dense-evolution 8.0.9

Micro-optimized High-Performance NISQ Statevector Quantum Circuit Simulator (Hardware-Adaptive Integration of Native NumPy, CUDA-Accelerated CuPy, and Linear Kernel Fusion via JAX JIT/XLA Compilation)

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Dense Statevector Quantum Simulator · JAX XLA · NISQ · VQE · QML

    

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▍ What It Is

Dense Evolution is a high-performance statevector simulator engineered for deep NISQ circuits, VQE pipelines, and QML workloads. It eliminates Kronecker product overhead entirely via stride-sliced linear kernel fusion compiled through JAX XLA — keeping memory at the theoretical minimum of 2ⁿ × 16 bytes.

The integrated dash.py dashboard provides live ipywidgets telemetry across 6 quantum observables per simulation run, directly inside Google Colab or Jupyter.

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▍ Install

# core engine
pip install dense-evolution

# full stack: JAX · GPU · dashboard
pip install dense-evolution\\\[full]

# development
git clone https://github.com/tatopenn-cell/Dense-Evolution.git
cd Dense-Evolution \\\&\\\& pip install -e .\\\[full]

Google Colab (3 lines):

!git clone https://github.com/tatopenn-cell/Dense-Evolution.git
%cd Dense-Evolution
!pip install -e .

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▍ Quick Start

from dense\\\_evolution import DenseSVSimulator, QASMParser

# parse any OpenQASM 2.0 string
qasm = """
OPENQASM 2.0;
include "qelib1.inc";
qreg q\\\[3];
h q\\\[0];
cx q\\\[0], q\\\[1];
cx q\\\[1], q\\\[2];
"""

parser = QASMParser()
circuit = parser.parse(qasm)

sim = DenseSVSimulator(n\\\_qubits=3)
sim.run\\\_circuit\\\_jit\\\_beast\\\_mode(circuit.ops)

print(sim.get\\\_probabilities())   # \\\[0.5, 0, 0, 0, 0, 0, 0, 0.5]  — GHZ state
print(sim.memory\\\_mb())           # 0.000128 MB

Dashboard (Colab / Jupyter):

import dash
from IPython.display import display, clear\\\_output

clear\\\_output()
display(dash.dashboard\\\_unificata)

---

▍ Architecture

dense\\\_evolution/
├── registry.py       hardware detection · JAX / CuPy / NumPy capability flags
├── gates.py          GATES{} · PARAMETRIC\\\_GATES{} · GATE\\\_IDS{}
├── noise\\\_model.py    Kraus channels · stochastic trajectory engine
├── parser.py         QASMParser · QASMCircuit · OpenQASM 2.0 / 3.0
├── compiler.py       \\\_apply\\\_gate\\\_fast\\\_step (jit) · \\\_compile\\\_and\\\_run\\\_circuit\\\_jit
├── simulator.py      DenseSVSimulator · vmap batch VQE · chunked execution
└── dash.py           ipywidgets dashboard · VQE engine · MD simulation

Data flow per run:

▶ Run
 └─ core\\\_calcolo\\\_quantistico()          parse → JIT execute → apply noise
     ├─ ottimizza\\\_vqe()                 Hellmann-Feynman AD → ADAM → df\\\_vqe\\\_telemetry
     ├─ run\\\_md\\\_simulation\\\_dummy()       QM/MM dynamics → df\\\_md\\\_telemetry + Pearson matrix
     └─ build\\\_panel\\\_\\\*(res)              matplotlib figure → display()

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▍ Core Features

Feature	Detail
Linear Kernel Fusion	Stride-sliced tensor ops via JAX XLA — zero Kronecker matrices
Circuit Chunking	Fixed-size JIT blocks eliminate tracer overhead on 1000+ gate circuits
Kraus Noise Channels	depolarizing amplitude\\\_damping phase\\\_damping bitflip combined — stochastic, O(2ⁿ) cost
VQE + ADAM	Hellmann-Feynman gradient via JAX AD · positional parameter injection into any QASM 2.0
vmap Batch Sweep	run\\\_parametric\\\_batch\\\_jit() evaluates full parameter grids in one JIT call
Backend Agnostic	NumPy CPU · JAX XLA CPU/TPU · CuPy CUDA — runtime selection, zero code changes
Live Dashboard	8-panel ipywidgets telemetry: probability, VQE energy, entropy, purity, gradient, noise, θ-correction, Pearson heatmap

