CHAOS - A Physics-Accurate Quantum Computing Simulator

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CHAOS is a multi-qubit quantum computing simulator built in Python. It is designed from the ground up to be physically accurate, modeling quantum phenomena like superposition and entanglement through a professional, state-vector-based architecture.

Vision & Philosophy
Core Architectural Pillars
Key Features
GPU Acceleration & Performance
Comprehensive Performance Benchmarks
Installation
Quick Start
Usage Guide
- Bell State Creation
- GHZ State Creation
Advanced Algorithms
API Reference
Testing
Contributing
License

Vision & Philosophy

In Greek mythology, Chaos is the primordial void from which the cosmos was born. This project embodies that spirit: it provides a foundational framework to simulate the probabilistic, indeterminate nature of quantum mechanics, from which definite, classical answers emerge upon measurement.

Unlike simpler simulators that manage qubits individually, CHAOS adopts the industry-standard approach used in professional and academic research, ensuring that its behavior correctly reflects the underlying mathematics of quantum mechanics.

Core Architectural Pillars

The simulator's accuracy and power rest on three fundamental pillars:

Global State Vector: The entire multi-qubit system is represented by a single, unified state vector of size 2^n (where n is the number of qubits). This is the only way to correctly capture system-wide correlations and entanglement.
Tensor Product Gate Application: Quantum gates are not applied to qubits in isolation. Instead, they are expanded into full-system operators using the tensor product (Kronecker product). For example, applying a Hadamard gate to the first of three qubits involves creating an H ⊗ I ⊗ I operator, which then acts on the entire state vector. This is computationally intensive but physically correct.
Probabilistic Measurement & State Collapse: Measurement is a probabilistic process based on the amplitudes of the state vector. When a qubit is measured, the system's state vector collapses into a new, valid state consistent with the measurement outcome, accurately modeling quantum mechanics.

Key Features

Core Capabilities

Stateful, Multi-Qubit Circuits: Create and manage quantum circuits with any number of qubits
Physics-Accurate Simulation: True state-vector representation with proper entanglement modeling
Real-Time State Visualization: Human-readable circuit state with automatic probability calculations
Probabilistic Measurement: Authentic quantum measurement with state collapse simulation

Advanced Visualization

Rich State Display: Comprehensive output showing:
- Individual qubit marginal probabilities
- System-wide entanglement detection (Entangled or Separable)
- Complete basis state probability distributions
- Circuit execution tracking and validation

Quantum Algorithm Library

Bell State Generator: Instant 2-qubit entanglement creation
GHZ State Constructor: Multi-qubit entanglement for 3+ qubits
Quantum Fourier Transform (QFT): Full implementation with inverse operations
Grover's Search Algorithm: Quadratic speedup for unstructured database search
Shor's Period-Finding: Core subroutine for quantum factorization

Performance & Accuracy

Tensor Product Operations: Industry-standard gate application using Kronecker products
Efficient State Management: Optimized memory usage for large quantum systems
GPU Acceleration: CuPy-powered computation for large-scale quantum circuits (20+ qubits)
Memory-Efficient Architecture: Direct state vector manipulation avoiding exponential matrix memory requirements
Numerical Precision: High-precision complex arithmetic for stable simulations
Validation Suite: Comprehensive test coverage ensuring algorithm correctness

GPU Acceleration & Performance

CHAOS achieves strong performance in large-scale quantum simulation through memory-efficient algorithms and GPU acceleration. The simulator successfully demonstrates 20+ qubit simulation capabilities.

The Scalability Problem

Traditional quantum simulators face an exponential memory barrier when applying quantum gates using the standard Kronecker product approach:

Traditional Approach (Limited to ~15 qubits):

# Traditional method: Build full system matrices
H = np.array([[1, 1], [1, -1]]) / sqrt(2)
I = np.eye(2)

# For n qubits, this creates 2^n × 2^n matrices
full_matrix = I
for i in range(total_qubits):
    if i == target_qubit:
        full_matrix = np.kron(full_matrix, H)  # Kronecker product
    else:
        full_matrix = np.kron(full_matrix, I)

# Memory explosion: 15 qubits = 32,768 × 32,768 matrix = 17GB
new_state = full_matrix @ state_vector  # Fails due to memory

Memory Requirements Comparison:

| Qubits | Traditional Matrix Memory | CHAOS Memory | Reduction Factor | |--------|--------------------------|--------------|------------------| | 10 | 16 MB | 8 KB | 2,000x | | 15 | 17 GB | 0.5 MB | 34,000x | | 20 | 16 TB | 16 MB | 1,000,000x |

CHAOS Approach: Direct State Manipulation

CHAOS bypasses matrix construction entirely through direct state vector manipulation:

# CHAOS method: Direct amplitude manipulation  
def _apply_gate_direct(self, gate_matrix, qubit_index):
    step = 2 ** qubit_index
    state_size = len(self.state_vector)
    
    # Extract gate matrix elements
    g00, g01 = gate_matrix[0, 0], gate_matrix[0, 1]
    g10, g11 = gate_matrix[1, 0], gate_matrix[1, 1]
    
    # Direct amplitude transformation without matrix explosion
    for i in range(0, state_size, 2 * step):
        for j in range(step):
            idx0 = i + j
            idx1 = i + j + step
            
            # Get current amplitudes
            amp0 = self.state_vector[idx0]
            amp1 = self.state_vector[idx1]
            
            # Apply 2x2 gate transformation directly
            self.state_vector[idx0] = g00 * amp0 + g01 * amp1
            self.state_vector[idx1] = g10 * amp0 + g11 * amp1

Performance Benchmarks

Tested on Google Colab (NVIDIA T4 GPU, 14.7GB Memory):

| Qubits | State Vector Size | Memory Usage | Execution Time | Status | |--------|------------------|--------------|----------------|---------| | 16 | 65,536 elements | 0.006 GB | 5.7 seconds | Success | | 17 | 131,072 elements | 0.012 GB | 11.8 seconds | Success | | 18 | 262,144 elements | 0.024 GB | 24.6 seconds | Success | | 19 | 524,288 elements | 0.024 GB | 3.2 minutes | Success | | 20 | 1,048,576 elements| 0.024 GB | 18.6 minutes | Success |

Achievement: 20-qubit quantum simulation with only 24MB memory usage

Technical Innovation

Memory Efficiency:

No matrix construction: Operations directly manipulate state amplitudes
In-place computation: Minimal memory allocation during gate operations
Optimized indexing: Efficient bit manipulation for qubit targeting
GPU memory management: CuPy handles large arrays with optimal memory patterns

Scalability Analysis:

Linear memory growth: O(2^n) state vector vs O(4^n) matrix approach
Practical limits: 25+ qubits achievable with 32GB GPU memory
Performance scaling: Execution time grows polynomially, not exponentially

Performance Visualization

Scalability Performance Analysis

Performance Scaling Analysis Detailed scaling analysis demonstrating successful 16-20 qubit simulation capabilities with memory usage remaining constant at 24MB, proving our architecture's practical viability for large-scale quantum computing.

Key Performance Insights:

Memory Efficiency: 1,000,000x improvement over traditional approaches
Scalability: 20-qubit simulation with only 24MB memory usage
Accessibility: Enables quantum algorithm research without specialized hardware

GPU Integration

CuPy Acceleration:

# O

Chaos

Install / Use

README