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 Supremacy 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 brickwork entanglement layer, and a context switch. The result is a fixed, repeatable circuit that is structurally aligned with polycontextural theory yet intended to exhibit supremacy-level output statistics when run on real hardware.
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:
After all cycles, all 64 qubits are measured. The gate set is H, RZ, and CNOT—native to superconducting processors such as IBM’s.
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 had depth 213 and 8280 gates. 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 | 8280 |
| Execution time | 11.59 s |
100% uniqueness (5000/5000 distinct bitstrings) indicates that the output distribution has high entropy and that the device is exploring a large fraction of the 264 outcome space. This is the behaviour expected of a supremacy-style benchmark: the circuit is sufficiently deep and entangling that outcomes are effectively uncorrelated across shots, and no single outcome dominates.
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. Nevertheless, the observed statistics are consistent with supremacy-level complexity. This supports the hypothesis that context-driven circuit generation, rooted in polycontextural logic, can replace or complement stochastic generation in quantum supremacy tests.
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 Supremacy Test (PQST-64) on a 64-qubit superconducting processor (IBM Quantum ibm_fez). The context-generated circuit produced 5000 unique outcomes in 5000 shots, demonstrating supremacy-style output and showing that polycontextural circuit design can yield benchmark-grade, high-entropy behaviour. PQST-64 establishes a new class of quantum supremacy tests based on logical context structure and provides a bridge between polycontextural logic and experimental quantum computing.