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| /* SYCAMORE SPEC TABLE */ |
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| @media(max-width:860px){.main{grid-template-columns:1fr}} |
| </style> |
| </head> |
| <body> |
| <div class="content"> |
|
|
| <div class="hdr"> |
| <div class="hdr-eyebrow">Primordial Architecture Series · Layer V · Theoretical Quantum Mapping</div> |
| <div class="hdr-title">HIR-SPU on <em>Sycamore</em></div> |
| <div class="hdr-ket">|HIR⟩ = α|GREEN⟩ + β|YELLOW⟩ + γ|RED⟩</div> |
| <div class="hdr-sub">Google Sycamore · 53-qubit NISQ · fSim native gate · T₁ ~15μs · Hybrid classical/quantum</div> |
| <div class="tags"> |
| <span class="tag ti">NISQ Amplitude Encoding</span> |
| <span class="tag tv">VQE Weight Optimization</span> |
| <span class="tag ts">Resonance as Born Probability</span> |
| <span class="tag tr">Classical Safety Wrapper</span> |
| <span class="tag tm">7-Qubit Resonance Circuit</span> |
| <span class="tag tg">fSim Gate Mapping</span> |
| </div> |
| </div> |
|
|
| |
| <div style="max-width:1260px;margin:0 auto 12px"> |
| <div class="insight"> |
| <div class="insight-title">◈ The Deepest Theoretical Finding</div> |
| <div class="insight-body"> |
| 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. |
| </div> |
| <div class="insight-eq"> |
| |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) |
| </div> |
| </div> |
| </div> |
|
|
| <div class="main"> |
|
|
| |
| <div> |
| |
| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">Sycamore Hardware Profile</div> |
| <div class="spec-row"><span class="spec-k">Processor</span><span class="spec-v">Google Sycamore</span></div> |
| <div class="spec-row"><span class="spec-k">Qubits</span><span class="spec-v good">53 (original) / 70 (Weber)</span></div> |
| <div class="spec-row"><span class="spec-k">Topology</span><span class="spec-v">2D grid, NN coupling only</span></div> |
| <div class="spec-row"><span class="spec-k">Native 2Q gate</span><span class="spec-v good">fSim(θ,φ)</span></div> |
| <div class="spec-row"><span class="spec-k">Native 1Q gates</span><span class="spec-v">Rx, Ry, Rz, √X, √Y</span></div> |
| <div class="spec-row"><span class="spec-k">T₁ coherence</span><span class="spec-v warn">~15–20 μs</span></div> |
| <div class="spec-row"><span class="spec-k">T₂ coherence</span><span class="spec-v warn">~20–30 μs</span></div> |
| <div class="spec-row"><span class="spec-k">1Q gate error</span><span class="spec-v good">~0.1%</span></div> |
| <div class="spec-row"><span class="spec-k">2Q gate error</span><span class="spec-v warn">~0.6%</span></div> |
| <div class="spec-row"><span class="spec-k">Readout error</span><span class="spec-v warn">~3–4%</span></div> |
| <div class="spec-row"><span class="spec-k">Max reliable depth</span><span class="spec-v warn">~20–30 layers</span></div> |
| <div class="spec-row"><span class="spec-k">Max reliable 2Q gates</span><span class="spec-v warn">~300–400</span></div> |
| <div class="spec-row"><span class="spec-k">Error correction</span><span class="spec-v bad">None (NISQ)</span></div> |
| <div class="spec-row"><span class="spec-k">Programming</span><span class="spec-v">Cirq / OpenFermion</span></div> |
| </div> |
|
|
| |
| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">fSim Native Gate</div> |
| <div style="padding:8px;font-family:var(--mono);font-size:8px;color:var(--dim);line-height:1.8"> |
| <div style="color:var(--indigo);font-size:9px;margin-bottom:5px">fSim(θ, φ)</div> |
| <div>|00⟩ → |00⟩</div> |
| <div>|01⟩ → cos(θ)|01⟩ − i·sin(θ)|10⟩</div> |
| <div>|10⟩ → −i·sin(θ)|01⟩ + cos(θ)|10⟩</div> |
| <div>|11⟩ → e^(−iφ)|11⟩</div> |
