STAR-PHASER GEMINI

One qubit = one photon in a two-dimensional path Hilbert space: |ψ⟩ = α|1⟩_A|0⟩_B + β|0⟩_A|1⟩_B. Quantum information lives in the amplitude ratio |α/β| (population) and differential phase Δφ = φ_A − φ_B (Bloch equator). Global phase φ_A + φ_B is unphysical — it cancels in all interferometric readouts.

Loss on one rail without heralding is an erasure — the photon left the {|0⟩,|1⟩} subspace but the defect location is known, which QEC treats more favorably than undetected depolarizing noise. Heralding + coincidence filtering enforce the single-photon subspace at runtime.

d=2 · SU(2) · no spectral crosstalk · no EOM scattering

Upgrade path: optional GAP4 transcode at encoding boundary → 2-color frequency qubit → open comb (d=10, SOLAR roadmap). Native GEMINI computation skips the transcoder entirely.

Single-qubit gates are programs on an 8-mode Clements mesh (28 MZIs, 32 thermo-optic heaters). Arbitrary U(2) per dual-rail pair decomposes into directional couplers (beam splitters) and one-rail phase shifters — Hadamard, R_z, Clifford+T all compile to mesh DAC tables.

Two-qubit entanglement is measurement-based, not deterministic χ⁽³⁾ CZ: Type-II fusion Bell measurements (P_succ = ½ ideal passive LO) + TFLN feed-forward (~11.2 ns budget) steer partner photons in delay spirals. External ceiling: 99.22% fusion fidelity on manufacturable Si (Giewont et al., 2024) — GEMINI targets >99% post-characterization.

Depth without OPC: V(N) = exp(−Nσ²/2) · with OPC every M≈10: V_∞ = exp(−Mσ²/2η)

v1 demo: 4-qubit GHZ >85% fidelity on modes 1–8 (four dual-rail pairs).

Eight independent Si₃N₄ micro-rings (R ≈ 50 µm, Q > 5×10⁵) produce heralded pairs via χ⁽³⁾ SFWM at mW-class C-band pumps. Idler clicks flag signal photons; FPGA schedules delivery through a three-stage binary switch tree (7 TFLN EO routers) with T=4 temporal retry slots per source.

Availability law: A = 1 − (1 − p)^K·T. At p=0.1, K=8, T=4 → A ≈ 96.6% [model]. Absolute photon-at-output probability PG1 remains switch-loss-limited (~47% [model]) — publish both A and PG1 separately on datasheets.

GEMINI deliberately uses spatial×temporal mux — not Fan 2025 spectral state-multiplexing (roadmap SOLAR path). Δf = N/A on this SKU.

Fab: LIGENTEC AN350-class MPW + proprietary TFLN bond + optional As₂S₃ OPC overlay (~34-week defer-As₂S₃ track available).

Two routing regimes on one chip: (1) classical path selection — herald-driven mux tree and feed-forward switches route which mode carries the photon without entangling; success requires low IL, high extinction, phase-stable equalized paths. (2) coherent superposition — MZI mesh routes amplitudes between rails; errors are multiplicative in gate fidelity.

K=8 / 3-stage tree = minimum depth for eight independent herald arms. Per-stage IL target <0.5 dB; extinction >20 dB; path skew ±0.5 µm. Source-stage OPC erases route-dependent phase so muxed photons remain mutually indistinguishable for HOM/fusion.

No 10-ch / 64-ch WDM demux on GEMINI — purely spatial until SOLAR

Technology-agnostic switch socket (P3): TFLN EO committed for mux + feed-forward; thermo-optic for gate mesh; MEMS for lab bring-up only.

Control loop: SPAD clicks → 64 ps TDC → FPGA (herald decode, mux select, FF LUT) ↔ AD5372 DAC (32 mesh heaters). Full thermal mesh refresh ~54 µs; feed-forward decision ~11.2 ns (FPGA-limited, switch <2% of budget).

GAP5 OPC visibility probe: V = exp(−σ_φ²/2) reports differential phase variance from heralded HOM interference — zero added test structures, in-situ during production operation. Drift alarm triggers DAC recalibration when V drops below threshold.

Calibration layers: fabrication trim (once per die) → periodic thermal sweep → mux path equalization (bright-pulse boot) → GAP5 in-situ witness → source_id coincidence validation every shot.

T9 gate: single-photon HOM before/after OPC on dual-rail Sagnac node

Hybrid Si₃N₄/As₂S₃ FWM nodes at mux output (GAP2 source-stage) and every M ≈ 10 gates in a recirculating storage loop (GAP1 lattice). Phase conjugation: φ → −φ on each rail; differential encoding lets common-mode pump phase cancel in symmetric layouts.

Without OPC: Var(φ) = N·σ² — visibility collapses ~50–100 gates. With OPC every M gates: V_∞ ≤ exp(−Mσ²/2η) — error bounded by interval M and efficiency η, not total depth N.

Optional CV path: Ge p-i-n balanced homodyne @ 15.3 GHz for quadrature readout — baseline CV hardware, not fault-tolerant GKP on shipped SKU. OPC preserves quadrature structure (Gaeta & Boyd, 1995 theory).

Single-photon OPC on-chip: [to-be-tested] · Campaign T9 gates all high-d OPC claims

Never state: OPC replaces QEC — it is an analog phase pre-layer beneath digital stabilizer extraction.

Physical qubit: dual-rail d=2. Stabilizer codes: surface, LDPC, XZZX (bias-aware — OPC Z-preference). Syndrome extraction reuses ancilla MZI programs + per-rail SPAD clicks → FPGA Pauli frame (Path A, v1 ship path).

Industry FT destination (Path B, roadmap): fusion-based quantum computation (FBQC) where resource-state tiles + Type-II fusions encode foliated surface codes — syndromes read from fusion outcomes. GEMINI v1 ships primitives only, not a fault-tolerant fusion network.

Loss maps to heralded erasure (cheap, ~25–50% theory threshold class). Post-OPC model: p_Z ~35.7% → ~1.2% at η≥0.5 — moves operating point toward surface-code Pauli threshold (~1%). A507 Stim/PyMatching simulation is software gating.

Logical qubit / break-even QEC: [roadmap] — not GEMINI ship date

Tier A — ship today: dual-rail LOQC processor; photonic AI inference on same 28-MZI mesh (configuration change: pump power, detector mode). Tier B — validation: 4-qubit GHZ >85%, HOM >85%, g²(0)<0.5, CAR >50:1. Tier C — roadmap: decimal/GF compute → SOLAR / NOVA.

Validation hierarchy gates marketing: Layer 1 timing → Layer 2 mesh cal → Layer 3 OPC probe (T9) → Layer 4 fusion+FF → Layer 5 GHZ/algorithms → Layer 6 FBQC factory [roadmap]. Do not skip to Layer 5 claims without Layer 3 evidence when OPC is featured.

External GHZ benchmark: 85.4% integrated Si (2024) — GEMINI >85% target is competitive with integrated photonics SoTA, not bulk telecom or cryo SNSPD platforms.

Customer personas: HPC pilot (no cryoplant), photonic QC research lab, AI/accelerator dual-use, government eval on US-friendly split-fab.