QFT

class QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name='qft')[source]

Quantum Fourier Transform Circuit.

The Quantum Fourier Transform (QFT) on \(n\) qubits is the operation

\[|j\rangle \mapsto \frac{1}{2^{n/2}} \sum_{k=0}^{2^n - 1} e^{2\pi ijk / 2^n} |k\rangle\]

The circuit that implements this transformation can be implemented using Hadamard gates on each qubit, a series of controlled-U1 (or Z, depending on the phase) gates and a layer of Swap gates. The layer of Swap gates can in principle be dropped if the QFT appears at the end of the circuit, since then the re-ordering can be done classically. They can be turned off using the do_swaps attribute.

For 4 qubits, the circuit that implements this transformation is:

../_images/qiskit.circuit.library.QFT_0_0.png

The inverse QFT can be obtained by calling the inverse method on this class. The respective circuit diagram is:

../_images/qiskit.circuit.library.QFT_1_0.png

One method to reduce circuit depth is to implement the QFT approximately by ignoring controlled-phase rotations where the angle is beneath a threshold. This is discussed in more detail in https://arxiv.org/abs/quant-ph/9601018 or https://arxiv.org/abs/quant-ph/0403071.

Here, this can be adjusted using the approximation_degree attribute: the smallest approximation_degree rotation angles are dropped from the QFT. For instance, a QFT on 5 qubits with approximation degree 2 yields (the barriers are dropped in this example):

../_images/qiskit.circuit.library.QFT_2_0.png

Construct a new QFT circuit.

Parameters
  • num_qubits (Optional[int]) – The number of qubits on which the QFT acts.

  • approximation_degree (int) – The degree of approximation (0 for no approximation).

  • do_swaps (bool) – Whether to include the final swaps in the QFT.

  • inverse (bool) – If True, the inverse Fourier transform is constructed.

  • insert_barriers (bool) – If True, barriers are inserted as visualization improvement.

  • name (str) – The name of the circuit.

Attributes

QFT.approximation_degree

The approximation degree of the QFT.

QFT.clbits

Returns a list of classical bits in the order that the registers were added.

QFT.data

Return the circuit data (instructions and context).

QFT.do_swaps

Whether the final swaps of the QFT are applied or not.

QFT.extension_lib

QFT.header

QFT.insert_barriers

Whether barriers are inserted for better visualization or not.

QFT.instances

QFT.n_qubits

Deprecated, use num_qubits instead.

QFT.num_clbits

Return number of classical bits.

QFT.num_parameters

Convenience function to get the number of parameter objects in the circuit.

QFT.num_qubits

The number of qubits in the QFT circuit.

QFT.parameters

Convenience function to get the parameters defined in the parameter table.

QFT.prefix

QFT.qregs

A list of the quantum registers associated with the circuit.

QFT.qubits

Returns a list of quantum bits in the order that the registers were added.

Methods

QFT.AND(qr_variables, qb_target, qr_ancillae)

Build a collective conjunction (AND) circuit in place using mct.

QFT.OR(qr_variables, qb_target, qr_ancillae)

Build a collective disjunction (OR) circuit in place using mct.

QFT.__getitem__(item)

Return indexed operation.

QFT.__len__()

Return number of operations in circuit.

QFT.add_register(*regs)

Add registers.

QFT.append(instruction[, qargs, cargs])

Append one or more instructions to the end of the circuit, modifying the circuit in place.

QFT.assign_parameters(param_dict[, inplace])

Assign parameters to new parameters or values.

QFT.barrier(*qargs)

Apply Barrier.

QFT.bind_parameters(value_dict)

Assign numeric parameters to values yielding a new circuit.

QFT.cast(value, _type)

Best effort to cast value to type.

QFT.cbit_argument_conversion(…)

Converts several classical bit representations (such as indexes, range, etc.) into a list of classical bits.

QFT.ccx(control_qubit1, control_qubit2, …)

Apply CCXGate.

QFT.ch(control_qubit, target_qubit, *[, …])

Apply CHGate.

QFT.cls_instances()

Return the current number of instances of this class, useful for auto naming.

QFT.cls_prefix()

Return the prefix to use for auto naming.

QFT.cnot(control_qubit, target_qubit, *[, …])

Apply CXGate.

QFT.combine(rhs)

Append rhs to self if self contains compatible registers.

