit index), a context-driven entanglement layer, and a context switch. The result is a fixed, repeatable circuit that is structurally aligned with polycontextural theory and intended to exhibit high-entropy sampling statistics when run on real hardware — without claiming verified classical hardness.
The PQST-64 circuit acts on 64 qubits, viewed as an 8×8 lattice. The circuit has 30 cycles. Each cycle consists of four layers:
Each of 30 cycles applies a proprietary context-driven layer stack (superposition, contextual phases, entanglement, context advance). Exact gate schedules and phase rules are not published here.
After all cycles, all 64 qubits are measured. Circuits compile to the target processor native gate set; schedules are proprietary.
The circuit was transpiled for IBM Quantum’s ibm_fez backend (156 qubits, superconducting) using Qiskit’s preset pass manager at optimization level 3. The transpiled circuit was compiled to IBM native gates (schedule proprietary). Execution was performed via the Qiskit Runtime Sampler with 5000 shots. Job ID: d6lena0fh9oc73emrrp0.
Execution completed in 11.59 s. All 5000 shots produced distinct 64-bit outcomes; no bitstring was observed more than once. Summary metrics are given in Table 1.
| Metric | Value |
|---|---|
| Backend | ibm_fez (156 qubits) |
| Logical qubits | 64 |
| Cycles (depth) | 30 |
| Shots | 5000 |
| Unique outcomes | 5000 |
| Uniqueness ratio | 100% |
| Transpiled depth | 213 |
| Transpiled gate count | Proprietary schedule |
| Execution time | 11.59 s |
100% uniqueness (5000/5000 distinct bitstrings) indicates that the observed sample set has high diversity across shots and that no single outcome dominates. This is consistent with a deep, entangling sampling circuit; it is not by itself a proof of quantum supremacy or classical intractability.
PQST-64 differs from standard RCS in that the circuit is not built from random gate choices; it is fully determined by the context-update rule and the fixed layer structure. The observed statistics are RCS-comparable on the metrics we report (entropy / uniqueness / heavy-output style counts). This supports studying context-driven circuit generation as a sampling-benchmark family, not as a sold advantage claim.
Future work may include: (i) formal comparison with an RCS circuit of the same qubit count and depth (e.g. cross-entropy benchmark, heavy-output probability); (ii) scaling to deeper circuits or larger qubit counts; (iii) varying the context alphabet and phase rules to study the impact on output complexity.
We have run the Polycontextural Quantum Sampling Test (PQST-64) on a 64-qubit superconducting processor (IBM Quantum ibm_fez). The context-generated circuit produced 5000 unique outcomes in 5000 shots, showing high-entropy sampling behaviour on real hardware. PQST-64 is a context-structured sampling benchmark family; primary architecture claims elsewhere on this site use multi-logic desks with public job IDs, not uniqueness alone.