Fig. 4

a Analog Hamiltonian evolution and b digital quantum circuit. In a, quench evolution is performed as a function of time under a time-independent Hamiltonian \(\hat{H}\), implementing a time evolution operator \(\hat{U}(t)\) and thereby transforming the initial all-zero qubit state, \(|\Psi (0)\rangle = |00\cdots 00\rangle\), into the target state, \(|\Psi (t)\rangle = \hat{U}(t)|\Psi (0)\rangle\), at a later time t. In b, single- and two-qubit gates are employed to construct a quantum circuit. By applying judiciously chosen quantum gates, the target quantum state, \(|\Psi _\text {target}\rangle\), is prepared via digitized state evolution