Learn the H-cat architecture

A cat state is a quantum superposition of two coherent states of light: |cat> = N(|alpha> + |-alpha>). The name comes from Schrodinger's cat: the light field is simultaneously in two macroscopically distinguishable states (positive and negative amplitude).

In phase space, a cat state looks like two Gaussian blobs (the coherent states) connected by interference fringes at the origin. The fringes are the quantum signature: they disappear if decoherence turns the superposition into a classical mixture.

Cat states encode one logical qubit. The logical |0> and |1> are the even and odd cat: |0_L> = |alpha> + |-alpha>, |1_L> = |alpha> - |-alpha>. Readout is done by measuring photon-number parity.

To make a cat state in the lab, you start with squeezed vacuum: light whose quantum noise is reduced in one quadrature at the expense of the other. Squeezing is generated by parametric down-conversion in a nonlinear medium (or a microring resonator on chip).

Photon subtraction means tapping off a small fraction of the squeezed light and detecting a photon. Conditioned on that detection (heralding), the remaining light collapses into an approximate cat state. More squeezing and more subtractions give higher-fidelity cats.

Key parameters: squeezing level (dB), number of subtractions (k), and the Fock-space truncation (N). The SDK's generate_cat() models all of these.

Small cats (low alpha) are easy to make but hard to compute with. Large cats (high alpha) have better error suppression but are harder to generate directly. Breeding solves this: interfere two small cats on a beamsplitter, measure one output, and conditioned on the result the other output is a larger cat.

Breeding is probabilistic but heralded. When it fails, you know and discard the state. When it succeeds, you have a higher-amplitude cat with known phase. Multiple rounds of breeding can build up to the target alpha.

Fusion creates entanglement between two cat qubits. The H-cat uses hybrid fusion: combine a homodyne measurement (continuous variable, gives analog quadrature data) with a photon detection (discrete variable, gives click/no-click).

The result is a deterministic Bell measurement conditioned on the herald. No post-selection is needed for the logical operation, only for confirming that the fusion succeeded. This makes the architecture scalable: you can build large cluster states without exponential overhead.

The key insight of the H-cat architecture: photon loss is detectable. When a photon is lost from a cat state, the photon number drops by one. If you monitor the photon number (via heralding or parity checks), you know which qubit lost a photon and when.

A known error location is called an erasure. Erasures are much easier to correct than unknown errors: the erasure threshold for the surface code is around 50%, compared to about 1% for depolarizing noise. This means the H-cat can tolerate far more loss than a traditional qubit can tolerate gate errors.

Seeing most errors is why the architecture tolerates far more loss than a machine with hidden errors could: with the full check-measurement machinery and its own losses simulated, the tolerance is a circuit-level threshold of 0.79 to 0.9 percent loss per cycle, and the machine is operated at a 0.4 to 0.5 percent spec to leave margin. The residual silent bit-flip rate is exponentially suppressed in cat size (it scales as exp(-2|alpha|^2)), so the dominant cost is heralded erasure, which the decoder handles cheaply. Numbers reflect full circuit-level noise (June 2026 campaign), superseding earlier phenomenological figures.

The surface code is a topological error-correcting code defined on a 2D grid of qubits. Each logical qubit uses d x d physical qubits (where d is the code distance). The code corrects any error pattern affecting fewer than d/2 qubits.

For erasures, the decoder knows which qubits were lost. It constructs a matching problem on only the erased locations, which is much easier to solve. Under full circuit-level noise the loss threshold is 0.79 to 0.9 percent loss per cycle, and the machine is operated at a 0.4 to 0.5 percent spec for margin. At that spec, reaching a 1e-9 logical error rate needs about 2,400 to 5,600 cats per logical qubit. Numbers reflect full circuit-level noise (June 2026 campaign), superseding earlier phenomenological figures.

We simulate this with stim (fast stabilizer circuit simulator) and decode with pymatching (minimum-weight perfect matching). The validation campaign confirms the threshold numerically.

The H-cat is designed for silicon nitride (SiN) integrated photonics. SiN has low propagation loss (< 0.1 dB/cm), a moderate nonlinearity (sufficient for on-chip squeezing via four-wave mixing), and is fabricated at standard CMOS foundries.

Key components on chip: microring resonators for squeezing and filtering (Q > 10^6 demonstrated), directional couplers for beamsplitters, and grating couplers for fiber I/O. Detectors are TES PNR (transition-edge sensors, photon-number-resolving) operating at millikelvin temperatures in a dilution refrigerator, fiber-coupled to the chip. Number resolution is essential: the architecture needs to count photons, not just detect clicks.

The platform targets GlobalFoundries' silicon-photonics process (45SPCLO), whose monolithic photonics-plus-CMOS integration supports multi-project wafer runs and eventual volume manufacturing.