Primordial Architecture Series · Layer V · Theoretical Quantum Mapping
HIR-SPU on Sycamore
|HIR⟩ = α|GREEN⟩ + β|YELLOW⟩ + γ|RED⟩
Google Sycamore · 53-qubit NISQ · fSim native gate · T₁ ~15μs · Hybrid classical/quantum
NISQ Amplitude Encoding VQE Weight Optimization Resonance as Born Probability Classical Safety Wrapper 7-Qubit Resonance Circuit fSim Gate Mapping
◈ The Deepest Theoretical Finding
Resonance Rn = (H·I²·R)^¼ is structurally identical to a quantum Born probability. If H, I, R are encoded as Ry-rotated qubit amplitudes where P(|0⟩) = score, then Rn emerges from quantum interference — not computed, but measured. Quantum decoherence is pressure. This is not metaphor. It is the natural physical interpretation.
|ψ_H⟩ = √H|0⟩ + √(1-H)|1⟩   →   P(all |000⟩) = H·I·R   →   Rn = √(√(H·I) · √(R·I)) = P(|0⟩ after fSim entanglement)^½   |   1 − Rn = P(decoherence)
Sycamore Hardware Profile
ProcessorGoogle Sycamore
Qubits53 (original) / 70 (Weber)
Topology2D grid, NN coupling only
Native 2Q gatefSim(θ,φ)
Native 1Q gatesRx, Ry, Rz, √X, √Y
T₁ coherence~15–20 μs
T₂ coherence~20–30 μs
1Q gate error~0.1%
2Q gate error~0.6%
Readout error~3–4%
Max reliable depth~20–30 layers
Max reliable 2Q gates~300–400
Error correctionNone (NISQ)
ProgrammingCirq / OpenFermion
fSim Native Gate
fSim(θ, φ)
|00⟩ → |00⟩
|01⟩ → cos(θ)|01⟩ − i·sin(θ)|10⟩
|10⟩ → −i·sin(θ)|01⟩ + cos(θ)|10⟩
|11⟩ → e^(−iφ)|11⟩
θ=π/2: iSWAP limit
φ=π: CZ limit
Sycamore default: θ≈π/2, φ≈π/6
HIR use: fSim computes H·I product amplitude in a single 2Q gate
Qubit Budget Analysis
Full Q16.16 register file
15 write regs × 32 bits
480
9× over Sycamore
18 ACTION_FLAGS bits
basis encoding
18
fits in Sycamore
Amplitude resonance circuit
H,I,R + 3 ancilla + output
7
ideal on Sycamore
VQE config optimizer
31 param ansatz
15–20
HEA ansatz
Grover batch search
N=1024 packets (2^10)
53
depth exceeds T₁
QRAM memory recall
N=2^k address + payload
∞
QRAM not physical
Implementation Ladder
NISQ — Sycamore Today
7-qubit amplitude resonance circuit · VQE config optimization · Sigmoid Ry rotation · Classical safety wrapper · Single-packet H/I/R amplitude encoding
Near-term fault-tolerant
Surface code · ~100 logical qubits · Grover over N~100 batch · Quantum walk over semantic memory graph · Quantum phase estimation for stability S
Long-term (1000+ logical qubits)
QRAM-based batch recall · Full Q16.16 arithmetic in quantum circuits · Quantum simulation of degradation dynamics Θ → Hamiltonian · HHL for pressure field linear systems
⬡ Hybrid Classical/Quantum Architecture
CLASSICAL · MANDATORY
Classical Safety Wrapper
Hard-zero flag checks (ACTION_FLAGS bits 5,7,8,13,15,17) · Safety invariants INV-1 through INV-8 · SHA-256 audit chain · FSM write-back · Permission state output · Any hard_red path short-circuits to HALT before quantum circuit runs
↓ only if all hard-zero checks pass
QUANTUM · SYCAMORE
Quantum Resonance Core
Amplitude-encode H, I, R as Ry-rotated qubits · fSim gates compute pairwise products · SFU-equivalent: amplitude IS the sqrt · Measure: P(|000⟩) = H·I·R · Rn derived from measurement statistics
↓ measurement result → classical comparison
QUANTUM/CLASSICAL
VQE Configuration Layer
Parameterized ansatz on 15-qubit subgraph · Classical COBYLA/SPSA optimizer loop · Cost: ⟨ψ(θ)|H_HIR|ψ(θ)⟩ where H_HIR encodes governance quality · Optimizes: k, w_W, w_F, w_WF, g_G, thresholds (31 params total)
↓ Rn ≥ 0.75 → GREEN · Rn ≥ 0.50 → YELLOW · else RED
CLASSICAL · MANDATORY
Audit Digest + Action Dispatch
SHA-256 digest written · Measurement result + gate scores stored in AuditRecord · Permission state → host · RED = preserve + escalate (no quantum circuit for RED path)
Sycamore 53-Qubit Grid — HIR Resonance Circuit Placement
H
qubit
F
anc
VQE
0
I
qubit
C
anc
VQE
1
VQE
2
VQE
3
R
qubit
Rn
out
VQE
4
VQE
5
VQE
6
VQE
7
VQE
8
free
free
VQE
9
VQE
10
free
VQE
11
free
free
free
free
free
VQE
12
free
free
free
free
free
free
free
free