QFT.compose(other[, qubits, clbits, front, …])

Compose circuit with other circuit or instruction, optionally permuting wires.

QFT.copy([name])

Copy the circuit.

QFT.count_ops()

Count each operation kind in the circuit.

QFT.crx(theta, control_qubit, target_qubit, *)

Apply CRXGate.

QFT.cry(theta, control_qubit, target_qubit, *)

Apply CRYGate.

QFT.crz(theta, control_qubit, target_qubit, *)

Apply CRZGate.

QFT.cswap(control_qubit, target_qubit1, …)

Apply CSwapGate.

QFT.cu1(theta, control_qubit, target_qubit, *)

Apply CU1Gate.

QFT.cu3(theta, phi, lam, control_qubit, …)

Apply CU3Gate.

QFT.cx(control_qubit, target_qubit, *[, …])

Apply CXGate.

QFT.cy(control_qubit, target_qubit, *[, …])

Apply CYGate.

QFT.cz(control_qubit, target_qubit, *[, …])

Apply CZGate.

QFT.dcx(qubit1, qubit2)

Apply DCXGate.

QFT.decompose()

Call a decomposition pass on this circuit, to decompose one level (shallow decompose).

QFT.depth()

Return circuit depth (i.e., length of critical path).

QFT.diag_gate(diag, qubit)

Deprecated version of QuantumCircuit.diagonal.

QFT.diagonal(diag, qubit)

Attach a diagonal gate to a circuit.

QFT.draw([output, scale, filename, style, …])

Draw the quantum circuit.

QFT.extend(rhs)

Append QuantumCircuit to the right hand side if it contains compatible registers.

QFT.fredkin(control_qubit, target_qubit1, …)

Apply CSwapGate.

QFT.from_qasm_file(path)

Take in a QASM file and generate a QuantumCircuit object.

QFT.from_qasm_str(qasm_str)

Take in a QASM string and generate a QuantumCircuit object.

QFT.h(qubit, *[, q])

Apply HGate.

QFT.hamiltonian(operator, time, qubits[, label])

Apply hamiltonian evolution to to qubits.

QFT.has_register(register)

Test if this circuit has the register r.

QFT.i(qubit, *[, q])

Apply IGate.

QFT.id(qubit, *[, q])

Apply IGate.

QFT.iden(qubit, *[, q])

Deprecated identity gate.

QFT.initialize(params, qubits)

Apply initialize to circuit.

QFT.inverse()

Invert this circuit.

QFT.is_inverse()

Whether the inverse Fourier transform is implemented.

QFT.iso(isometry, q_input, q_ancillas_for_output)

Attach an arbitrary isometry from m to n qubits to a circuit.

QFT.isometry(isometry, q_input, …[, …])

Attach an arbitrary isometry from m to n qubits to a circuit.

QFT.iswap(qubit1, qubit2)

Apply iSwapGate.

QFT.mcmt(gate, control_qubits, target_qubits)

Apply a multi-control, multi-target using a generic gate.

QFT.mcrx(theta, q_controls, q_target[, …])

Apply Multiple-Controlled X rotation gate

QFT.mcry(theta, q_controls, q_target, q_ancillae)

Apply Multiple-Controlled Y rotation gate

QFT.mcrz(lam, q_controls, q_target[, …])

Apply Multiple-Controlled Z rotation gate

QFT.mct(control_qubits, target_qubit[, …])

Apply MCXGate.

QFT.mcu1(lam, control_qubits, target_qubit)

Apply MCU1Gate.

QFT.mcx(control_qubits, target_qubit[, …])

Apply MCXGate.

QFT.measure(qubit, cbit)

Measure quantum bit into classical bit (tuples).

QFT.measure_active([inplace])

Adds measurement to all non-idle qubits.

QFT.measure_all([inplace])

Adds measurement to all qubits.

QFT.mirror()

Mirror the circuit by reversing the instructions.

QFT.ms(theta, qubits)

Apply MSGate.

QFT.num_connected_components([unitary_only])

How many non-entangled subcircuits can the circuit be factored to.

QFT.num_nonlocal_gates()

Return number of non-local gates (i.e.

QFT.num_tensor_factors()

Computes the number of tensor factors in the unitary (quantum) part of the circuit only.