| <div style="margin-top:6px;border-top:1px solid var(--dimmer);padding-top:5px"> |
| <div style="color:var(--mint)">θ=π/2: iSWAP limit</div> |
| <div style="color:var(--mint)">φ=π: CZ limit</div> |
| <div style="color:var(--gold)">Sycamore default: θ≈π/2, φ≈π/6</div> |
| <div style="margin-top:5px;color:var(--violet)">HIR use: fSim computes H·I product amplitude in a single 2Q gate</div> |
| </div> |
| </div> |
| </div> |
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| |
| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">Qubit Budget Analysis</div> |
| <div style="padding:2px 0"> |
| <div class="qb-row"> |
| <div> |
| <div class="qb-name">Full Q16.16 register file</div> |
| <div class="qb-note">15 write regs × 32 bits</div> |
| </div> |
| <div style="text-align:right"> |
| <div class="qb-count qb-over">480</div> |
| <div class="qb-note qb-over">9× over Sycamore</div> |
| </div> |
| </div> |
| <div class="qb-row"> |
| <div> |
| <div class="qb-name">18 ACTION_FLAGS bits</div> |
| <div class="qb-note">basis encoding</div> |
| </div> |
| <div style="text-align:right"> |
| <div class="qb-count qb-feasible">18</div> |
| <div class="qb-note qb-feasible">fits in Sycamore</div> |
| </div> |
| </div> |
| <div class="qb-row"> |
| <div> |
| <div class="qb-name">Amplitude resonance circuit</div> |
| <div class="qb-note">H,I,R + 3 ancilla + output</div> |
| </div> |
| <div style="text-align:right"> |
| <div class="qb-count qb-feasible">7</div> |
| <div class="qb-note qb-feasible">ideal on Sycamore</div> |
| </div> |
| </div> |
| <div class="qb-row"> |
| <div> |
| <div class="qb-name">VQE config optimizer</div> |
| <div class="qb-note">31 param ansatz</div> |
| </div> |
| <div style="text-align:right"> |
| <div class="qb-count qb-feasible">15–20</div> |
| <div class="qb-note qb-feasible">HEA ansatz</div> |
| </div> |
| </div> |
| <div class="qb-row"> |
| <div> |
| <div class="qb-name">Grover batch search</div> |
| <div class="qb-note">N=1024 packets (2^10)</div> |
| </div> |
| <div style="text-align:right"> |
| <div class="qb-count qb-warn">53</div> |
| <div class="qb-note qb-warn">depth exceeds T₁</div> |
| </div> |
| </div> |
| <div class="qb-row"> |
| <div> |
| <div class="qb-name">QRAM memory recall</div> |
| <div class="qb-note">N=2^k address + payload</div> |
| </div> |
| <div style="text-align:right"> |
| <div class="qb-count qb-over">∞</div> |
| <div class="qb-note qb-over">QRAM not physical</div> |
| </div> |
| </div> |
| </div> |
| </div> |
|
|
| |
| <div class="panel"> |
| <div class="pt">Implementation Ladder</div> |
| <div style="padding:7px"> |
| <div class="impl-row"> |
| <div class="impl-v iv-nisq">NISQ — Sycamore Today</div> |
| <div class="impl-body">7-qubit amplitude resonance circuit · VQE config optimization · Sigmoid Ry rotation · Classical safety wrapper · Single-packet H/I/R amplitude encoding</div> |
| </div> |
| <div class="impl-row"> |
| <div class="impl-v iv-ft">Near-term fault-tolerant</div> |
| <div class="impl-body">Surface code · ~100 logical qubits · Grover over N~100 batch · Quantum walk over semantic memory graph · Quantum phase estimation for stability S</div> |
| </div> |
| <div class="impl-row"> |
| <div class="impl-v iv-future">Long-term (1000+ logical qubits)</div> |
| <div class="impl-body">QRAM-based batch recall · Full Q16.16 arithmetic in quantum circuits · Quantum simulation of degradation dynamics Θ → Hamiltonian · HHL for pressure field linear systems</div> |
| </div> |
| </div> |
| </div> |
| </div> |
|
|
| |
| <div> |
|
|
| |
| <div style="margin-bottom:10px"> |
| <div style="font-family:var(--mono);font-size:9px;letter-spacing:2px;color:var(--indigo);text-align:center;margin-bottom:7px;text-transform:uppercase">⬡ Hybrid Classical/Quantum Architecture</div> |
