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Figure 3 | EPJ Quantum Technology

Figure 3

From: Few-qubit quantum-classical simulation of strongly correlated lattice fermions

Figure 3

Quantum gates for one Trotter step. A single Trotter step is shown for (a) the XY method and (b) the CZ ϕ method. Here, B is the entangling gate \(B = \exp (-i\frac{U}{4}\hat{\sigma}^{z}_{1} \hat{\sigma}^{z}_{3} \frac{\tau}{N} )\), A is a two-qubit gate given by \({A = \exp (-i\frac{V}{2}\hat{\sigma}^{z}_{l} \hat{\sigma}^{z}_{m} \frac{\tau}{N} )}\), acting on qubits l and m, and the quantum gates C and D are single qubit \(\hat{\sigma}^{z}\)-gates, given by \(C = \exp [i (\frac{U}{4}-\frac{\mu}{2} )\hat{\sigma}^{z}_{l} \frac{\tau}{N} ]\) and \(D = \exp (i\frac{\epsilon_{c}}{2} \hat{\sigma}^{z}_{l}\frac{\tau}{N} )\), acting on qubit l. Finally, \(X_{\phi}\) and \(Y_{\phi}\) are ϕ-rotations along the x and y axis, respectively.

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