Phase 35 — Quantum-Classical Hybrid Computing & Variational Algorithms — Planning

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Phase 35 — Quantum-Classical Hybrid Computing & Variational Algorithms

Motivation

As ASI-Build matures through neuromorphic (Phase 34) and continual learning (Phase 33) capabilities, the next frontier is quantum-classical hybrid computing. NISQ-era quantum processors (Preskill 2018) offer potential speedups for optimization, sampling, and kernel evaluation — but only when tightly integrated with classical co-processors in variational loops. Phase 35 builds the infrastructure to construct, optimize, and execute quantum circuits within ASI-Build's existing pipeline, enabling quantum advantage estimation for specific sub-problems while maintaining full classical fallback.

Sub-Phase Roadmap

35.1 — QuantumCircuitBuilder

Programmable quantum circuit construction & compilation

Core capability: construct, optimize, and transpile parameterized quantum circuits to target hardware gate sets.

• Circuit DAG representation — gates as directed acyclic graph nodes with qubit-wire edges, enabling topological optimization passes (Iten et al. 2016)
• Universal gate decomposition — decompose arbitrary unitaries into {H, CNOT, Rz} or hardware-native sets via Solovay-Kitaev (Dawson & Nielsen 2006) or KAK decomposition
• Depth optimization — gate cancellation, commutation analysis, and template matching to minimize circuit depth
• Noise channel composition — Kraus operator representation of depolarizing, amplitude damping, and readout error channels (Nielsen & Chuang 2000, Ch. 8)
• Backend abstraction — unified interface to statevector, density matrix, and shot-based simulators with hardware provider plugins

References: Nielsen & Chuang (2000) Quantum Computation and Quantum Information; Preskill (2018) "Quantum Computing in the NISQ Era and Beyond"; Dawson & Nielsen (2006) "The Solovay-Kitaev Algorithm"; Iten et al. (2016) "Quantum Circuit Optimization"

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35.2 — VariationalOptimizer

Classical-quantum optimization loops for variational algorithms

Core capability: implement VQE, QAOA, and custom variational ansätze with robust classical optimization and barren plateau diagnostics.

• VQE energy surface — compute molecular Hamiltonian expectation values via Jordan-Wigner or Bravyi-Kitaev mappings (Peruzzo et al. 2014)
• QAOA circuit structure — alternating cost/mixer layers with tunable depth p (Farhi, Goldstone & Gutmann 2014)
• Parameter-shift rule — exact gradient computation for parameterized gates: ∂⟨O⟩/∂θ = [⟨O⟩(θ+π/2) − ⟨O⟩(θ−π/2)] / 2 (Schuld et al. 2019)
• Optimizer comparison — COBYLA (derivative-free), SPSA (stochastic perturbation), quantum natural gradient (Stokes et al. 2020)
• Barren plateau diagnostics — variance of gradient components as function of circuit depth and qubit count (McClean et al. 2018)

References: Peruzzo et al. (2014) "A Variational Eigenvalue Solver on a Photonic Quantum Processor"; Farhi, Goldstone & Gutmann (2014) "A Quantum Approximate Optimization Algorithm"; McClean et al. (2018) "Barren Plateaus in Quantum Neural Network Training Landscapes"; Stokes et al. (2020) "Quantum Natural Gradient"

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35.3 — QuantumFeatureMap

Quantum kernel methods & data encoding for QML

Core capability: encode classical data into quantum states and compute kernel functions for classification and regression.

• Encoding strategies — amplitude encoding (exponential compression), angle/rotation encoding (linear depth), data re-uploading (Pérez-Salinas et al. 2020)
• Kernel Gram matrix — K(x_i, x_j) = |⟨φ(x_i)|φ(x_j)⟩|² computed via SWAP test or direct overlap (Havlíček et al. 2019)
• Expressibility quantification — frame potential comparison against Haar-random circuits (Sim et al. 2019)
• Entangling capacity — Meyer-Wallach measure and Scott entanglement quantification
• Classification pipeline — quantum kernel → classical SVM/GP for downstream prediction (Schuld & Killoran 2019)

References: Havlíček et al. (2019) "Supervised Learning with Quantum-Enhanced Feature Spaces"; Schuld & Killoran (2019) "Quantum Machine Learning in Feature Hilbert Spaces"; Huang et al. (2021) "Power of Data in Quantum Machine Learning"; Pérez-Salinas et al. (2020) "Data Re-uploading for a Universal Quantum Classifier"

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35.4 — EntanglementManager

Entanglement resource management & quantification

Core capability: prepare, quantify, verify, and distill entangled states as computational resources.

• Bell & GHZ preparation — deterministic preparation of maximally entangled states with verification circuits
• Entanglement measures — von Neumann entropy S(ρ_A) = −Tr(ρ_A log ρ_A), concurrence, negativity, and log-negativity (Plenio & Virmani 2007)
• Entanglement witnesses — construct observables W such that Tr(Wρ) < 0 implies entanglement (Terhal 2002)
• Distillation protocols — extract high-fidelity EPR pairs from noisy entangled states via LOCC (Bennett et al. 1996)
• Resource accounting — track entanglement budget across circuit execution, enforce monogamy constraints

References: Horodecki et al. (2009) "Quantum Entanglement" (Rev. Mod. Phys.); Plenio & Virmani (2007) "An Introduction to Entanglement Measures"; Terhal (2002) "Detecting Quantum Entanglement"

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35.5 — QuantumClassicalOrchestrator

Unified hybrid pipeline orchestration

Core capability: coordinate quantum and classical resources in a single execution pipeline with automatic advantage estimation.

• Qubit allocation — map logical qubits to physical qubits with connectivity-aware placement (Li et al. 2019 SABRE)
• Circuit routing — SWAP insertion for non-adjacent interactions, minimizing overhead depth
• Hybrid backpropagation — adjoint differentiation through quantum layers embedded in classical neural networks (Bergholm et al. 2018 PennyLane)
• Benchmark suite — standardized test cases: Max-Cut QAOA, H₂ VQE, quantum kernel SVM on synthetic datasets
• Advantage estimation — compare quantum vs. classical wall-clock time and solution quality with statistical confidence intervals

References: Bharti et al. (2022) "Noisy Intermediate-Scale Quantum Algorithms" (Rev. Mod. Phys.); Cerezo et al. (2021) "Variational Quantum Algorithms"; Li et al. (2019) "Tackling the Qubit Mapping Problem with SABRE"

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Dependency Graph

35.1 QuantumCircuitBuilder
 ├──▶ 35.2 VariationalOptimizer (circuit construction)
 ├──▶ 35.3 QuantumFeatureMap (encoding circuits)
 └──▶ 35.4 EntanglementManager (entangled state prep)
35.2 ──▶ 35.5 QuantumClassicalOrchestrator
35.3 ──▶ 35.5
35.4 ──▶ 35.5

Integration Points with Prior Phases

• Phase 34 (Neuromorphic): Spiking neural networks as classical co-processors in hybrid loops
• Phase 33 (Continual Learning): Catastrophic forgetting prevention for quantum-trained model parameters
• Phase 20 (Reasoning): Quantum-enhanced combinatorial optimization for logical inference
• Phase 22 (Creative Intelligence): Quantum sampling for divergent generation

Success Criteria

• Construct and simulate circuits up to 30 qubits with < 1% gate error
• VQE converges to chemical accuracy (1.6 mHa) for H₂, LiH
• Quantum kernel achieves competitive accuracy on standard QML benchmarks
• Entanglement witness correctly identifies entangled vs separable states
• Orchestrator demonstrates measurable speedup on Max-Cut instances