dense-evolution 8.1.9

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

---

▍ 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 8 panels per simulation run, directly inside Google Colab or Jupyter.

---

▍ Install

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 .

---

▍ Quick Start

from dense_evolution import DenseSVSimulator, QASMParser

# parse any OpenQASM 2.0 / 3.0 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)

probs = sim.get_probabilities()
sv    = sim.get_statevector()

Dashboard (Colab / Jupyter):

import dash
from IPython.display import display, clear_output

clear_output()
display(dash.dashboard_unificata)

Anti-OOM for large circuits:

from dense_evolution import Chunk

sim = Chunk(27)                                    # logical 27 qubits
circuit_ops = [['h', i] for i in range(27)]
sim.run_chunk(circuit_ops, chunk_size_gates=500)   # SafeMemoryGuard active

---

▍ Architecture

dense_evolution/
├── registry.py     hardware detection · JAX/CuPy/NumPy flags · NoiseModel (Kraus channels)
├── gates.py        GATES{} · PARAMETRIC_GATES{} · GATE_IDS{}
├── healing.py      predictive state engine · Phi_AB · vettore dinamico · MemoryReflectionEngine
├── parser.py       QASMParser · QASMCircuit · OpenQASM 2.0 / 3.0
├── compiler.py     QuantumTranspiler · _apply_gate_fast_step (jit) · gate decomposition
├── chunk.py        SafeMemoryGuard · MemoryChunker · CircuitChunker · Chunk (Anti-OOM)
├── simulator.py    DenseSVSimulator · run_parametric_batch_jit · vmap batch VQE
└── dash.py         ipywidgets dashboard · VQE engine · QM/MM · MD simulation · 3D wavefunction

ia_utils/
└── vector_healing.py   median_healing · enhanced_dense_healing_hybrid (NaN/Inf-safe, lazy JAX import)

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()

---

▍ Core Features

Feature	Detail
Linear Kernel Fusion	Stride-sliced tensor ops via JAX XLA — zero Kronecker matrices
Parametric Batch JIT	run_parametric_batch_jit() evaluates full parameter grids in one jax.vmap + jax.jit call
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 · positional parameter injection into any OpenQASM 2.0 circuit
Anti-OOM Engine	SafeMemoryGuard blocks execution before JAX raises RESOURCE_EXHAUSTED
Predictive Healing	healing.py — Φ_AB alignment, dynamic vector, Σ-sync, MemoryReflectionEngine
Vector Sequence Healing	ia_utils/ — median_healing, enhanced_dense_healing_hybrid — NaN/Inf-safe, lazy JAX import
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

---

▍ Scientific Validation & Applications

To demonstrate the numerical accuracy and stability of Dense Evolution, the simulator was stress-tested across 3,500 continuous spatial sampling points to compute the Silicon Dimer (Si2) Dissociation Curve via Variational Quantum Eigensolver (VQE).

• Physical Accuracy: The simulation successfully maps the exact Born-Oppenheimer Potential Energy Curve (PEC), capturing the deep quantum ground state bound minimum at ~3.55 Å with negative total energy, before converging asymptotically toward full molecular dissociation.
• Numerical Precision: Calculations are locked at Double Precision (float64), proving the simulator's resilience against cumulative machine epsilon errors (~ 1.11 × 10⁻¹⁶) across thousands of sequential circuit executions.
• Run this molecular experiment instantly on Google Colab Free Tier: Open Notebook on Google Colab

---

============================================================
🔬 MOLECULAR VQE: EXACT POTENTIAL ENERGY CURVE (PEC)
============================================================
Distanza R: 1.200 Å | Energia Totale Molecola: +155.761158 eV
Distanza R: 1.671 Å | Energia Totale Molecola: +34.372692 eV
Distanza R: 2.142 Å | Energia Totale Molecola: +6.583098 eV
Distanza R: 2.614 Å | Energia Totale Molecola: +0.727422 eV
Distanza R: 3.085 Å | Energia Totale Molecola: -0.253226 eV
Distanza R: 3.557 Å | Energia Totale Molecola: -0.273498 eV
Distanza R: 4.028 Å | Energia Totale Molecola: -0.170948 eV
Distanza R: 4.500 Å | Energia Totale Molecola: -0.093048 eV

Variational Quantum Chemistry Plot

Below is the physical validation plot showing the Born-Oppenheimer potential energy curve:

👉 For the full suite of physical benchmarks, including the Transverse Field Ising Model (TFIM) and Phase Transition mappings, visit the main Dense-Evolution-Ising-Tests repository. You can also view the raw script for this specific molecular run here.

