Efficient quantum computing operations
View Patent ↗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.
1. A method of performing a quantum Fourier transform in a quantum computing circuit using input qubits and ancilla qubits each capable of occupying multiple states, comprising:
forming the quantum computing circuit as a collection of two-qubit gates operating on input qubits;
interacting the ancilla qubits with the input qubits to cause the ancilla qubits to be transformed to a state corresponding to an output of a discrete Fourier transform of a classical state of the input qubits;
non-destructively resetting the input qubits to a ground state by physically interacting the input qubits with the ancilla qubits; and
transforming the ancilla qubits to a state representative of a quantum Fourier transform of the input qubits.
2. The method of claim 1 , whereby the quantum circuit has a depth that scales logarithmically as a function of a number of input qubits transformed, and including a number of ancilla qubits that is proportional to the number of input qubits times the depth of the quantum circuit.
3. A method according to claim 1 of factoring an integer using a quantum circuit, comprising:
performing a classical computation that receives as input the integer as an n-bit binary integer and that produces as output the quantum circuit of claim 1
implementing Shor's quantum factoring algorithm in the quantum circuit and creating a corresponding output of the quantum circuit; and
performing classical computation on the quantum circuit output to generate a factorization of the input number.
4. The method of claim 1 , including using n input qubits and forming the quantum circuit to have a depth of O(log n).
5. A method of performing a quantum Fourier transform in a quantum computing circuit, comprising:
forming quantum computing circuit as a collection of two-qubit gates operating on input qubits;
using ancilla qubits to replicate a state corresponding to an output of a discrete Fourier transform of a classical state of the input qubits; and
transforming the ancilla qubits to a state representative of a quantum Fourier transform of the input qubits.
6. A quantum computing circuit, comprising:
a collection of two-qubit gates adapted to operate on a sequence of input qubits;
a collection of ancilla qubits adapted to physically interact with the input qubits;
means for physically interacting the input qubits with the input qubits to cause the ancilla qubits to be transformed to a state corresponding to an output of a discrete Fourier transform of a classical state of the input qubits; and
means for transforming the ancilla qubits to a state representative of a quantum Fourier transform of the sequence of input qubits.