Abstract: A method of performing a quantum Fourier transform in a quantum computing circuit is disclosed. The method includes forming a quantum computing circuit as a collection of two-qubit gates operating on a sequence of input qubits. Auxiliary qubits are then interacted with the original input qubits to place the auxiliary qubits in a state corresponding to an output of a discrete Fourier transform of a classical state of the input qubits. The original input qubits are then re-set to their ground state by physically interacting the input qubits with the auxiliary qubits. The auxiliary qubits are then transformed to a state representative of a quantum Fourier transform of the sequence of input qubits.

Abstract: A method for quantum computing, comprising creating an n qubit Fourier basis state of a n qubit computational basis state, generating multiple copies of the n qubit Fourier basis state in additional sets of n qubits, and estimating the phase of the Fourier basis state from the copies of the Fourier basis state.