Category: optimization | Difficulty: advanced | Qubits: 4 | Gates: 19 | Depth: 9
Quantum simulation of the 1D transverse-field Ising model H = -J Σ ZᵢZᵢ₊₁ - h Σ Xᵢ. The first-order Trotter-Suzuki decomposition approximates e^{-iHt} ≈ (e^{iJdtZZ})^⊗ · (e^{ihdtX})^⊗ for small dt. The ZZ coupling is implemented via CNOT-Rz-CNOT; the X field via Rx rotations. Higher accuracy requires more Trotter steps (smaller dt) or higher-order formulas.
State approximating e^{-iHt}|++++⟩ after one Trotter step
The OpenQASM 2.0 circuit is in circuit.qasm.
OPENQASM 2.0;
include "qelib1.inc";
// First-order Trotter step: H = -J*ZZ - h*X, J=1, h=0.5, dt=0.1
qreg q[4];
creg c[4];
// Initial state: |++++>
h q[0]; h q[1]; h q[2]; h q[3];
// ZZ coupling terms: exp(i*J*dt*ZZ) via CNOT-Rz-CNOT (2*J*dt = 0.2)
cx q[0],q[1]; rz(0.2) q[1]; cx q[0],q[1];
cx q[1],q[2]; rz(0.2) q[2]; cx q[1],q[2];
cx q[2],q[3]; rz(0.2) q[3]; cx q[2],q[3];
// Transverse field: exp(i*h*dt*X) = Rx(2*h*dt) = Rx(0.1)
rx(0.1) q[0]; rx(0.1) q[1]; rx(0.1) q[2]; rx(0.1) q[3];
measure q[0] -> c[0];
measure q[1] -> c[1];
measure q[2] -> c[2];
measure q[3] -> c[3];
trotter ising quantum-simulation variational many-body
MIT — part of the OpenQC Algorithm Catalog.