QuantumCircuit

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

Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}

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

Return the circuit data (instructions and context).

Returns

a list-like object containing the CircuitInstructions for each instruction.

Return type

QuantumCircuitData

Default value: 'include "qelib1.inc";'

Return the global phase of the current circuit scope in radians.

Default value: 'OPENQASM 2.0;'

Default value: 183

Return any associated layout information about the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or PassManager.run() to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

Return the number of ancilla qubits.

Return number of classical bits.

The number of parameter objects in the circuit.

Return number of qubits.

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

Returns

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

Raises

AttributeError(opens in a new tab) – When circuit is not scheduled.

The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

Examples

The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])

To respect numerical sorting, a ParameterVector can be used.

>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])

Returns

The sorted Parameter objects in the circuit.

Default value: 'circuit'

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

add_bits(bits)

Add Bits to the circuit.

add_calibration(gate, qubits, schedule, params=None)

Register a low-level, custom pulse definition for the given gate.

Parameters

• gate (Union[Gate, str(opens in a new tab)]) – Gate information.
• qubits (Union[int(opens in a new tab), Tuple[int(opens in a new tab)]]) – List of qubits to be measured.
• schedule (Schedule) – Schedule information.
• params (Optional[List[Union[float(opens in a new tab), Parameter]]]) – A list of parameters.

Raises

Exception(opens in a new tab) – if the gate is of type string and params is None.

add_register(*regs)

Add registers.

append(instruction, qargs=None, cargs=None)

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

The qargs and cargs will be expanded and broadcast according to the rules of the given Instruction, and any non-Bit specifiers (such as integer indices) will be resolved into the relevant instances.

If a CircuitInstruction is given, it will be unwrapped, verified in the context of this circuit, and a new object will be appended to the circuit. In this case, you may not pass qargs or cargs separately.

Parameters

• instruction (Operation |CircuitInstruction) – Instruction instance to append, or a CircuitInstruction with all its context.
• qargs (Sequence[QubitSpecifier] | None) – specifiers of the Qubits to attach instruction to.
• cargs (Sequence[ClbitSpecifier] | None) – specifiers of the Clbits to attach instruction to.

Returns

a handle to the CircuitInstructions that were actually added to the circuit.

Return type

qiskit.circuit.InstructionSet

Raises

CircuitError – if the operation passed is not an instance of Instruction .

assign_parameters(parameters: Mapping[Parameter, ParameterExpression | float] | Sequence[ParameterExpression | float], inplace: Literal[False] = False, *, flat_input: bool = False, strict: bool = True) → QuantumCircuit

assign_parameters(parameters: Mapping[Parameter, ParameterExpression | float] | Sequence[ParameterExpression | float], inplace: Literal[True] = False, *, flat_input: bool = False, strict: bool = True) → None

Assign parameters to new parameters or values.

If parameters is passed as a dictionary, the keys must be Parameter instances in the current circuit. The values of the dictionary can either be numeric values or new parameter objects.

If parameters is passed as a list or array, the elements are assigned to the current parameters in the order of parameters which is sorted alphabetically (while respecting the ordering in ParameterVector objects).

The values can be assigned to the current circuit object or to a copy of it.

Parameters

• parameters – Either a dictionary or iterable specifying the new parameter values.
• inplace – If False, a copy of the circuit with the bound parameters is returned. If True the circuit instance itself is modified.
• flat_input – If True and parameters is a mapping type, it is assumed to be exactly a mapping of {parameter: value}. By default (False), the mapping may also contain ParameterVector keys that point to a corresponding sequence of values, and these will be unrolled during the mapping.
• strict – If False, any parameters given in the mapping that are not used in the circuit will be ignored. If True (the default), an error will be raised indicating a logic error.

Raises

• CircuitError – If parameters is a dict and contains parameters not present in the circuit.
• ValueError(opens in a new tab) – If parameters is a list/array and the length mismatches the number of free parameters in the circuit.

Returns

A copy of the circuit with bound parameters if inplace is False, otherwise None.

