1. A method of constructing an L-shaped two-dimensional quantum computational cluster that provides a basis for constructing cluster architectures suitable for carrying out universal quantum computation, comprising: (a) selecting a first qubit, a second qubit, a third qubit, and a fourth qubit from a first linear chain containing at least four qubits, wherein the first qubit, the second qubit, the third qubit, and the fourth qubit are arranged consecutively along the first linear chain; (b) constructing a first 2×2 box cluster containing the first qubit, the second qubit, the third qubit, and the fourth qubit, wherein said construction comprises: (1) applying Hadamard rotations to the second qubit and the third qubit; and (2) applying a swap operation between the second qubit and the third qubit to create a bond between the first qubit and the fourth qubit; and (c) measuring the second qubit, thereby deleting bonds between the second and third qubits and between the second and fourth qubits to create the L-shaped two-dimensional quantum computational cluster.