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Physics-Based Solver
Physics-Based Solver

Quantum CFD Achieves 100× Circuit Compression

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Challenges

Scaling VQLS-based PDE solvers is fundamentally limited by circuit depth:

  • Block encodings for PDE operators often grow exponentially with system size.
  • Hand-crafted circuits (e.g., Qiskit) introduce unnecessary gates and deep control paths.
  • Deep circuits break hybrid workflows:
    • Increased simulation cost
    • Slower variational optimization
    • Higher noise accumulation
  • For structured PDE systems (like 2D Poisson), inefficient encoding made large-grid experiments impractical.

Core bottleneck: circuit depth, not algorithm design.

Results

Using Classiq’s compiler-driven synthesis and NVIDIA CUDA-Q GPU-accelerated simulation, the framework achieved major scalability gains:

  • Circuit depth reduction: up to 100× lower than Qiskit-based circuits
  • Block encoding efficiency: logarithmic scaling with grid size via structured sparsity exploitation
  • GPU-accelerated hybrid execution: large-scale VQLS experiments became feasible
  • Experimentation throughput: significantly more VQLS iterations and parametric sweeps
  • Impact: Hybrid quantum-classical PDE solvers now scale to practical engineering problem sizes (e.g., 2D Poisson).

BQPhy hybrid quantum-classical PDE solver improves circuit compression for scalable CFD

100× Circuit Compression

Classiq’s compiler-generated circuits achieved up to 100× lower depth, enabling larger PDE grids.

GPU-Accelerated Hybrid Execution
CUDA-Q simulation dramatically increased runtime performance—allowing wide parametric studies.
Scalable Block Encoding
Structured sparsity enabled efficient encodings, making VQLS viable for real scientific and engineering PDEs.
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