Architecture and validation
How the H-cat photonic quantum computer works, and how the validation campaign proves each subsystem meets spec.
Overview
The H-cat is a hybrid continuous-variable / discrete-variable (CV-DV) photonic quantum computer. Each logical qubit is encoded in a cat state: a superposition of coherent states in an optical mode, entangled with a single photon that acts as a herald and a parity anchor.
The architecture achieves fault tolerance through the erasure properties of photon loss: when a photon is lost, you know it happened (heralding), which converts errors into erasures. Erasures are far cheaper to correct than unknown errors.
Architecture pipeline
Five stages, each validated independently:
| Stage | Function | Key metric |
|---|---|---|
| 1. Squeeze | Generate squeezed vacuum | 6 dB on-chip squeezing |
| 2. Subtract | Photon subtraction (TES PNR tap) | F > 0.99 cat fidelity |
| 3. Breed | Entangle cats via beamsplitter | Heralding rate > 50% |
| 4. Fuse | Deterministic CV-DV fusion | Bell fidelity > 0.98 |
| 5. Correct | Surface code w/ erasure decoder | Circuit-level threshold 0.79 to 0.9 percent loss/cycle |
Cat states
A cat state is |cat+> = N(|alpha> + |-alpha>), an even superposition of two coherent states in phase space. Our cats are generated by squeezing followed by photon subtraction, yielding odd cats with high fidelity at moderate squeezing (3.5-8 dB usable, 6 dB target).
The Wigner function of a cat state shows characteristic interference fringes at the origin, with two Gaussian blobs at +/- alpha. Parity measurements read the logical qubit.
Breeding
Cat breeding entangles two small cats into a larger cat via beamsplitter interference and heralded detection. The protocol is probabilistic but heralded: failure is known and the state is discarded, not corrupted.
The SDK models realistic breeding with finite squeezing, detector dark counts, and mode mismatch.
Fusion
Hybrid fusion creates entanglement between cat qubits using a combination of homodyne detection (CV) and single-photon detection (DV). The fusion is deterministic conditioned on the herald: no post-selection required.
Loss and error model
Photon loss is the dominant error channel. Most loss is heralded: a lost photon flips the cat's photon-number parity, so you know it happened and the error becomes an erasure. The residual silent (unheralded) part is a Pauli channel; the bit-flip rate is exponentially suppressed in cat size, scaling as exp(-2|alpha|^2), so moderate-amplitude cats (alpha = 2) keep silent errors low. The digital twin measures both rates directly on the real (mixed) bred cat and corrects the Poisson formula: the silent Pauli rate is about 2.9x the Poisson value at 1 percent loss (the bred cat is mixed, which fattens the multi-photon-loss tail), while heralded erasure is a few percent below Poisson.
Crucially, loss is detectable (the photon number drops), converting errors to erasures. Erasure thresholds are far higher than depolarizing thresholds for the same code. The circuit-level loss threshold, with the syndrome-extraction machinery and its own losses simulated, is 0.79 to 0.9 percent loss per cycle (0.79 percent with the validated silent-Pauli correction, the default; 0.898 percent uncorrected). Numbers reflect full circuit-level noise (June 2026 campaign), superseding earlier phenomenological figures.
Fault tolerance
We use the surface code with an erasure-aware decoder (pymatching). The threshold analysis uses stim with the full circuit-level noise model: noisy fusion erasure and Pauli, measurement error, preparation error, and idle loss, with per-shot erasure-reweighted decoding. Key result: the circuit-level loss threshold is 0.79 to 0.9 percent loss per cycle. The machine is operated at a 0.4 to 0.5 percent per-cycle loss spec to leave margin (the retired 1 percent point is above threshold, where no fault-tolerant distance exists). A validated qLDPC scaling code gives an additional roughly 10x reduction in hardware modes per logical. Numbers reflect full circuit-level noise (June 2026 campaign), superseding earlier phenomenological figures.
Photonic devices
The physical platform is silicon nitride (SiN) integrated photonics, fabricated at a standard commercial foundry (GlobalFoundries 45SPCLO). Key components:
- Microring resonators (Q > 10^6) for squeezing and filtering
- Waveguide beamsplitters for interference
- Grating couplers for fiber I/O
- TES PNR detectors (transition-edge sensors, photon-number-resolving, cryogenic, fiber-coupled)
Device simulations use Meep (FDTD) for ring resonances and MPB (eigenmode) for waveguide dispersion. Detectors operate at millikelvin temperatures in a dilution refrigerator.
Resource model
The resource model (v2) converts a target logical error rate into a full device specification: code distance, number of cat states per logical qubit, physical modes per cat, and total hardware footprint. This is the engine behind the Resource Analyzer tool. The distance comes from the circuit-level fit Lambda = (p_th / gamma)^1.61 with p_th = 0.79 percent (corrected, default) or 0.898 percent (uncorrected), and cats per logical = 2d^2 - 1. The loss-to-error split is the Poisson closed form corrected by the digital-twin factors.
Inputs: target error rate, physical loss per cycle (gamma), cat amplitude (alpha), squeezing level, outer code. Output: complete bill of materials for the quantum computer.
At the 0.5 percent per-cycle loss spec the analyzer returns distance 53 and 5,617 cats per logical, identical to the validated v2 model (operating spec 0.4 to 0.5 percent, about 2,400 to 5,600 cats per logical at 1e-9; at 1 percent loss it honestly reports the above-threshold regime, where no fault-tolerant distance exists). The roadmap at the unchanged rack budgets is 25 logical/rack (Gen-1 NISQ), 250 (Gen-2 error-detected), 5 qLDPC (Gen-3 fault-tolerant, surface does not fit the 50k-mode rack), and 65 qLDPC (Gen-4). Numbers reflect full circuit-level noise (June 2026 campaign), superseding earlier phenomenological figures.
Validation campaign
Every claim is backed by simulation. The validation campaign uses:
- QuTiP: cat state generation, loss channels, parity readout
- Strawberry Fields: Gaussian boson sampling cross-checks
- stim + pymatching: surface code thresholds with circuit noise
- Meep: SiN ring resonator FDTD simulations
- MPB: waveguide eigenmode dispersion
Surface-code decoding now includes the full circuit-level syndrome-extraction noise model (June 2026 campaign), not just the loss channel. Specific numbers a reviewer can check:
- Circuit-level fault-tolerance threshold 0.79 to 0.90 percent loss per cycle (full circuit-level noise, stim + PyMatching).
- Two independent codebases (QuTiP and Strawberry Fields) agree on cat fidelity to 4e-5.
- Master-equation (mesolve) evolution agrees with the closed-form loss channel to 1e-9.
- End-to-end digital twin runs from device parameters to logical error in one continuous density-matrix pipeline.
- A pytest regression suite pins every headline number (9 passed: 6 historical, 3 new v2 pins).