---

▍ API Reference

DenseSVSimulator

sim = DenseSVSimulator(
    n_qubits   : int,
    use_gpu    : bool = False,
    use_float32: bool = False,
)

Method	Description
set_initial_state(state=None)	Reset to |0⟩ⁿ or inject custom statevector
run_circuit(circuit, transpile=True)	Plain (non-JIT) gate execution — takes the tuple format below
run_circuit_jit_beast_mode(circuit)	JIT-compiled gate execution — primary execution path
run_circuit_with_chunking(circuit, chunk_size=500)	Chunked execution for long circuits
run_parametric_batch_jit(base_circuit, parameter_batch)	vmap over parameter grid — returns full batch of statevectors
get_probabilities() → np.ndarray	|ψ_i|² for all basis states
get_statevector() → np.ndarray	Full complex statevector
measure(qubit_idx) → int	Projective measurement with state collapse
memory_mb() → float	Current RAM usage in MB
apply_gate_1q(gate, qubit)	Apply arbitrary 2×2 unitary
apply_gate_2q(gate, q1, q2)	Apply arbitrary 4×4 unitary

QASMParser

parser  = QASMParser()
circuit = parser.parse(qasm_str)   # → QASMCircuit
valid, msg = parser.validate(circuit)

QASMCircuit fields: n_qubits, n_cbits, ops (list of gate dicts, e.g. {'name': 'h', 'qubits': [0], 'params': []}). Use circuit.to_tuples() to convert ops to the (name, qubit0[, qubit1, ...][, param0, ...]) tuple format that run_circuit / run_circuit_jit_beast_mode expect — don't build that format by hand.

NoiseModel

noise = NoiseModel()
noise.apply_to_sv(sv, n=4, model='depolarizing', p=0.01, rng=rng)
desc  = NoiseModel.kraus_description('amplitude_damping')

End-to-end: parse → run → apply noise

parser  = QASMParser()
circuit = parser.parse(qasm_str)                  # → QASMCircuit
sim     = DenseSVSimulator(n_qubits=circuit.n_qubits)
sim.run_circuit(circuit.to_tuples())               # dicts -> tuples, then execute

sv_noisy = NoiseModel().apply_to_sv(
    sim.get_statevector(), n=circuit.n_qubits, model='depolarizing', p=0.01,
    rng=np.random.default_rng(42),
)

Chunk (Anti-OOM)

sim = Chunk(
    n_qubits         : int,
    chunk_size_gates : int   = 500,
    memory_threshold : float = 0.15,   # block below 15% free RAM
    use_gpu          : bool  = False,
    use_float32      : bool  = False,
)
sim.run_chunk(circuit, chunk_size_gates=500)

Backward-compatibility aliases: chunk1 = MemoryChunker, chunk2 = Chunk, Chunk2Incrociato = Chunk.

ia_utils.vector_healing

from ia_utils.vector_healing import median_healing, enhanced_dense_healing_hybrid

healed, radius   = median_healing(vettori, radius_baseline=None)
healed, metadata = enhanced_dense_healing_hybrid(vettori, radius_baseline=None, median_fallback_threshold=0.1)

See IA Utils — Vector Sequence Healing above for details.

---

▍ Gate Library

Fixed gates (no parameters):

Gate	Symbol	Gate	Symbol
h	Hadamard	x	Pauli-X
y	Pauli-Y	z	Pauli-Z
s	S gate	sdg	S† gate
t	T gate	tdg	T† gate
sx	√X gate	id	Identity
cx	CNOT	cz	CZ
cy	CY	swap	SWAP
iswap	iSWAP	ecr	ECR
ccx	Toffoli

Parametric gates:

Gate	Parameters	Description
rx(θ)	θ	X-rotation
ry(θ)	θ	Y-rotation
rz(θ)	θ	Z-rotation
p(λ)	λ	Phase gate
u1(λ)	λ	U1 (≡ p)
u2(φ, λ)	φ, λ	U2 rotation
u3(θ, φ, λ)	θ, φ, λ	Generic single-qubit
cp(λ, ctrl, tgt)	λ	Controlled-Phase
crz(λ, ctrl, tgt)	λ	Controlled-RZ

---

▍ Noise Models

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

Model	Kraus operators	Physical process
ideal	I	Noiseless
depolarizing	{√(1−p)I, √(p/3)X, √(p/3)Y, √(p/3)Z}	Isotropic Pauli error
amplitude_damping	{K₀=diag(1,√(1−γ)), K₁=[[0,√γ],[0,0]]}	T₁ energy relaxation
phase_damping	{K₀, K₁}	T₂ dephasing
bitflip	{√(1−p)I, √p·X}	Bit flip σₓ
combined	depolarizing(p/2) ∘ amplitude_damping(p/3)	Worst-case NISQ

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

---

▍ Mitigation & Predictive Healing

Active error tracking and stabilization integrated natively into the simulation runtime via healing.py.

