  Quantum logic gates are the key elements in quantum computing. Here we
investigate the possibility of achieving a scalable and compact quantum
computing based on stationary electron-spin qubits, by using the giant optical
circular birefringence induced by quantum-dot spins in double-sided optical
microcavities as a result of cavity quantum electrodynamics. We design the
compact quantum circuits for implementing universal and deterministic quantum
gates for electron-spin systems, including the two-qubit CNOT gate and the
three-qubit Toffoli gate. They are compact and economic, and they do not
require additional electron-spin qubits. Moreover, our devices have good
scalability and are attractive as they both are based on solid-state quantum
systems and the qubits are stationary. They are feasible with the current
experimental technology, and both high fidelity and high efficiency can be
achieved when the ratio of the side leakage to the cavity decay is low.