| <div class="hybrid-layers"> |
| <div class="hl hl-c"> |
| <div class="hl-badge">CLASSICAL · MANDATORY</div> |
| <div class="hl-label">Classical Safety Wrapper</div> |
| <div class="hl-sub">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</div> |
| </div> |
| <div class="hl-arr">↓ only if all hard-zero checks pass</div> |
| <div class="hl hl-q"> |
| <div class="hl-badge">QUANTUM · SYCAMORE</div> |
| <div class="hl-label">Quantum Resonance Core</div> |
| <div class="hl-sub">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</div> |
| </div> |
| <div class="hl-arr">↓ measurement result → classical comparison</div> |
| <div class="hl hl-qc"> |
| <div class="hl-badge">QUANTUM/CLASSICAL</div> |
| <div class="hl-label">VQE Configuration Layer</div> |
| <div class="hl-sub">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)</div> |
| </div> |
| <div class="hl-arr">↓ Rn ≥ 0.75 → GREEN · Rn ≥ 0.50 → YELLOW · else RED</div> |
| <div class="hl hl-m"> |
| <div class="hl-badge">CLASSICAL · MANDATORY</div> |
| <div class="hl-label">Audit Digest + Action Dispatch</div> |
| <div class="hl-sub">SHA-256 digest written · Measurement result + gate scores stored in AuditRecord · Permission state → host · RED = preserve + escalate (no quantum circuit for RED path)</div> |
| </div> |
| </div> |
| </div> |
|
|
| |
| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">Sycamore 53-Qubit Grid — HIR Resonance Circuit Placement</div> |
| <div class="chip-grid"> |
| |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-used-h pulsing-qubit"><div class="q-label">H<br>qubit</div></div> |
| <div class="qbit q-used-anc"><div class="q-label">F<br>anc</div></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>0</div></div> |
| <div class="qbit q-used-i pulsing-qubit"><div class="q-label">I<br>qubit</div></div> |
| <div class="qbit q-used-anc"><div class="q-label">C<br>anc</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>1</div></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>2</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>3</div></div> |
| <div class="qbit q-used-r pulsing-qubit"><div class="q-label">R<br>qubit</div></div> |
| <div class="qbit q-used-out"><div class="q-label">Rn<br>out</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>4</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>5</div></div> |
| <div class="qbit q-dead"></div> |
| |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>6</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>7</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>8</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>9</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>10</div></div> |
| <div class="qbit q-dead"></div> |
| |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>11</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-used-vqe"><div class="q-label">VQE<br>12</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-dead"></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-free"><div class="q-label">free</div></div> |
| <div class="qbit q-dead"></div> |
| </div> |
| <div style="padding:0 10px 8px;display:flex;gap:10px;flex-wrap:wrap;font-family:var(--mono);font-size:7.5px"> |
| <span style="color:var(--mint)">■ H gate qubit</span> |
| <span style="color:var(--sky)">■ I gate qubit</span> |
| <span style="color:var(--violet)">■ R gate qubit</span> |
| <span style="color:var(--gold)">■ Fidelity/Cohesion ancilla</span> |
| <span style="color:var(--rose)">■ Rn output qubit</span> |
| <span style="color:var(--indigo)">■ VQE ansatz (13 qubits)</span> |
