Measurement-Based Quantum Computing

Loss-Tolerant CV Cluster-State Compiler

Graph state compiler for measurement-based quantum computing with continuous variables. Optimizes interferometer phases to maximize entanglement under fabrication tolerances with nullifier variance analysis and Monte Carlo sensitivity sweeps.

⟨δ²⟩ < 1
SNU Entanglement Witness
99.2%
Success Rate (σφ = 0.1°)
0.7 dB
Critical Loss/Layer
4-12
Mode Scalability

System Architecture

MBQC Pipeline

Squeezed Vacuum Sources

N single-mode squeezed states (6-7 dB)

Programmable Mesh

Clements/Reck interferometer (BS + φ)

CV Cluster State

Graph-encoded entanglement resource

Homodyne Measurement

Adaptive quadrature detection

Supported Graph Topologies

Square

4 modes

Hexagonal

7 modes

GHZ Rail

8 modes

Nullifier Definition

δj = pj - Σk Ajk xk

⟨δj²⟩ < 1 SNU indicates genuine multipartite entanglement

Interactive Design Tools

Comprehensive toolchain for CV cluster state design, optimization, and tolerance analysis

Graph State Designer

Design and visualize CV cluster state graphs with customizable topologies. Define adjacency matrices and compute nullifier structures.

Square Hexagonal GHZ-Rail

Nullifier Variance Analyzer

Calculate nullifier variances ⟨δ²⟩ as entanglement witnesses. Propagate covariance matrices through symplectic transformations.

Covariance Symplectic

Mesh Phase Optimizer

Optimize interferometer phases for Clements or Reck architectures. Minimize average nullifier variance across all modes.

Clements Reck

Loss Tolerance Simulator

Model per-component optical loss through the mesh. Identify critical loss thresholds for entanglement preservation.

0.7 dB/layer V_lossy

Monte Carlo Analyzer

Fabrication tolerance analysis with phase errors and splitter imbalance. Statistical success rate under realistic manufacturing variations.

σφ Sweep Statistics

State Visualizer

Visualize covariance matrices, Wigner functions, and entanglement structure of generated cluster states.

Wigner Covariance

Performance Analysis

Loss Tolerance Results

Loss/Layer Avg ⟨δ²⟩ Entangled Modes Status
0.0 dB 0.25 8/8
0.5 dB 0.58 8/8
0.7 dB 0.92 6/8
1.0 dB 1.35 2/8

8-mode square graph, 6 dB squeezing

Fabrication Tolerance (12-mode Hex)

Phase Error σφ BS Imbalance Success Rate
0.1° ±1% 99.2%
0.5° ±3% 94.7%
1.0° ±5% 78.3%
2.0° ±10% 42.1%

Success: ⟨δj²⟩ < 1.2 SNU for all modes

Documentation & Resources

Theory

Comprehensive background on CV cluster states, nullifiers, symplectic transformations, and MBQC.

API Reference

Complete Python API documentation for ClusterCompiler, GraphState, MeshOptimizer, and more.

Tutorials

Step-by-step guides from basic graph design to advanced Monte Carlo tolerance analysis.

Examples

Production-ready code samples for common cluster state generation and analysis workflows.

GitHub Repository

Full source code, installation instructions, and contribution guidelines.

Related Projects

Explore CV-QKD Link Optimizer and CV Squeezer for complementary quantum photonics tools.