Model	Operators	Description
dephasing_tracking	Δ_pre_emp ∘ Σ	Predictive deviation vs ideal eigenstate
phi_ab_alignment	Φ_AB(state_A, state_B, ipg)	Semantic + coherence alignment between two quantum states
vettore_dinamico	V_din = K · log(E_B/E_A) · Φ_AB	Log-differential energetic evolution vector
kappa_stabilization	κ-strength routine	Proactive statevector profile shielding
richardson_integration	{λ₁=1.0, λ₂=2.0}	Dual-point zero-noise trajectory approximation

All core functions compiled via @jax.jit. Event history managed by MemoryReflectionEngine with JAX Zero-Drift spectral aggregation.

---

▍ IA Utils — Vector Sequence Healing

ia_utils/vector_healing.py — standalone module for cleaning sequences of vectors (e.g. hidden states / embeddings) that may contain NaN or Inf entries. Both functions preprocess the input (Inf → NaN → column-mean imputation) before healing, so corrupted values never propagate into the output.

Function	Approach	Returns
median_healing(vettori, radius_baseline=None)	scipy.ndimage.median_filter, dynamic radius min(20, max(3, n // 3))	(healed: np.ndarray, radius: int)
enhanced_dense_healing_hybrid(vettori, radius_baseline=None, median_fallback_threshold=0.1)	Blends the dense_evolution.healing Φ-trigger logic with a median fallback, decided per-step	(healed: np.ndarray, metadata: dict)

enhanced_dense_healing_hybrid metadata:

Key	Type	Description
fallback_triggered	bool	True if the median fallback or dense blending fired at least once
adaptive_radius_used	int	Baseline radius actually applied
reconstruction_error	float	Mean norm of the correction applied vs. the sanitized input

import numpy as np
from ia_utils.vector_healing import median_healing, enhanced_dense_healing_hybrid

vettori = np.random.default_rng(0).normal(size=(50, 128))
vettori[10, 3] = np.nan          # simulate a corrupted hidden state
vettori[30, 7] = np.inf

healed, radius = median_healing(vettori)

healed_hybrid, meta = enhanced_dense_healing_hybrid(vettori)
print(meta)
# {'fallback_triggered': True, 'adaptive_radius_used': 16, 'reconstruction_error': 11.48}

jax is imported lazily inside enhanced_dense_healing_hybrid — median_healing and the module import itself work without the [jax] extra installed; only calling enhanced_dense_healing_hybrid requires it.

---

▍ Anti-OOM Chunk Engine

All operations parcellized dynamically using a 4-layer architectural shield.

Layer	Class	Role
1	SafeMemoryGuard	Pre-allocation RAM check — blocks before JAX raises RESOURCE_EXHAUSTED
2	MemoryChunker	Geometry calculator — computes num_chunks, chunk_dim, chunk_size_bits from available RAM without any JAX allocation
3	CircuitChunker	Per-slice execution — SafeMemoryGuard fires before every gate-slice dispatch
4	Chunk	Top-level wrapper — logical n_qubits decoupled from physical allocation at safe_qubits

Benchmark vs PennyLane — Windows CPU (8 GB RAM)

Dense Evolution maintains constant ~2 GB RAM at any qubit count via dynamic chunking. PennyLane allocates the full statevector — OOM beyond 26q.

Qubits	Hilbert Space	PennyLane	PennyLane RAM	Dense Evolution	Dense RAM	Chunk Geometry
24	16,777,216	✅	307 MB	✅	516 MB	1× (2²⁷)
26	67,108,864	✅	1,074 MB	✅	2,050 MB	1× (2²⁷)
28	268,435,456	❌ OOM	—	✅	2,050 MB	2× (2²⁷)
30	1,073,741,824	❌ OOM	—	✅	2,048 MB	8× (2²⁷)
32	4,294,967,296	❌ OOM	—	✅	2,048 MB	32× (2²⁷)

from dense_evolution import Chunk

sim = Chunk(27)
sim.run_chunk([['h', i] for i in range(27)], chunk_size_gates=500)

print(sim)
# Chunk(n_qubits=27, safe_qubits=27, num_chunks=1,
#       chunk_size_bits=27, mem_per_chunk=2048.0 MB, ram_free=42.3%, has_jax=True)

---

▍ Benchmarks

Measured on Google Colab Free Tier (CPU runtime)

Metric	Value
Numerical drift (30-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
Anti-OOM latency reduction (static JIT cache)	−86.47%

---

▍ 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 ×3 · R7 Pearson heatmap
Fisica Stato	Bloch projection · Schmidt rank · coherence vector
Mosaico	2D probability density map up to 1008 qubits
VQE Results	6-subplot: 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

---

▍ 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:

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

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

---

▍ 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.