| <span style="color:var(--dim)">□ free</span> |
| </div> |
| </div> |
|
|
| |
| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">7-Qubit Amplitude Resonance Circuit — Single Evidence Packet</div> |
| <div class="circuit"> |
| <div class="circuit-title">State prep + fSim entanglement → Rn measurement (~8 two-qubit gates, ~100ns, within T₁)</div> |
| |
| <div class="circuit-row"> |
| <span class="q-wire-label" style="color:var(--mint)">q_H</span> |
| <span class="q-wire" style="flex:0.5"></span> |
| <span class="gate-box g-ry">Ry(2·arcsin(√H))</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-ctrl">ctrl</span> |
| <span class="q-wire"></span> |
| <span class="circuit-comment">H score → amplitude</span> |
| </div> |
|
|
| <div class="circuit-row"> |
| <span class="q-wire-label" style="color:var(--sky)">q_I</span> |
| <span class="q-wire" style="flex:0.5"></span> |
| <span class="gate-box g-ry">Ry(2·arcsin(√I))</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="circuit-comment">I score → amplitude</span> |
| </div> |
|
|
| <div class="circuit-row"> |
| <span class="q-wire-label" style="color:var(--violet)">q_R</span> |
| <span class="q-wire" style="flex:0.5"></span> |
| <span class="gate-box g-ry">Ry(2·arcsin(√R))</span> |
| <span class="q-wire"></span> |
| <span class="q-wire" style="flex:0.8"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="circuit-comment">R score → amplitude</span> |
| </div> |
|
|
| <div class="circuit-row"> |
| <span class="q-wire-label" style="color:var(--gold)">q_F(anc)</span> |
| <span class="q-wire" style="flex:0.5"></span> |
| <span class="gate-box g-h">|0⟩</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="circuit-comment">Fidelity = √(H·I)</span> |
| </div> |
|
|
| <div class="circuit-row"> |
| <span class="q-wire-label" style="color:var(--gold)">q_C(anc)</span> |
| <span class="q-wire" style="flex:0.5"></span> |
| <span class="gate-box g-h">|0⟩</span> |
| <span class="q-wire"></span> |
| <span class="q-wire" style="flex:0.8"></span> |
| <span class="gate-box g-fsim">fSim</span> |
| <span class="q-wire"></span> |
| <span class="circuit-comment">Cohesion = √(R·I)</span> |
| </div> |
|
|
| <div class="circuit-row"> |
| <span class="q-wire-label" style="color:var(--rose)">q_Rn(out)</span> |
| <span class="q-wire" style="flex:0.5"></span> |
| <span class="gate-box g-h">|0⟩</span> |
| <span class="q-wire"></span> |
| <span class="q-wire" style="flex:1.6"></span> |
| <span class="gate-box g-ctrl">fSim</span> |
| <span class="q-wire"></span> |
| <span class="gate-box g-meas">M</span> |
| <span class="circuit-comment">P(|0⟩) = Rn²</span> |
| </div> |
|
|
| <div style="margin-top:8px;font-family:var(--mono);font-size:8px;color:var(--dim);border-top:1px solid var(--dimmer);padding-top:6px;line-height:1.7"> |
| <span style="color:var(--gold)">Hard-zero pre-check (classical):</span> If ANY of {domination_pattern, consent_violated, schema_invalid, invariant_violated} = 1 → bypass circuit entirely → classical RED/HALT |
| <br> |
| <span style="color:var(--violet)">Measurement:</span> P(q_Rn=|0⟩) = Rn² · repeat N_shots times · estimate Rn = √(count_0 / N_shots) |
| <br> |
| <span style="color:var(--indigo)">Gate count:</span> 3 Ry (single-qubit) + 5 fSim (two-qubit) · Total circuit time ≈ 3×25ns + 5×12ns ≈ 135ns ≪ T₁ ~15μs |
| </div> |
| </div> |
| </div> |
|
|
| |
| <div style="display:grid;grid-template-columns:1fr 1fr;gap:8px;margin-bottom:10px"> |
|
|
| <div class="algo-card ac-vqe"> |
| <span class="algo-status st-nisq">NISQ ✓</span> |
| <div class="algo-title">VQE — Config Weight Optimization</div> |
| <div class="algo-sub">Variational Quantum Eigensolver</div> |