QFT.num_unitary_factors()

Computes the number of tensor factors in the unitary (quantum) part of the circuit only.

QFT.qasm([formatted, filename])

Return OpenQASM string.

QFT.qbit_argument_conversion(…)

Converts several qubit representations (such as indexes, range, etc.) into a list of qubits.

QFT.r(theta, phi, qubit, *[, q])

Apply RGate.

QFT.rcccx(control_qubit1, control_qubit2, …)

Apply RC3XGate.

QFT.rccx(control_qubit1, control_qubit2, …)

Apply RCCXGate.

QFT.remove_final_measurements([inplace])

Removes final measurement on all qubits if they are present.

QFT.reset(qubit)

Reset q.

QFT.rx(theta, qubit, *[, label, q])

Apply RXGate.

QFT.rxx(theta, qubit1, qubit2)

Apply RXXGate.

QFT.ry(theta, qubit, *[, label, q])

Apply RYGate.

QFT.ryy(theta, qubit1, qubit2)

Apply RYYGate.

QFT.rz(phi, qubit, *[, q])

Apply RZGate.

QFT.rzx(theta, qubit1, qubit2)

Apply RZXGate.

QFT.rzz(theta, qubit1, qubit2)

Apply RZZGate.

QFT.s(qubit, *[, q])

Apply SGate.

QFT.sdg(qubit, *[, q])

Apply SdgGate.

QFT.size()

Returns total number of gate operations in circuit.

QFT.snapshot(label[, snapshot_type, qubits, …])

Take a statevector snapshot of the internal simulator representation.

QFT.snapshot_density_matrix(label[, qubits])

Take a density matrix snapshot of simulator state.

QFT.snapshot_expectation_value(label, op, qubits)

Take a snapshot of expectation value <O> of an Operator.

QFT.snapshot_probabilities(label, qubits[, …])

Take a probability snapshot of the simulator state.

QFT.snapshot_stabilizer(label)

Take a stabilizer snapshot of the simulator state.

QFT.snapshot_statevector(label)

Take a statevector snapshot of the simulator state.

QFT.squ(unitary_matrix, qubit[, mode, …])

Decompose an arbitrary 2*2 unitary into three rotation gates.

QFT.swap(qubit1, qubit2)

Apply SwapGate.

QFT.t(qubit, *[, q])

Apply TGate.

QFT.tdg(qubit, *[, q])

Apply TdgGate.

QFT.to_gate([parameter_map])

Create a Gate out of this circuit.

QFT.to_instruction([parameter_map])

Create an Instruction out of this circuit.

QFT.toffoli(control_qubit1, control_qubit2, …)

Apply CCXGate.

QFT.u1(theta, qubit, *[, q])

Apply U1Gate.

QFT.u2(phi, lam, qubit, *[, q])

Apply U2Gate.

QFT.u3(theta, phi, lam, qubit, *[, q])

Apply U3Gate.

QFT.uc(gate_list, q_controls, q_target[, …])

Attach a uniformly controlled gates (also called multiplexed gates) to a circuit.

QFT.ucg(angle_list, q_controls, q_target[, …])

Deprecated version of uc.

QFT.ucrx(angle_list, q_controls, q_target)

Attach a uniformly controlled (also called multiplexed) Rx rotation gate to a circuit.

QFT.ucry(angle_list, q_controls, q_target)

Attach a uniformly controlled (also called multiplexed) Ry rotation gate to a circuit.

QFT.ucrz(angle_list, q_controls, q_target)

Attach a uniformly controlled (also called multiplexed gates) Rz rotation gate to a circuit.

QFT.ucx(angle_list, q_controls, q_target)

Deprecated version of ucrx.

QFT.ucy(angle_list, q_controls, q_target)

Deprecated version of ucry.

QFT.ucz(angle_list, q_controls, q_target)

Deprecated version of ucrz.

QFT.unitary(obj, qubits[, label])

Apply unitary gate to q.

QFT.width()

Return number of qubits plus clbits in circuit.

QFT.x(qubit, *[, label, ctrl_state, q])

Apply XGate.

QFT.y(qubit, *[, q])

Apply YGate.

QFT.z(qubit, *[, q])

Apply ZGate.

QFT.__getitem__(item)

Return indexed operation.

QFT.__len__()

Return number of operations in circuit.