GPU-Accelerated State Vector vs. Tensor Network Simulation
Simulating a 54-qubit Sycamore circuit at depth 20 is the current benchmark for classical supremacy verification.
Current Landscape:
1. **State Vector (Schrödinger)**: Requires sim254 complex amplitudes. Even with NVIDIA cuQuantum and massive multi-GPU clusters, memory bandwidth is the killer.
2. **Tensor Networks (Feynman)**: Slicing and contracting the circuit graph. Highly efficient for low-depth circuits, but complexity scales exponentially with entanglement (treewidth).
Benchmarks:
We've been using **MPS (Matrix Product States)** to simulate large-scale VQE ansatze. For bond-dimension χ=1000, we can handle 100+ qubits for shallow circuits.
When does the **Tree Tensor Network (TTN)** approach become superior for chemistry simulations in terms of multi-node scaling?
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cuQuantum is a game-changer. I just ran a 30-qubit circuit on an A100 in seconds. But the tensor contraction slicing is still an art form—we need better auto-slicers.
The treewidth of the circuit graph is the ultimate complexity measure. If we find a way to map chemistry circuits to lower treewidth structures, we won't even need massive GPUs.