Examples

Create a parameterized circuit and assign the parameters in-place.

from qiskit.circuit import QuantumCircuit, Parameter
 
circuit = QuantumCircuit(2)
params = [Parameter('A'), Parameter('B'), Parameter('C')]
circuit.ry(params[0], 0)
circuit.crx(params[1], 0, 1)
circuit.draw('mpl')
circuit.assign_parameters({params[0]: params[2]}, inplace=True)
circuit.draw('mpl')

Bind the values out-of-place by list and get a copy of the original circuit.

from qiskit.circuit import QuantumCircuit, ParameterVector
 
circuit = QuantumCircuit(2)
params = ParameterVector('P', 2)
circuit.ry(params[0], 0)
circuit.crx(params[1], 0, 1)
 
bound_circuit = circuit.assign_parameters([1, 2])
bound_circuit.draw('mpl')
 
circuit.draw('mpl')

barrier(*qargs, label=None)

Apply Barrier. If qargs is empty, applies to all qubits in the circuit.

Parameters

• qargs (QubitSpecifier) – Specification for one or more qubit arguments.
• label (str(opens in a new tab)) – The string label of the barrier.

Returns

handle to the added instructions.

Return type

qiskit.circuit.InstructionSet

bind_parameters(values)

Assign numeric parameters to values yielding a new circuit.

If the values are given as list or array they are bound to the circuit in the order of parameters (see the docstring for more details).

To assign new Parameter objects or bind the values in-place, without yielding a new circuit, use the assign_parameters() method.

Parameters

values (Mapping(opens in a new tab)[Parameter, float(opens in a new tab)] | Sequence(opens in a new tab)[float(opens in a new tab)]) – {parameter: value, ...} or [value1, value2, ...]

Raises

• CircuitError – If values is a dict and contains parameters not present in the circuit.
• TypeError(opens in a new tab) – If values contains a ParameterExpression.

Returns

Copy of self with assignment substitution.

Return type

QuantumCircuit

break_loop()

Apply BreakLoopOp.

Returns

A handle to the instruction created.

Raises

CircuitError – if this method was called within a builder context, but not contained within a loop.

Return type

InstructionSet

static cast(value, type_)

Best effort to cast value to type. Otherwise, returns the value.

Return type

S | T

cbit_argument_conversion(clbit_representation)

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

Parameters

clbit_representation (Object) – representation to expand

Returns

Where each tuple is a classical bit.

Return type

List(tuple(opens in a new tab))

ccx(control_qubit1, control_qubit2, target_qubit, ctrl_state=None)

Apply CCXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit1 (QubitSpecifier) – The qubit(s) used as the first control.
• control_qubit2 (QubitSpecifier) – The qubit(s) used as the second control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

ccz(control_qubit1, control_qubit2, target_qubit, label=None, ctrl_state=None)

Apply CCZGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit1 (QubitSpecifier) – The qubit(s) used as the first control.
• control_qubit2 (QubitSpecifier) – The qubit(s) used as the second control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘10’). Defaults to controlling on the ‘11’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

ch(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CHGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

clear()

Clear all instructions in self.

Clearing the circuits will keep the metadata and calibrations.

classmethod cls_instances()

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

Return type

int(opens in a new tab)

classmethod cls_prefix()

Return the prefix to use for auto naming.

Return type

str(opens in a new tab)

cnot(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

compose(other, qubits=None, clbits=None, front=False, inplace=False, wrap=False)

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

other can be narrower or of equal width to self.

Parameters

• other (qiskit.circuit.Instruction orQuantumCircuit) – (sub)circuit or instruction to compose onto self. If not a QuantumCircuit, this can be anything that append will accept.
• qubits (list(opens in a new tab)[Qubit|int(opens in a new tab)]) – qubits of self to compose onto.
• clbits (list(opens in a new tab)[Clbit|int(opens in a new tab)]) – clbits of self to compose onto.
• front (bool(opens in a new tab)) – If True, front composition will be performed. This is not possible within control-flow builder context managers.
• inplace (bool(opens in a new tab)) – If True, modify the object. Otherwise return composed circuit.
• wrap (bool(opens in a new tab)) – If True, wraps the other circuit into a gate (or instruction, depending on whether it contains only unitary instructions) before composing it onto self.

Returns

the composed circuit (returns None if inplace==True).