| <div class="algo-body"> |
| 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). |
| </div> |
| <div class="algo-speedup sp-cond">Quadratic in precision. Classical competitive for small param count.</div> |
| </div> |
|
|
| <div class="algo-card ac-amp"> |
| <span class="algo-status st-nisq">NISQ ✓</span> |
| <div class="algo-title">QAE — Resonance Estimation</div> |
| <div class="algo-sub">Quantum Amplitude Estimation</div> |
| <div class="algo-body"> |
| 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. |
| </div> |
| <div class="algo-speedup sp-yes">O(1/ε) vs O(1/ε²) classical — quadratic precision speedup</div> |
| </div> |
|
|
| <div class="algo-card ac-grover"> |
| <span class="algo-status st-ft">Fault-tolerant only</span> |
| <div class="algo-title">Grover — Batch Packet Search</div> |
| <div class="algo-sub">Grover's Algorithm / Amplitude Amplification</div> |
| <div class="algo-body"> |
| 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). |
| </div> |
| <div class="algo-speedup sp-cond">O(√N) — quadratic. Blocked by decoherence on NISQ.</div> |
| </div> |
|
|
| <div class="algo-card ac-walk"> |
| <span class="algo-status st-ft">Fault-tolerant only</span> |
| <div class="algo-title">Quantum Walk — Semantic Memory Graph</div> |
| <div class="algo-sub">Quantum Walk / Szegedy Walk</div> |
| <div class="algo-body"> |
| 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. |
| </div> |
| <div class="algo-speedup sp-cond">O(√N) graph exploration. Requires ~log₂(N) + payload qubits.</div> |
| </div> |
|
|
| <div class="algo-card ac-qram"> |
| <span class="algo-status st-theory">Theoretical only</span> |
| <div class="algo-title">QRAM — Quantum Memory Recall</div> |
| <div class="algo-sub">Quantum Random Access Memory</div> |
| <div class="algo-body"> |
| 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. |
| </div> |
| <div class="algo-speedup sp-no">Theoretical. No physical QRAM in existence.</div> |
| </div> |
|
|
| <div class="algo-card ac-tension"> |
| <span class="algo-status st-no">Blocked</span> |
| <div class="algo-title">Σ — Sigmoid Repair Gate</div> |
| <div class="algo-sub">Θ = σ(Θ_base + θ_C·C + θ_E·E − θ_K·K)</div> |
| <div class="algo-body"> |
| 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. |
| </div> |
| <div class="algo-speedup sp-cond">Natural quantum encoding. No speedup vs classical for single evaluation.</div> |
| </div> |
|
|
| </div> |
|
|
| |
| <div class="panel"> |
| <div class="pt">Classical / Quantum Boundary — Per Component</div> |
| <div class="boundary"> |
| <div class="br" style="background:rgba(99,102,241,.06)"> |
| <div class="br-idx" style="font-size:7px;color:var(--dim)">—</div> |
| <div class="br-comp" style="color:var(--dim);font-size:8px">Component</div> |
| <div class="br-cls" style="color:var(--dim);font-size:8px">Layer</div> |
| <div class="br-reason" style="color:var(--dim);font-size:8px">Reason</div> |
| </div> |
| <div class="br"><div class="br-idx">1</div><div class="br-comp">Hard-zero safety invariants (INV 1–8)</div><div class="br-cls"><span class="cls-c">CLASSICAL</span></div><div class="br-reason">Must be deterministic. Superposition of "maybe domination" is architecturally prohibited.</div></div> |
| <div class="br"><div class="br-idx">2</div><div class="br-comp">ACTION_FLAGS bitfield (18 bits)</div><div class="br-cls"><span class="cls-h">HYBRID</span></div><div class="br-reason">Basis-encode as 18 qubits. Hard-zero flags measured classically first, then residual flags enter quantum circuit.</div></div> |
