SilverSight/experiments/bosonic_continuous/SYSTEM_SPEC.md

BMCTE v2 System Specification

Core Execution Model (Single Path)

There is only one pipeline:

U (N×N unitary) ↓ sample S ~ μ_U ↓ M = U_S (p×p submatrix) ↓ A = Ryser(M) ↓ w = |A|² ↓ accumulate histogram

No branching on p. No distinguishable approximation mode.

GPU Architecture

Kernel A — Sampling (O(Np))

• categorical sampling per column
• vectorized CDF tables
• warp-parallel RNG streams

Kernel B — Gather

• construct p×p matrix in registers
• coalesced memory reads from U
• shared-memory staging optional

Kernel C — Ryser Permanent

Bitmask subset expansion:

• iterate over 2^p subsets
• compute column sums
• multiply row products

Cost: O(p·2^p)

Kernel D — Reduction

• atomic histogram accumulation
• or block-level reduction trees

Fused Kernel (Final Form)

for k in 1..K:
    S = sample(U)
    M = gather(U, S)
    A = ryser(M)
    histogram += |A|^2
return normalize(histogram)

Compiler IR (BMCTE-IR v2)

SAMPLE(U) → S GATHER(U, S) → M RYSER(M) → A WEIGHT(A) → w REDUCE() → output

Optimization Rules

1. Fuse sampling + gather into single kernel
2. Keep M fully register-resident (p ≤ 8 ideal)
3. Inline Ryser loop (no function calls)
4. Batch Monte Carlo samples per dispatch
5. Avoid memory round trips entirely

Distributed Execution

Each worker:

P̂_i = Σ_{k∈batch} w_k

Final aggregation:

P̂ = Σ_i P̂_i

No synchronization during sampling phase.

Complexity Class

BMCTE: O(K(Np + p·2^p))