Algorithms — SCPN-Quantum-Control

Variational Algorithms

VQE Production

Variational Quantum Eigensolver with K_nm-informed ansätze. 0.05% ground state error on 4-qubit IBM hardware. COBYLA, SPSA, L-BFGS-B optimisers.

ADAPT-VQE Production

Adaptive circuit growth. Operator pool from XY generators. Gradient-driven gate selection minimises circuit depth while maintaining accuracy.

VarQITE Stable

Variational Quantum Imaginary Time Evolution. McLachlan variational principle. Converges to ground state without eigenvalue knowledge.

AVQDS Stable

Adaptive Variational Quantum Dynamics Solver. Real-time evolution with adaptive circuit depth. Tracks synchronisation order parameter R(t).

QSVT Experimental

Quantum Singular Value Transformation. Block-encoding of XY Hamiltonian. Optimal query complexity for time evolution.

Time Evolution

Trotter Decomposition Production

First and second-order Suzuki-Trotter. Configurable step count and ordering. Hardware-validated on IBM Heron r2 up to depth 770.

Floquet DTC Stable

Discrete Time Crystal simulation. Periodic driving of XY Hamiltonian. Subharmonic response detection. Many-body localisation analysis.

Open Quantum Systems

Lindblad Master Equation Production

Full Lindbladian evolution with configurable decay, dephasing, and jump operators. Models real hardware decoherence. Rust-accelerated operator construction.

MCWF Stable

Monte Carlo Wave Function method. Stochastic quantum trajectories with jump detection. Memory-efficient for large systems. Rust engine for sampling.

Trapped-Ion Noise Models Stable

Heating rate, motional dephasing, off-resonant coupling. Arbitrary trap topologies. Cross-platform comparison with superconducting results.

Error Mitigation

ZNE Production

Zero-Noise Extrapolation. Unitary folding with 4 extrapolation methods (linear, polynomial, exponential, Richardson). Hardware-validated.

PEC Production

Probabilistic Error Cancellation. Quasi-probability decomposition of noisy channels. Overhead scaling analysis included.

Dynamical Decoupling Stable

XY4, X2, CPMG pulse sequences. Inserted between Trotter steps. Suppresses low-frequency noise on idle qubits.

Z₂ Parity Stable

Symmetry-based error detection. XY Hamiltonian conserves total Z parity. Post-selection discards parity-violating shots.

Symmetry Verification Stable

Generalised symmetry-based post-selection. Applicable to any conserved quantity of the XY model.

Analysis & Diagnostics

3 Novel Synchronisation Witnesses

Correlation witness, Fiedler witness, topological witness. NISQ-ready formalism for detecting quantum synchronisation without full state tomography.

Persistent Homology

Topological data analysis of quantum states. Betti curves, persistence diagrams. Detects phase transitions in synchronisation landscapes.

OTOC Scrambling

Out-of-Time-Order Correlators. Information scrambling rate. Butterfly velocity. Chaos detection in coupled oscillator dynamics. 4.4× Rust acceleration.

Krylov Complexity

Operator growth in Krylov basis. Lanczos coefficients. Complexity saturation analysis. Distinguishes integrable from chaotic dynamics.

DLA Parity Theorem

Novel exact result: dim(DLA) = 2^2N−1 − 2 for the XY Hamiltonian. Closed-form, independently verified. Submitted for publication.

BKT Scaling

Berezinskii-Kosterlitz-Thouless finite-size scaling analysis. Critical coupling detection. Universal scaling collapse.

Quantum Error Correction

Toric Code Stable

2D toroidal stabiliser code. Anyonic excitations. Topological protection for quantum information stored in synchronised states.

Surface Code Stable

Planar code on arbitrary lattice topologies. Syndrome extraction. Minimum-weight perfect matching decoder.

UPDE Repetition Code Stable

16-layer SCPN protection scheme. Biological surface code analogy. Maps consciousness layers to QEC stabilisers.

Multiscale QEC New v0.9.5

Concatenated codes across 5 SCPN domains. Knill 2005 threshold. Syndrome flow analysis. Rust-accelerated decoding.

Code Example

# Kuramoto-to-quantum pipeline in 10 lines
from scpn_quantum_control.bridge import KnmCompiler
from scpn_quantum_control.phase import TrotterEvolution
from scpn_quantum_control.analysis import order_parameter

# Define coupling matrix (4 oscillators)
K = [[0, 1.2, 0.5, 0], [1.2, 0, 0.8, 0.3],
[0.5, 0.8, 0, 1.0], [0, 0.3, 1.0, 0]]
omega = [1.0, 1.5, 0.8, 1.2] # natural frequencies

# Compile to quantum circuit
compiler = KnmCompiler(K, omega)
H = compiler.hamiltonian() # XY Hamiltonian
circuit = TrotterEvolution(H, dt=0.1, steps=20).circuit()

# Measure synchronisation
R = order_parameter(circuit, shots=8192)
print(f"Order parameter R = {R:.4f}")