■ H gate qubit ■ I gate qubit ■ R gate qubit ■ Fidelity/Cohesion ancilla ■ Rn output qubit ■ VQE ansatz (13 qubits) □ free
7-Qubit Amplitude Resonance Circuit — Single Evidence Packet
State prep + fSim entanglement → Rn measurement (~8 two-qubit gates, ~100ns, within T₁)
q_H Ry(2·arcsin(√H)) fSim ctrl H score → amplitude
q_I Ry(2·arcsin(√I)) fSim fSim I score → amplitude
q_R Ry(2·arcsin(√R)) fSim R score → amplitude
q_F(anc) |0⟩ fSim fSim Fidelity = √(H·I)
q_C(anc) |0⟩ fSim Cohesion = √(R·I)
q_Rn(out) |0⟩ fSim M P(|0⟩) = Rn²
Hard-zero pre-check (classical): If ANY of {domination_pattern, consent_violated, schema_invalid, invariant_violated} = 1 → bypass circuit entirely → classical RED/HALT
Measurement: P(q_Rn=|0⟩) = Rn² · repeat N_shots times · estimate Rn = √(count_0 / N_shots)
Gate count: 3 Ry (single-qubit) + 5 fSim (two-qubit) · Total circuit time ≈ 3×25ns + 5×12ns ≈ 135ns ≪ T₁ ~15μs
NISQ ✓
VQE — Config Weight Optimization
Variational Quantum Eigensolver
Optimize k, w_W, w_F, w_WF, g_G and 26 other config params as VQE ansatz parameters. Cost function: ⟨ψ(θ)|H_HIR|ψ(θ)⟩ = expected governance quality. Hardware-efficient ansatz on 15-20 qubit subgraph. Classical optimizer: COBYLA (gradient-free, noise-tolerant).
Quadratic in precision. Classical competitive for small param count.
NISQ ✓
QAE — Resonance Estimation
Quantum Amplitude Estimation
Classical: compute Rn in O(1) per packet but with ε² samples for precision ε. Quantum: O(1/ε) samples via amplitude estimation — quadratic speedup in precision. For Rn near threshold (0.75, 0.50), high precision required → QAE shines. 7-qubit circuit on Sycamore. ~135ns circuit time.
O(1/ε) vs O(1/ε²) classical — quadratic precision speedup
Fault-tolerant only
Grover — Batch Packet Search
Grover's Algorithm / Amplitude Amplification
Search over N evidence packets for those where Rn ≥ threshold. Classical: O(N). Quantum: O(√N). For N=1024 packets: 32× speedup. On Sycamore: circuit depth ∝ √N × eval_depth → ~640 layers for N=1024 → exceeds T₁. Requires fault-tolerant hardware (surface code, ~100 logical qubits).
O(√N) — quadratic. Blocked by decoherence on NISQ.
Fault-tolerant only
Quantum Walk — Semantic Memory Graph
Quantum Walk / Szegedy Walk
RAM memory `links[]` field creates a graph over memory objects. Classical random walk: O(N) to explore graph, find related memories. Quantum walk: O(√N) steps to reach any node from any start. Useful for semantic memory traversal and associative recall. Requires coherent superposition over node space → fault-tolerant.
O(√N) graph exploration. Requires ~log₂(N) + payload qubits.
Theoretical only
QRAM — Quantum Memory Recall
Quantum Random Access Memory
Load N memory objects into superposition: (1/√N)Σ|i⟩|Mem_i⟩. Apply Recall Score oracle, Grover amplify → O(√N) retrieval. Problem: No physical QRAM exists. The bucket-brigade QRAM architecture requires O(N) active components, defeating the advantage. This remains a major open hardware problem.
Theoretical. No physical QRAM in existence.
Blocked
Σ — Sigmoid Repair Gate
Θ = σ(Θ_base + θ_C·C + θ_E·E − θ_K·K)
The repair traction gate is literally a quantum rotation: Ry(2·arcsin(√Θ)) → |ψ⟩ with P(|0⟩)=Θ. The sigmoid argument z = linear combination of C, E, K → expectation value of Z operators. Mathematically beautiful. Computationally: 1 qubit, 1 gate. Faster classically. Quantum only makes sense here if C, E, K are themselves in quantum superposition.
Natural quantum encoding. No speedup vs classical for single evaluation.
Classical / Quantum Boundary — Per Component
—
Component
Layer
Reason
1
Hard-zero safety invariants (INV 1–8)
CLASSICAL
Must be deterministic. Superposition of "maybe domination" is architecturally prohibited.
2
ACTION_FLAGS bitfield (18 bits)
HYBRID
Basis-encode as 18 qubits. Hard-zero flags measured classically first, then residual flags enter quantum circuit.
3
H, I, R gate scoring
HYBRID
Score computation classical (linear penalty sums). Score encoding as Ry-rotated amplitude → quantum.