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▍ Benchmarks

Measured on Google Colab Free Tier (CPU runtime)

Metric	Value
Numerical drift (80-layer Ansatz, 1360 gates)	Δ = 1.11 × 10⁻¹⁶
Memory footprint @ 20q	32 MB (float64) · 16 MB (float32)
JIT compile overhead (first run)	< 400 ms
Gate throughput after warm-up	> 10⁶ gates/s (CPU)
Maximum tested qubits (Colab Free)	24q stable · 33q high-RAM runtime

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▍ Dashboard Panels

Panel	Contents
Overview	R0 header · R1 P(|n⟩) histogram + Top-12 states · R2 wavefunction helix 3D + metrics table · R3 noise analysis + shot histogram · R4–R6 VQE telemetry × 6 · R7 Pearson heatmap
Fisica Stato	Bloch projection · Schmidt rank · coherence vector
Mosaico 1008q	2D probability density map up to 1008 qubits
VQE Results	6-subplot telemetry: energy convergence, entropy, purity, ‖∇L‖, noise factor, θ-correction
MD Results	6-subplot MD telemetry + masked Pearson correlation heatmap
Performance	Gate throughput · JIT compile time · RAM usage

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▍ Circuit Library (30+ presets)

All circuits are stored as OpenQASM 2.0 strings in QASM\\\_LIBRARY.

Standard — Bell Φ⁺, QFT 4q/8q, Toffoli, Adder 2-bit, Deutsch-Jozsa, Bernstein-Vazirani
Algorithms — Grover 3q/4q, Simon 4q, Shor 15, HHL, QAOA Max-Cut 4q, QPE 5q, Quantum Walk, Teleportation, BB84
Topological — Anyonic Braiding 6q, Charge Pump 8q, Arecibo DeepField 16q Peptide / Biological — Furin RRAR 8q, Hemoglobin MVLSPADK 8q, Stress Tests — Hardware Stress, Quantum Supremacy, Interference Stress,

▍ VQE Engine

Positional parameter injection — QASMParser tokenizes all literals to 0.0 for JIT speed. VQE recovers parameters by:

1. counting parametric gates (rx ry rz p u1 cp crz) → n\\\_params
2. initializing θ ∈ ℝⁿ uniform in \\\[−π, π]
3. injecting θ\\\[i] sequentially by gate order in the AST via risolvi\\\_qasm()

Compatible with any custom OpenQASM 2.0 string without pre-labelling.

Gradient & update rule:

$$\frac{\partial E}{\partial \theta_i} = \langle\psi(\theta)|,\frac{\partial H}{\partial \theta_i},|\psi(\theta)\rangle \qquad \theta \leftarrow \theta - \frac{\alpha,\hat{m}_t}{\sqrt{\hat{v}_t}+\varepsilon}$$

Telemetry columns (→ df\\\_vqe\\\_telemetry):

Column	Unit	Description
VQE\\\_Energy	Ha	⟨ψ|H|ψ⟩
Entropy	bit	−Tr(ρ log₂ ρ)
Purity	—	Tr(ρ²) ∈ [1/d, 1]
Gradient	—	‖∇L‖ — barren plateau detection
Noise\\\_Factor	—	fidelity-derived noise proxy
Theta\\\_Correction	rad	ADAM step norm

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▍ Hamiltonian Library

Auto-filtered by qubit count to prevent shape mismatch.

Molecule	Qubits	Bond length	E₀ (Ha)
H₂	2	0.74 Å	−1.13
H₃⁺	3	0.85 Å	−1.28
LiH	4	1.40 Å	−2.31
H₂O	5	0.96 Å	−4.12

Custom: JSON array of diagonal eigenvalues, length 2^n\\\_qubits.

