VQE example for the Toric Code Model #55
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This module implements VQE optimization for finding ground states of the generalized 2D toric code Hamiltonian with open boundary conditions and provides comparison among different ansätze: FLDC, GLDC, and FDC.
refraction-ray
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Nov 6, 2025
| Build the generalized 2D toric code Hamiltonian with open boundary conditions. | ||
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| The Hamiltonian is: H = -(1-h)∑A_v - (1-h)∑B_p - h∑(hx*X_i + hz*Z_i) | ||
| where A_v are vertex operators (X products) and B_p are plaquette operators (Z products). |
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more elaboration on how plaquette operators is defined at the boundary
| circuit.RZ(q1, theta=params[7]) | ||
| circuit.RY(q2, theta=params[8]) | ||
| circuit.RZ(q1, theta=params[9]) | ||
| circuit.RZ(q2, theta=params[10]) |
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how this is su4 gate as su4 gate has 15 parameters? though it is ok for demonstration here, the latest version of tc has native c.su4(i, i+1, theta=vec_15).
| c: tc.Circuit, h: float, hx: float, hz: float, Lx: int, Ly: int | ||
| ) -> float: | ||
| """Calculate toric code energy for a given circuit state.""" | ||
| H = build_toric_hamiltonian(Lx=Lx, Ly=Ly, h=h, hx=hx, hz=hz) |
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then H is built every iteration? a bad design
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In general looks good, but some changes are required as comments |
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This module implements VQE optimization for finding ground states of the generalized 2D toric code Hamiltonian with open boundary conditions and provides comparison among different ansätze: FLDC, GLDC, and FDC. The new example demonstrates how to build the model, configure ansätze, run optimization, and compare energies and convergence behavior.