Return type

QuantumCircuit

Raises

• CircuitError – if no correct wire mapping can be made between the two circuits, such as if other is wider than self.
• CircuitError – if trying to emit a new circuit while self has a partially built control-flow context active, such as the context-manager forms of if_test(), for_loop() and while_loop().
• CircuitError – if trying to compose to the front of a circuit when a control-flow builder block is active; there is no clear meaning to this action.

Examples

>>> lhs.compose(rhs, qubits=[3, 2], inplace=True)

            ┌───┐                   ┌─────┐                ┌───┐
lqr_1_0: ───┤ H ├───    rqr_0: ──■──┤ Tdg ├    lqr_1_0: ───┤ H ├───────────────
            ├───┤              ┌─┴─┐└─────┘                ├───┤
lqr_1_1: ───┤ X ├───    rqr_1: ┤ X ├───────    lqr_1_1: ───┤ X ├───────────────
         ┌──┴───┴──┐           └───┘                    ┌──┴───┴──┐┌───┐
lqr_1_2: ┤ U1(0.1) ├  +                     =  lqr_1_2: ┤ U1(0.1) ├┤ X ├───────
         └─────────┘                                    └─────────┘└─┬─┘┌─────┐
lqr_2_0: ─────■─────                           lqr_2_0: ─────■───────■──┤ Tdg ├
            ┌─┴─┐                                          ┌─┴─┐        └─────┘
lqr_2_1: ───┤ X ├───                           lqr_2_1: ───┤ X ├───────────────
            └───┘                                          └───┘
lcr_0: 0 ═══════════                           lcr_0: 0 ═══════════════════════
 
lcr_1: 0 ═══════════                           lcr_1: 0 ═══════════════════════

continue_loop()

Apply ContinueLoopOp.

Returns

A handle to the instruction created.

Raises

CircuitError – if this method was called within a builder context, but not contained within a loop.

Return type

InstructionSet

control(num_ctrl_qubits=1, label=None, ctrl_state=None)

Control this circuit on num_ctrl_qubits qubits.

Parameters

• num_ctrl_qubits (int(opens in a new tab)) – The number of control qubits.
• label (str(opens in a new tab)) – An optional label to give the controlled operation for visualization.
• ctrl_state (str(opens in a new tab) orint(opens in a new tab)) – The control state in decimal or as a bitstring (e.g. ‘111’). If None, use 2**num_ctrl_qubits - 1.

Returns

The controlled version of this circuit.

Return type

QuantumCircuit

Raises

CircuitError – If the circuit contains a non-unitary operation and cannot be controlled.

copy(name=None)

Copy the circuit.

Parameters

name (str(opens in a new tab)) – name to be given to the copied circuit. If None, then the name stays the same.

Returns

a deepcopy of the current circuit, with the specified name

Return type

QuantumCircuit

copy_empty_like(name=None)

Return a copy of self with the same structure but empty.

That structure includes:

• name, calibrations and other metadata
• global phase
• all the qubits and clbits, including the registers

Parameters

name (str(opens in a new tab)) – Name for the copied circuit. If None, then the name stays the same.

Returns

An empty copy of self.

Return type

QuantumCircuit

count_ops()

Count each operation kind in the circuit.

Returns

a breakdown of how many operations of each kind, sorted by amount.

Return type

OrderedDict

cp(theta, control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CPhaseGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterValueType) – The angle of the rotation.
• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

crx(theta, control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CRXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterValueType) – The angle of the rotation.
• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cry(theta, control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CRYGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterValueType) – The angle of the rotation.
• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

crz(theta, control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CRZGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterValueType) – The angle of the rotation.
• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cs(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CSGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

csdg(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CSdgGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cswap(control_qubit, target_qubit1, target_qubit2, label=None, ctrl_state=None)

Apply CSwapGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit1 (QubitSpecifier) – The qubit(s) targeted by the gate.
• target_qubit2 (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. '1'). Defaults to controlling on the '1' state.

Returns

A handle to the instructions created.