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▍ Noise Models

All channels applied as post-circuit Kraus operations on the full statevector.

Model	Kraus operators	Physical process
ideal	I	noiseless
depolarizing	{√(1−p)I, √(p/3)X,Y,Z}	isotropic Pauli error
amplitude\\\_damping	{K₀, K₁}	T₁ energy relaxation
phase\\\_damping	{K₀, K₁}	T₂ dephasing
bitflip	{√(1−p)I, √p·X}	bit flip σₓ
combined	depolarizing(p/2) ∘ amp_damp(p/3)	worst-case NISQ

Fidelity: Bhattacharyya F = Σᵢ √(pᵢqᵢ) and TVD = ½Σᵢ|pᵢ−qᵢ| computed on every noisy run.

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▍ Troubleshooting

Error	Cause	Fix
TypeError: cond branches must have equal output types	JAX dtype mismatch between 1q/2q branches	de.patch\\\_dense\\\_parametric(de.DenseSVSimulator) — runs automatically on import
VQE telemetry empty	VQE disabled or no parametric gates	Enable VQE Settings checkbox; use circuits with rx/ry/rz gates
Hamiltonian shape mismatch	JSON array length ≠ 2^n_qubits	Supply exactly 2^n values (e.g. 16 for 4q)
Barren plateau span not visible	< 3 consecutive epochs with ‖g‖ < 0.01·max‖g‖	Increase epochs or reduce learning rate
Dashboard blank in JupyterLab	Extension missing	jupyter labextension install @jupyter-widgets/jupyterlab-manager
Memory error on high-qubit circuits	2ⁿ × 16 bytes: 24q = 268 MB, 30q = 16 GB	Use use\\\_float32=True to halve; cap at 24q on standard runtimes

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### 🚀 Quantum Error Mitigation & Predictive Healing Engine

To significantly suppress non-unitary quantum noise and phase dephasing channels without the massive physical hardware overhead of standard Error Correction, this release introduces a high-performance, JAX-accelerated **Predictive Healing Engine** natively integrated into the simulation runtime.

Unlike static Zero-Noise Extrapolation (ZNE) protocols that can compound errors over deep variational quantum circuits, the new framework implements an active predictive mitigation topology controlled via a dynamic, multi-variable stabilization parameter ($\kappa$):

* ** Dephasing Tracking:** The engine monitors phase drift by calculating the predictive deviation ($$\Delta_{pre\_emp}$$) of the synchronization function ($\Sigma$) relative to the ideal target eigenstate.

* **Hardware-Adaptive $\kappa$-Stabilization:** Upon reaching the critical dephasing threshold, a calibrated learning routine dynamically scales the coherence strength ($\kappa$). This proactively shields the statevector profile *prior* to Richardson extrapolation.

* **Coupled Richardson Integration:** The healed quantum energy values are subsequently mapped to dual-point stretched noise density thresholds ($\lambda_1 = 1.0, \lambda_2 = 2.0$), stabilizing the final zero-noise trajectory approximation without creating non-linear numerical artifacts.

All computational cores—including spatial alignment tensors ($\Phi_{AB}$) and life-vector dynamics ($V_{vita}$)—are decorated with @jax.jit, triggering full **XLA Kernel Fusion** to execute mass-parallelized trajectory sweeps (over 10,000+ simultaneous simulation tracks) under a fraction of a second.

▍ License

Business Source License 1.1 — converts automatically to Apache 2.0 on 1 June 2029.

• Non-commercial use: unrestricted
• Commercial use: ≤ 24 allocated qubits · ≤ 1000 circuits/day · ≤ 10,000 shots/circuit
• Attribution required on all copies: © 2026 Salvatore Pennacchio <[e-mail]> — Dense Evolution

Full text: LICENSE.md

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_{© 2026 Salvatore Pennacchio — Dense Evolution v8.0.9}