Real-time decoders are the classical bottleneck of fault-tolerant quantum computing. We are building an FPGA Relay belief-propagation decoder for bivariate-bicycle codes (the code family behind IBM's [[144,12,12]] "gross" code), using the same verified-generation flow as our classical LDPC products.
We publish progress the same way we publish products: measured, or labeled as a target.
| Milestone | Status |
|---|---|
| Floating-point golden model of Relay-BP (relay legs, ensemble, disordered memory strengths), exact against the published algorithm | DONE MEASURED |
| Convergence on circuit-level depolarizing noise, windowed decoding matrix (1008 checks × 8785 error mechanisms) | 100/100 trials MEASURED |
| Pipelined BP iteration on FPGA, small-scale (2-cycle check/bit update) | 118 MHz MEASURED |
| Mid-scale distance-5 decoder, fully parallel, placed and routed (xcvu9p) | 476,318 LUT · ~85.7 MHz MEASURED |
| Early termination on a stalled belief, worst-case decode latency | -32% at +0.47% LUT MEASURED |
| Model vs RTL bit-exactness, every test vector | 0 LSB MEASURED |
| Published FPGA reference at gross scale (for context) | ~2.1M LUT · 83 MHz |
| Full gross-code real-time decoder, fixed-point, system integration | TARGET |
The distance-5 clock is bounded by wiring, not logic, so it lands on the published silicon envelope rather than beating it. The genuine headroom is algorithmic. The full optimization journey is in the case study, with the circuit-level detail in the technical report. An honest negative result, because they matter: a fully parallel decoder at full gross-code scale does not fit synthesizable resource budgets. Our folded dataflow reconstruction is bit-exact and is the path forward.
Quantum LDPC decoding is belief propagation on a quasi-cyclic code, exactly the structure our 5G NR and CCSDS generators already emit, verify, and timing-close. The quantum program reuses that proven machinery.
Decoder logical-error rates are statistical claims; they are only credible if the hardware is provably the same algorithm as the model that produced the curves. Our three-layer equivalence chain guarantees exactly that.
We are open to collaborations with quantum-hardware teams that need real-time decoding: co-development, evaluation on your syndrome streams, or a custom code family.
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