Return type

InstructionSet

csx(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CSXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cu(theta, phi, lam, gamma, control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CUGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterValueType) – The $\theta$ rotation angle of the gate.
• phi (ParameterValueType) – The $\phi$ rotation angle of the gate.
• lam (ParameterValueType) – The $\lambda$ rotation angle of the gate.
• gamma (ParameterValueType) – The global phase applied of the U gate, if applied.
• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cx(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the control.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cy(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CYGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the controls.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

cz(control_qubit, target_qubit, label=None, ctrl_state=None)

Apply CZGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (QubitSpecifier) – The qubit(s) used as the controls.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• label (str(opens in a new tab) | None) – The string label of the gate in the circuit.
• ctrl_state (str(opens in a new tab) |int(opens in a new tab) | None) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Returns

A handle to the instructions created.

Return type

InstructionSet

dcx(qubit1, qubit2)

Apply DCXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• qubit1 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.
• qubit2 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

decompose(gates_to_decompose=None, reps=1)

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

Parameters

• gates_to_decompose (type(opens in a new tab) orstr(opens in a new tab) orlist(opens in a new tab)(type(opens in a new tab), str(opens in a new tab))) – Optional subset of gates to decompose. Can be a gate type, such as HGate, or a gate name, such as ‘h’, or a gate label, such as ‘My H Gate’, or a list of any combination of these. If a gate name is entered, it will decompose all gates with that name, whether the gates have labels or not. Defaults to all gates in circuit.
• reps (int(opens in a new tab)) – Optional number of times the circuit should be decomposed. For instance, reps=2 equals calling circuit.decompose().decompose(). can decompose specific gates specific time

Returns

a circuit one level decomposed

Return type

QuantumCircuit

delay(duration, qarg=None, unit='dt')

Apply Delay. If qarg is None, applies to all qubits. When applying to multiple qubits, delays with the same duration will be created.

Parameters

• duration (int(opens in a new tab) orfloat(opens in a new tab) orParameterExpression) – duration of the delay.
• qarg (Object) – qubit argument to apply this delay.
• unit (str(opens in a new tab)) – unit of the duration. Supported units: 's', 'ms', 'us', 'ns', 'ps', and 'dt'. Default is 'dt', i.e. integer time unit depending on the target backend.

Returns

handle to the added instructions.

Return type

qiskit.circuit.InstructionSet

Raises

CircuitError – if arguments have bad format.

depth(filter_function=<function QuantumCircuit.<lambda>>)

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

Parameters

filter_function (callable) – A function to filter instructions. Should take as input a tuple of (Instruction, list(Qubit), list(Clbit)). Instructions for which the function returns False are ignored in the computation of the circuit depth. By default filters out “directives”, such as barrier or snapshot.

Returns

Depth of circuit.

Return type

int(opens in a new tab)

Notes

The circuit depth and the DAG depth need not be the same.

diagonal(diag, qubit)

Attach a diagonal gate to a circuit.

The decomposition is based on Theorem 7 given in “Synthesis of Quantum Logic Circuits” by Shende et al. (https://arxiv.org/pdf/quant-ph/0406176.pdf(opens in a new tab)).

Parameters

• diag (list(opens in a new tab)) – list of the 2^k diagonal entries (for a diagonal gate on k qubits). Must contain at least two entries
• qubit (QuantumRegister |list(opens in a new tab)) – list of k qubits the diagonal is acting on (the order of the qubits specifies the computational basis in which the diagonal gate is provided: the first element in diag acts on the state where all the qubits in q are in the state 0, the second entry acts on the state where all the qubits q[1],…,q[k-1] are in the state zero and q[0] is in the state 1, and so on)

Returns

the diagonal gate which was attached to the circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the list of the diagonal entries or the qubit list is in bad format; if the number of diagonal entries is not 2^k, where k denotes the number of qubits

draw(output=None, scale=None, filename=None, style=None, interactive=False, plot_barriers=True, reverse_bits=None, justify=None, vertical_compression='medium', idle_wires=True, with_layout=True, fold=None, ax=None, initial_state=False, cregbundle=None, wire_order=None, expr_len=30)

Draw the quantum circuit. Use the output parameter to choose the drawing format:

text: ASCII art TextDrawing that can be printed in the console.

mpl: images with color rendered purely in Python using matplotlib.

latex: high-quality images compiled via latex.

latex_source: raw uncompiled latex output.