| <div class="br"><div class="br-idx">3</div><div class="br-comp">H, I, R gate scoring</div><div class="br-cls"><span class="cls-h">HYBRID</span></div><div class="br-reason">Score computation classical (linear penalty sums). Score encoding as Ry-rotated amplitude → quantum.</div></div> |
| <div class="br"><div class="br-idx">4</div><div class="br-comp">Fidelity = √(H·I)</div><div class="br-cls"><span class="cls-q">QUANTUM</span></div><div class="br-reason">fSim gate on q_H, q_I gives amplitude = √(H·I) in a single 2Q operation. Natural quantum computation.</div></div> |
| <div class="br"><div class="br-idx">5</div><div class="br-comp">Cohesion = √(R·I)</div><div class="br-cls"><span class="cls-q">QUANTUM</span></div><div class="br-reason">Same as Fidelity. fSim on q_R, q_I. Natural quantum computation.</div></div> |
| <div class="br"><div class="br-idx">6</div><div class="br-comp">Resonance Rn = √(F·C)</div><div class="br-cls"><span class="cls-q">QUANTUM</span></div><div class="br-reason">Born probability: P(q_Rn=|0⟩) = Rn². Resonance IS the quantum measurement probability. Not metaphor.</div></div> |
| <div class="br"><div class="br-idx">7</div><div class="br-comp">B = H+I+R+k(HI+HR+IR)</div><div class="br-cls"><span class="cls-h">HYBRID</span></div><div class="br-reason">ZZ correlators on Sycamore give ⟨Z_H·Z_I⟩ = HI term. VQE computes ⟨B⟩ as Hamiltonian expectation.</div></div> |
| <div class="br"><div class="br-idx">8</div><div class="br-comp">P = w_W·W + w_F·F + w_WF·WF</div><div class="br-cls"><span class="cls-c">CLASSICAL</span></div><div class="br-reason">W, F are environmental inputs from host agent. Classical scalars. No quantum advantage for linear combination.</div></div> |
| <div class="br"><div class="br-idx">9</div><div class="br-comp">S = A·B − P</div><div class="br-cls"><span class="cls-c">CLASSICAL</span></div><div class="br-reason">Subtract classical P from quantum-estimated ⟨B⟩. Result is classical scalar.</div></div> |
| <div class="br"><div class="br-idx">10</div><div class="br-comp">Repair gate Θ = σ(z)</div><div class="br-cls"><span class="cls-h">HYBRID</span></div><div class="br-reason">z is classically computed. Θ can be encoded as Ry rotation for downstream quantum operations.</div></div> |
| <div class="br"><div class="br-idx">11</div><div class="br-comp">Config weights (31 params)</div><div class="br-cls"><span class="cls-q">QUANTUM</span></div><div class="br-reason">VQE on 15-20 qubit HEA ansatz. NISQ-native. Quadratic speedup in precision for config optimization.</div></div> |
| <div class="br"><div class="br-idx">12</div><div class="br-comp">8 failure flag checks</div><div class="br-cls"><span class="cls-c">CLASSICAL</span></div><div class="br-reason">Deterministic boolean predicates. No quantum advantage. Must remain classical for safety guarantee.</div></div> |
| <div class="br"><div class="br-idx">13</div><div class="br-comp">Permission FSM (GREEN/YELLOW/RED)</div><div class="br-cls"><span class="cls-c">CLASSICAL</span></div><div class="br-reason">Threshold comparison on classical Rn estimate. FSM output is a definite classical state, not a superposition.</div></div> |
| <div class="br"><div class="br-idx">14</div><div class="br-comp">SHA-256 audit chain</div><div class="br-cls"><span class="cls-c">CLASSICAL</span></div><div class="br-reason">~2400 gates for quantum SHA-256. No known speedup. Exceeds Sycamore coherence by 6×. Stays classical.</div></div> |
| <div class="br"><div class="br-idx">15</div><div class="br-comp">Memory Recall Score batch</div><div class="br-cls"><span class="cls-q">QUANTUM</span></div><div class="br-reason">Grover/Tensor core on large N. Fault-tolerant quantum: O(√N). Current Sycamore: N≤64 before decoherence.</div></div> |
| </div> |
