We present a theory of quantum circuits based on coded qubits encoded in chirality of electron spin complexes in lateral gated semiconductor triple quantum dot molecules with one-electron spin in each dot. Using microscopic Hamiltonian we show how to initialize, coherently control, and measure the quantum state of a chirality-based coded qubit using static magnetic field and voltage tuning of individual dots. The microscopic model of two interacting coded qubits is established and mapped to an Ising Hamiltonian, resulting in nonlocal double-qubit gates.