Parameters

• output (str(opens in a new tab)) – select the output method to use for drawing the circuit. Valid choices are text, mpl, latex, latex_source. By default the text drawer is used unless the user config file (usually ~/.qiskit/settings.conf) has an alternative backend set as the default. For example, circuit_drawer = latex. If the output kwarg is set, that backend will always be used over the default in the user config file.
• scale (float(opens in a new tab)) – scale of image to draw (shrink if < 1.0). Only used by the mpl, latex and latex_source outputs. Defaults to 1.0.
• filename (str(opens in a new tab)) – file path to save image to. Defaults to None.
• style (dict(opens in a new tab) orstr(opens in a new tab)) – dictionary of style or file name of style json file. This option is only used by the mpl or latex output type. If style is a str, it is used as the path to a json file which contains a style dict. The file will be opened, parsed, and then any style elements in the dict will replace the default values in the input dict. A file to be loaded must end in .json, but the name entered here can omit .json. For example, style='iqp.json' or style='iqp'. If style is a dict and the 'name' key is set, that name will be used to load a json file, followed by loading the other items in the style dict. For example, style={'name': 'iqp'}. If style is not a str and name is not a key in the style dict, then the default value from the user config file (usually ~/.qiskit/settings.conf) will be used, for example, circuit_mpl_style = iqp. If none of these are set, the clifford style will be used. The search path for style json files can be specified in the user config, for example, circuit_mpl_style_path = /home/user/styles:/home/user. See: DefaultStyle for more information on the contents.
• interactive (bool(opens in a new tab)) – when set to true, show the circuit in a new window (for mpl this depends on the matplotlib backend being used supporting this). Note when used with either the text or the latex_source output type this has no effect and will be silently ignored. Defaults to False.
• reverse_bits (bool(opens in a new tab)) – when set to True, reverse the bit order inside registers for the output visualization. Defaults to False unless the user config file (usually ~/.qiskit/settings.conf) has an alternative value set. For example, circuit_reverse_bits = True.
• plot_barriers (bool(opens in a new tab)) – enable/disable drawing barriers in the output circuit. Defaults to True.
• justify (string) – options are left, right or none. If anything else is supplied, it defaults to left justified. It refers to where gates should be placed in the output circuit if there is an option. none results in each gate being placed in its own column.
• vertical_compression (string) – high, medium or low. It merges the lines generated by the text output so the drawing will take less vertical room. Default is medium. Only used by the text output, will be silently ignored otherwise.
• idle_wires (bool(opens in a new tab)) – include idle wires (wires with no circuit elements) in output visualization. Default is True.
• with_layout (bool(opens in a new tab)) – include layout information, with labels on the physical layout. Default is True.
• fold (int(opens in a new tab)) – sets pagination. It can be disabled using -1. In text, sets the length of the lines. This is useful when the drawing does not fit in the console. If None (default), it will try to guess the console width using shutil.get_terminal_size(). However, if running in jupyter, the default line length is set to 80 characters. In mpl, it is the number of (visual) layers before folding. Default is 25.
• ax (matplotlib.axes.Axes(opens in a new tab)) – Only used by the mpl backend. An optional Axes object to be used for the visualization output. If none is specified, a new matplotlib Figure will be created and used. Additionally, if specified there will be no returned Figure since it is redundant.
• initial_state (bool(opens in a new tab)) – Optional. Adds |0> in the beginning of the wire. Default is False.
• cregbundle (bool(opens in a new tab)) – Optional. If set True, bundle classical registers. Default is True, except for when output is set to "text".
• wire_order (list(opens in a new tab)) – Optional. A list of integers used to reorder the display of the bits. The list must have an entry for every bit with the bits in the range 0 to (num_qubits + num_clbits).
• expr_len (int(opens in a new tab)) – Optional. The number of characters to display if an Expr is used for the condition in a ControlFlowOp. If this number is exceeded, the string will be truncated at that number and ‘…’ added to the end.

Returns

TextDrawing or matplotlib.figure or PIL.Image or str(opens in a new tab):

• TextDrawing (output=’text’)

  A drawing that can be printed as ascii art.

