Data

Rydberg System

\[ \hat{H}_{\mathrm{Rydberg}} = \sum_{i < j}^{N} \frac{C_6}{\lVert \mathbf{r}_i - \mathbf{r}_j \rVert} \hat{n}_i \hat{n}_j - \delta \sum_{i}^{N} \hat{n}_i - \frac{\Omega}{2} \sum_{i}^{N} \hat{\sigma}_i^{(x)}, \]

\[ C_6 = \Omega \left( \frac{R_b}{a} \right)^6, \quad V_{ij} = \frac{a^6}{\lVert \mathbf{r}_i - \mathbf{r}_j \rVert^6} \]

• \(N = L \times L =\) number of atoms/qubits
• \(i, j =\) qubit index
• \(V_{ij} =\) blockade interaction between qubits \(i\) and \(j\)
• \(a =\) Lattice spacing
• \(R_b =\) Rydberg blockade radius
• \(\mathbf{r}_i =\) the position of qubit \(i\)
• \(\hat{n}_i =\) number operator at qubit \(i\)
• \(\delta =\) detuning at qubit \(i\)
• \(\Omega =\) Rabi frequency at qubit \(i\)

Dataset

Consider setting \(\Omega = 1\) and varying the other Hamiltonian parameters independently :

• \(L = [5, 6, 11, 12, 15, 16]\)
• \(\delta / \Omega = [-0.36, -0.13, 0.93, 1.05, 1.17, 1.29, 1.52, 1.76, 2.94, 3.17]\)
• \(R_b / a = [1.05, 1.15, 1.3]\)
• \(\beta \Omega = [0.5, 1, 2, 4, 8, 16, 32, 48, 64]\)

Data available on Pennylane Datasets