4
Fidelity = √(H·I)
QUANTUM
fSim gate on q_H, q_I gives amplitude = √(H·I) in a single 2Q operation. Natural quantum computation.
5
Cohesion = √(R·I)
QUANTUM
Same as Fidelity. fSim on q_R, q_I. Natural quantum computation.
6
Resonance Rn = √(F·C)
QUANTUM
Born probability: P(q_Rn=|0⟩) = Rn². Resonance IS the quantum measurement probability. Not metaphor.
7
B = H+I+R+k(HI+HR+IR)
HYBRID
ZZ correlators on Sycamore give ⟨Z_H·Z_I⟩ = HI term. VQE computes ⟨B⟩ as Hamiltonian expectation.
8
P = w_W·W + w_F·F + w_WF·WF
CLASSICAL
W, F are environmental inputs from host agent. Classical scalars. No quantum advantage for linear combination.
9
S = A·B − P
CLASSICAL
Subtract classical P from quantum-estimated ⟨B⟩. Result is classical scalar.
10
Repair gate Θ = σ(z)
HYBRID
z is classically computed. Θ can be encoded as Ry rotation for downstream quantum operations.
11
Config weights (31 params)
QUANTUM
VQE on 15-20 qubit HEA ansatz. NISQ-native. Quadratic speedup in precision for config optimization.
12
8 failure flag checks
CLASSICAL
Deterministic boolean predicates. No quantum advantage. Must remain classical for safety guarantee.
13
Permission FSM (GREEN/YELLOW/RED)
CLASSICAL
Threshold comparison on classical Rn estimate. FSM output is a definite classical state, not a superposition.
14
SHA-256 audit chain
CLASSICAL
~2400 gates for quantum SHA-256. No known speedup. Exceeds Sycamore coherence by 6×. Stays classical.
15
Memory Recall Score batch
QUANTUM
Grover/Tensor core on large N. Fault-tolerant quantum: O(√N). Current Sycamore: N≤64 before decoherence.
⚑ The Fundamental Tension
DETERMINISM vs SUPERPOSITION The HIR safety invariants require hard determinism — domination_pattern=1 MUST halt unconditionally. Quantum superposition allows "a little domination" which the architecture explicitly prohibits. The safety layer is irreconcilably classical.
AUDIT INTEGRITY vs DECOHERENCE The audit chain requires SHA-256. A quantum SHA-256 circuit needs ~2400 gates. At 0.6% two-qubit error rate, P(no error) = 0.994^2400 ≈ 5.5×10⁻⁶. The audit chain cannot live in the quantum layer.
HARD ZEROS vs AMPLITUDES Write Gate W = Q×P×H×I×R — multiplicative hard-zero. In quantum, zero amplitude on any factor → zero product. But a single erroneous qubit flip from noise could introduce a small non-zero amplitude where the hard-zero should hold. Safety gates must be classically pre-checked.
READOUT DESTROYS STATE Every quantum measurement collapses the resonance superposition. To estimate Rn with precision ε, you need O(1/ε²) circuit shots classically or O(1/ε) with QAE. Each shot re-prepares and re-runs the circuit. No single-shot Rn without error.
COHERENCE vs CIRCUIT DEPTH Full Q16.16 register file needs 480 qubits and hundreds of gate layers. Sycamore's T₁ allows ~20 layers. The only viable NISQ path is amplitude encoding — sacrificing precision for coherence.
Qubit Encodings — Bloch Sphere
|0⟩ |ψ_H⟩
H qubit
Ry(2·arcsin(√H))|0⟩
Rn |ψ_Rn⟩
Rn output
P(|0⟩) = Rn²
|1⟩ HARD RED
Safety collapse
hard_red → |1⟩ classical
Quantum Identities
Rn = P(|0…0⟩ after fSim) = Born probability
1 − Rn = P(decoherence) = physical pressure
fSim(π/2,φ)(|H⟩⊗|I⟩) = amplitude √(H·I) in |00⟩
Ry(2·arcsin(√Θ))|0⟩ = repair gate in quantum
⟨Z_H Z_I⟩ = HI correlation = B interaction term
SHA-256 depth: ~2400 gates → P(clean) ≈ 5.5×10⁻⁶
Q16.16 full regfile: 480 qubits → 9× Sycamore limit
7-qubit Rn circuit: 135ns ≪ T₁ = 15,000ns → ✓
HIR Hamiltonian (VQE)
H_HIR =
− (Z_H + Z_I + Z_R)
− k(Z_HZ_I + Z_HZ_R + Z_IZ_R)
+ w_W·W + w_F·F_op + w_WF·WF_op
+ λ·penalty(hard_zeros)
Minimize ⟨ψ(θ)|H_HIR|ψ(θ)⟩
θ* = optimal config weights
VQE finds θ* that maximizes governance quality under observed pressure
H gate / quantum ✓
I gate / hybrid
R gate / resonance
VQE / quantum core
Ancilla / config
Classical safety / blocked
Free qubit
Primordial HIR-SPU · Quantum Architecture Map (Theoretical) · Collin D. Weber · Google Sycamore · April 30, 2026