| </div> |
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| </div> |
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| <div> |
| |
| <div class="tension" style="margin-bottom:10px"> |
| <div class="tension-title">⚑ The Fundamental Tension</div> |
| <div class="tension-item"> |
| <span class="t-label">DETERMINISM vs SUPERPOSITION</span> |
| 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. |
| </div> |
| <div class="tension-item"> |
| <span class="t-label">AUDIT INTEGRITY vs DECOHERENCE</span> |
| 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. |
| </div> |
| <div class="tension-item"> |
| <span class="t-label">HARD ZEROS vs AMPLITUDES</span> |
| 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. |
| </div> |
| <div class="tension-item"> |
| <span class="t-label">READOUT DESTROYS STATE</span> |
| 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. |
| </div> |
| <div class="tension-item"> |
| <span class="t-label">COHERENCE vs CIRCUIT DEPTH</span> |
| 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. |
| </div> |
| </div> |
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| |
| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">Qubit Encodings — Bloch Sphere</div> |
| <div class="bloch-row"> |
| <div class="bloch"> |
| <div class="bloch-sphere" style="border-color:rgba(52,211,153,.4);background:radial-gradient(rgba(52,211,153,.08),transparent)"> |
| <svg viewBox="0 0 54 54" width="54" height="54"> |
| <ellipse cx="27" cy="27" rx="24" ry="10" fill="none" stroke="rgba(52,211,153,.2)" stroke-width="1"/> |
| <line x1="27" y1="3" x2="27" y2="51" stroke="rgba(255,255,255,.1)" stroke-width="1"/> |
| <line x1="27" y1="27" x2="27" y2="5" stroke="#34d399" stroke-width="2" stroke-linecap="round"/> |
| <circle cx="27" cy="5" r="2.5" fill="#34d399"/> |
| <text x="27" y="56" font-size="6" fill="#34d399" text-anchor="middle" font-family="mono">|0⟩</text> |
| <text x="27" y="2" font-size="6" fill="#34d399" text-anchor="middle" font-family="mono">|ψ_H⟩</text> |
| </svg> |
| </div> |
| <div class="bloch-label" style="color:var(--mint)">H qubit</div> |
| <div class="bloch-eq">Ry(2·arcsin(√H))|0⟩</div> |
| </div> |
| <div class="bloch"> |
| <div class="bloch-sphere" style="border-color:rgba(99,102,241,.4);background:radial-gradient(rgba(99,102,241,.08),transparent)"> |
| <svg viewBox="0 0 54 54" width="54" height="54"> |
| <ellipse cx="27" cy="27" rx="24" ry="10" fill="none" stroke="rgba(99,102,241,.2)" stroke-width="1"/> |
| <line x1="27" y1="3" x2="27" y2="51" stroke="rgba(255,255,255,.1)" stroke-width="1"/> |
| <line x1="27" y1="27" x2="39" y2="14" stroke="#6366f1" stroke-width="2" stroke-linecap="round"/> |
| <circle cx="39" cy="14" r="2.5" fill="#6366f1"/> |
| <text x="27" y="56" font-size="6" fill="#6366f1" text-anchor="middle" font-family="mono">Rn</text> |
| <text x="27" y="2" font-size="6" fill="#6366f1" text-anchor="middle" font-family="mono">|ψ_Rn⟩</text> |
| </svg> |
| </div> |
| <div class="bloch-label" style="color:var(--indigo)">Rn output</div> |
| <div class="bloch-eq">P(|0⟩) = Rn²</div> |
| </div> |
| <div class="bloch"> |
| <div class="bloch-sphere" style="border-color:rgba(244,114,182,.4);background:radial-gradient(rgba(244,114,182,.08),transparent)"> |
| <svg viewBox="0 0 54 54" width="54" height="54"> |
| <ellipse cx="27" cy="27" rx="24" ry="10" fill="none" stroke="rgba(244,114,182,.2)" stroke-width="1"/> |
| <line x1="27" y1="3" x2="27" y2="51" stroke="rgba(255,255,255,.1)" stroke-width="1"/> |
| <line x1="27" y1="27" x2="27" y2="51" stroke="#f472b6" stroke-width="2" stroke-linecap="round"/> |
| <circle cx="27" cy="51" r="2.5" fill="#f472b6"/> |