• matplotlib.figure.Figure (output=’mpl’)

  A matplotlib figure object for the circuit diagram.

• PIL.Image (output=’latex’)

  An in-memory representation of the image of the circuit diagram.

• str (output=’latex_source’)

  The LaTeX source code for visualizing the circuit diagram.

Raises

• VisualizationError – when an invalid output method is selected
• ImportError(opens in a new tab) – when the output methods requires non-installed libraries.

Example

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
q = QuantumRegister(1)
c = ClassicalRegister(1)
qc = QuantumCircuit(q, c)
qc.h(q)
qc.measure(q, c)
qc.draw(output='mpl', style={'backgroundcolor': '#EEEEEE'})

ecr(qubit1, qubit2)

Apply ECRGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• qubit1 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubits to apply the gate to.
• qubit2 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubits to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

find_bit(bit)

Find locations in the circuit which can be used to reference a given Bit.

Parameters

bit (Bit) – The bit to locate.

Returns

A 2-tuple. The first element (index)

contains the index at which the Bit can be found (in either qubits, clbits, depending on its type). The second element (registers) is a list of (register, index) pairs with an entry for each Register in the circuit which contains the Bit (and the index in the Register at which it can be found).

Return type

namedtuple(int(opens in a new tab), List[Tuple(Register, int(opens in a new tab))])

Notes

The circuit index of an AncillaQubit will be its index in qubits, not ancillas.

Raises

• CircuitError – If the supplied Bit was of an unknown type.
• CircuitError – If the supplied Bit could not be found on the circuit.

Return type

BitLocations

for_loop(indexset: Iterable[int], loop_parameter: Parameter | None, body: None, qubits: None, clbits: None, *, label: str | None) → qiskit.circuit.controlflow.for_loop.ForLoopContext

for_loop(indexset: Iterable[int], loop_parameter: Parameter | None, body: QuantumCircuit, qubits: Sequence[Qubit | QuantumRegister | int | slice | Sequence[Qubit | int]], clbits: Sequence[Clbit | ClassicalRegister | int | slice | Sequence[Clbit | int]], *, label: str | None) → InstructionSet

Create a for loop on this circuit.

There are two forms for calling this function. If called with all its arguments (with the possible exception of label), it will create a ForLoopOp with the given body. If body (and qubits and clbits) are not passed, then this acts as a context manager, which, when entered, provides a loop variable (unless one is given, in which case it will be reused) and will automatically build a ForLoopOp when the scope finishes. In this form, you do not need to keep track of the qubits or clbits you are using, because the scope will handle it for you.

For example:

from qiskit import QuantumCircuit
qc = QuantumCircuit(2, 1)
 
with qc.for_loop(range(5)) as i:
    qc.h(0)
    qc.cx(0, 1)
    qc.measure(0, 0)
    qc.break_loop().c_if(0, True)

Parameters

• indexset (Iterable[int(opens in a new tab)]) – A collection of integers to loop over. Always necessary.

• loop_parameter (Optional[Parameter]) –

  The parameter used within body to which the values from indexset will be assigned. In the context-manager form, if this argument is not supplied, then a loop parameter will be allocated for you and returned as the value of the with statement. This will only be bound into the circuit if it is used within the body.

  If this argument is None in the manual form of this method, body will be repeated once for each of the items in indexset but their values will be ignored.

• body (Optional[QuantumCircuit]) – The loop body to be repeatedly executed. Omit this to use the context-manager mode.

• qubits (Optional[Sequence[QubitSpecifier]]) – The circuit qubits over which the loop body should be run. Omit this to use the context-manager mode.

• clbits (Optional[Sequence[ClbitSpecifier]]) – The circuit clbits over which the loop body should be run. Omit this to use the context-manager mode.

• label (Optional[str(opens in a new tab)]) – The string label of the instruction in the circuit.

Returns

depending on the call signature, either a context manager for creating the for loop (it will automatically be added to the circuit at the end of the block), or an InstructionSet handle to the appended loop operation.

Return type

InstructionSet or ForLoopContext

Raises

CircuitError – if an incorrect calling convention is used.

fredkin(control_qubit, target_qubit1, target_qubit2)

Apply CSwapGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) used as the control.
• target_qubit1 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) targeted by the gate.
• target_qubit2 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) targeted by the gate.

