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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

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
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

---

▍ 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_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 tuples).

NoiseModel

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

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.

---

▍ 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.

---

▍ 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

v8.1.6

• 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 <jtatopenn@libero.it> — Dense Evolution

Full text: LICENSE.md

---

_{© 2026 Salvatore Pennacchio — Dense Evolution}