| <text x="27" y="56" font-size="6" fill="#f472b6" text-anchor="middle" font-family="mono">|1⟩</text> |
| <text x="27" y="2" font-size="6" fill="#f472b6" text-anchor="middle" font-family="mono">HARD RED</text> |
| </svg> |
| </div> |
| <div class="bloch-label" style="color:var(--rose)">Safety collapse</div> |
| <div class="bloch-eq">hard_red → |1⟩ classical</div> |
| </div> |
| </div> |
| </div> |
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| <div class="panel" style="margin-bottom:10px"> |
| <div class="pt">Quantum Identities</div> |
| <div style="padding:8px;font-family:var(--mono);font-size:8px;line-height:2;color:var(--dim)"> |
| <div><span style="color:var(--mint)">Rn</span> = P(|0…0⟩ after fSim) = Born probability</div> |
| <div><span style="color:var(--indigo)">1 − Rn</span> = P(decoherence) = physical pressure</div> |
| <div><span style="color:var(--violet)">fSim(π/2,φ)(|H⟩⊗|I⟩)</span> = amplitude √(H·I) in |00⟩</div> |
| <div><span style="color:var(--gold)">Ry(2·arcsin(√Θ))|0⟩</span> = repair gate in quantum</div> |
| <div><span style="color:var(--sky)">⟨Z_H Z_I⟩</span> = HI correlation = B interaction term</div> |
| <div style="margin-top:5px;border-top:1px solid var(--dimmer);padding-top:5px;color:var(--dim)"> |
| <span style="color:var(--rose)">SHA-256 depth</span>: ~2400 gates → P(clean) ≈ 5.5×10⁻⁶<br> |
| <span style="color:var(--rose)">Q16.16 full regfile</span>: 480 qubits → 9× Sycamore limit<br> |
| <span style="color:var(--mint)">7-qubit Rn circuit</span>: 135ns ≪ T₁ = 15,000ns → ✓ |
| </div> |
| </div> |
| </div> |
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| <div class="panel"> |
| <div class="pt">HIR Hamiltonian (VQE)</div> |
| <div style="padding:8px"> |
| <div style="font-family:var(--mono);font-size:8px;color:var(--dim);line-height:1.8;background:#020408;padding:7px;border-radius:3px"> |
| <div style="color:var(--violet)">H_HIR = </div> |
| <div style="color:var(--mint)"> − (Z_H + Z_I + Z_R)</div> |
| <div style="color:var(--indigo)"> − k(Z_HZ_I + Z_HZ_R + Z_IZ_R)</div> |
| <div style="color:var(--gold)"> + w_W·W + w_F·F_op + w_WF·WF_op</div> |
| <div style="color:var(--rose)"> + λ·penalty(hard_zeros)</div> |
| <div style="margin-top:5px;color:var(--dim);font-size:7.5px"> |
| Minimize ⟨ψ(θ)|H_HIR|ψ(θ)⟩<br> |
| θ* = optimal config weights<br> |
| VQE finds θ* that maximizes governance quality under observed pressure |
| </div> |
| </div> |
| </div> |
| </div> |
| </div> |
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| <div class="legend" style="max-width:1260px;margin:0 auto"> |
| <div class="leg-i"><div class="leg-d" style="background:var(--mint)"></div>H gate / quantum ✓</div> |
| <div class="leg-i"><div class="leg-d" style="background:var(--sky)"></div>I gate / hybrid</div> |
| <div class="leg-i"><div class="leg-d" style="background:var(--violet)"></div>R gate / resonance</div> |
| <div class="leg-i"><div class="leg-d" style="background:var(--indigo)"></div>VQE / quantum core</div> |
| <div class="leg-i"><div class="leg-d" style="background:var(--gold)"></div>Ancilla / config</div> |
| <div class="leg-i"><div class="leg-d" style="background:var(--rose)"></div>Classical safety / blocked</div> |
| <div class="leg-i"><div class="leg-d" style="background:var(--dim)"></div>Free qubit</div> |
| </div> |
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| <div style="text-align:center;margin-top:14px;font-family:var(--mono);font-size:8px;color:rgba(255,255,255,.1);letter-spacing:1px"> |
| Primordial HIR-SPU · Quantum Architecture Map (Theoretical) · Collin D. Weber · Google Sycamore · April 30, 2026 |
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