---

▍ Circuit Library (30+ presets)

All circuits 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

---

▍ Changelog

v8.1.9

• Fixed: ia_utils/vector_healing.py — enhanced_dense_healing_hybrid had an unreachable third branch (a dense/blend fallback): the underlying trigger signal from evaluate_phi_trigger is strictly binary (0.0/1.0), so the branch could never execute. Collapsed to the genuine 2-state logic (pass-through vs. median fallback); runtime output is unchanged since the branch never ran.
• Fixed: dashboard_core.py — run_simulation / run_vqe_telemetry mutated the process-wide JAX jax_enable_x64 flag without ever restoring it, so running one float32 simulation silently downgraded numerical precision for unrelated code later in the same process (e.g. the Vector Healing page, which sets no precision of its own). Both now save/restore the flag around their own execution.
• Docs: README's NoiseModel example called a nonexistent .apply() method with a wrong parameter name (n_qubits instead of n) — corrected to apply_to_sv(sv, n=..., ...). Documented QASMCircuit.to_tuples() and DenseSVSimulator.run_circuit, which already existed and work correctly but were never mentioned in the README.

v8.1.8

• Fixed: parser.py — controlled two-qubit gates (cx/cy/cz/cp/crz) parsed from QASM in the dashboard layer had control and target swapped relative to compiler.py's documented (gate, control, target) contract, breaking entanglement for circuits run through the dashboard. The core QASMCircuit.to_tuples() path was already correct.
• Fixed: parser.py — range syntax (q[0:3]) on single-qubit gates only applied to the first qubit in the range, silently dropping the rest. Now expands into one gate application per qubit, matching the parser's own documented contract.
• Fixed: from dense_evolution import Chunk raised ImportError — Chunk is now re-exported from the package root. Added get_probabilities()/get_statevector() to Chunk for parity with DenseSVSimulator.
• Removed: dense_evolution/test2.py and stress_test.py — byte-identical, assertion-free debug scripts that shipped inside every install with 0% test coverage. Their one real check (Kraus noise is genuinely stochastic across independent runs) is now a real regression test.

v8.1.7

• ia_utils/ — new package: median_healing, enhanced_dense_healing_hybrid for vector sequence healing (NaN/Inf-safe)
• jax import in ia_utils.vector_healing made lazy — importable without the [jax] extra
• Fixed reconstruction_error telemetry returning NaN when input contained NaN/Inf
• Added scipy to core dependencies (was used but undeclared)

v8.1.6

• Modular package structure (dense_evolution/ directory)
• Split registry.py, gates.py, healing.py, chunk.py into dedicated modules

v8.1.5

• chunk.py — SafeMemoryGuard: hard block at configurable free-RAM threshold (default 15%), soft warning at 2× threshold, gc.collect() before every check
• chunk.py — Chunk no longer subclasses DenseSVSimulator; inner simulator allocated at safe_qubits only — eliminates RESOURCE_EXHAUSTED on 28q–34q circuits
• chunk.py — CircuitChunker.split_circuit RAM-checks every gate-slice before dispatch
• chunk.py — MemoryChunker attributes (num_chunks, chunk_size_bits, dtype) forwarded as @property on Chunk for benchmark compatibility

v8.1.0

• healing.py — Predictive State Engine: calculate_phi_ab, calculate_vettore_dinamico, calculate_delta_preemp, evaluate_phi_trigger, calculate_jax_reflection — all @jax.jit
• MemoryReflectionEngine — event logging + JAX Zero-Drift spectral aggregation

v8.0.x

• run_parametric_batch_jit() — jax.vmap over full parameter grids in single XLA call
• run_circuit_jit_beast_mode() — static JIT compilation with QuantumTranspiler
• OpenQASM 2.0/3.0 dual-mode parser with paren-depth-aware expression splitting
• NoiseModel Kraus channels in registry.py

---

▍ 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 · ≤ 1,000 circuits/day · ≤ 10,000 shots/circuit
• Attribution required: © 2026 Salvatore Pennacchio <[e-mail]> — Dense Evolution

Full text: LICENSE.md

---

_{© 2026 Salvatore Pennacchio — Dense Evolution}