1. A method for generating a Toffoli state, having a first fidelity, from a plurality of single qubit magic states having a second fidelity such that using the single qubit magic states to construct a Toffoli state directly would result in a Toffoli state with fidelity less than the first fidelity comprising: preparing each of first and second qubits in a high-fidelity state that can be generated with a set of Clifford gates; preparing N target qubits in the single qubit magic state, where N is an integer greater than one; performing a series of gates on the first qubit, the second qubits, and the N target qubits, such that a system comprising the first qubit, the second qubits, and the N target qubits is in a state ½|000 1. .. 0 N +½|010 1. .. 0 N +½|100 1. .. 0 N +½|111 1. .. 1 N , wherein the indexed values 1 through N represent the N target qubits; performing a parity check on the N target qubits to provide at least a first measurement value; and accepting the first qubit, the second qubit, and a first target qubit as the Toffoli state if the first measurement values assume a desired value.