Returns

A handle to the instructions created.

Return type

InstructionSet

static from_instructions(instructions, *, qubits=(), clbits=(), name=None, global_phase=0, metadata=None)

Construct a circuit from an iterable of CircuitInstructions.

Parameters

• instructions (Iterable[CircuitInstruction |tuple(opens in a new tab)[qiskit.circuit.Instruction] | tuple(opens in a new tab)[qiskit.circuit.Instruction, Iterable[Qubit]] | tuple(opens in a new tab)[qiskit.circuit.Instruction, Iterable[Qubit], Iterable[Clbit]]]) – The instructions to add to the circuit.
• qubits (Iterable[Qubit]) – Any qubits to add to the circuit. This argument can be used, for example, to enforce a particular ordering of qubits.
• clbits (Iterable[Clbit]) – Any classical bits to add to the circuit. This argument can be used, for example, to enforce a particular ordering of classical bits.
• name (str(opens in a new tab) | None) – The name of the circuit.
• global_phase (ParameterValueType) – The global phase of the circuit in radians.
• metadata (dict(opens in a new tab) | None) – Arbitrary key value metadata to associate with the circuit.

Returns

The quantum circuit.

Return type

QuantumCircuit

static from_qasm_file(path)

Read an OpenQASM 2.0 program from a file and convert to an instance of QuantumCircuit.

Parameters

path (str(opens in a new tab)) – Path to the file for an OpenQASM 2 program

Returns

The QuantumCircuit object for the input OpenQASM 2.

Return type

QuantumCircuit

static from_qasm_str(qasm_str)

Convert a string containing an OpenQASM 2.0 program to a QuantumCircuit.

Parameters

qasm_str (str(opens in a new tab)) – A string containing an OpenQASM 2.0 program.

Returns

The QuantumCircuit object for the input OpenQASM 2

Return type

QuantumCircuit

get_instructions(name)

Get instructions matching name.

Parameters

name (str(opens in a new tab)) – The name of instruction to.

Returns

list of (instruction, qargs, cargs).

Return type

list(opens in a new tab)(tuple(opens in a new tab))

h(qubit)

Apply HGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

hamiltonian(operator, time, qubits, label=None)

Apply hamiltonian evolution to qubits.

This gate resolves to a UnitaryGate as $U(t) = exp(-i t H)$, which can be decomposed into basis gates if it is 2 qubits or less, or simulated directly in Aer for more qubits.

Parameters

• operator (matrix or Operator) – a hermitian operator.
• time (float(opens in a new tab) orParameterExpression) – time evolution parameter.
• qubits (Union[int(opens in a new tab), Tuple[int(opens in a new tab)]]) – The circuit qubits to apply the transformation to.
• label (str(opens in a new tab)) – unitary name for backend [Default: None].

Returns

The quantum circuit.

Return type

QuantumCircuit

has_calibration_for(instruction)

Return True if the circuit has a calibration defined for the instruction context. In this case, the operation does not need to be translated to the device basis.

has_register(register)

Test if this circuit has the register r.

Parameters

register (Register) – a quantum or classical register.

Returns

True if the register is contained in this circuit.

Return type

bool(opens in a new tab)

i(qubit)

Apply IGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

id(qubit)

Apply IGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

if_else(condition, true_body, false_body, qubits, clbits, label=None)

Apply IfElseOp.

from qiskit.circuit import QuantumCircuit, Qubit, Clbit
bits = [Qubit(), Qubit(), Clbit()]
qc = QuantumCircuit(bits)
qc.h(0)
qc.cx(0, 1)
qc.measure(0, 0)
with qc.if_test((bits[2], 0)) as else_:
    qc.h(0)
with else_:
    qc.x(0)

Parameters

• condition (tuple(opens in a new tab)[ClassicalRegister, int(opens in a new tab)] | tuple(opens in a new tab)[Clbit, int(opens in a new tab)] | tuple(opens in a new tab)[Clbit, bool(opens in a new tab)]) – A condition to be evaluated at circuit runtime which, if true, will trigger the evaluation of true_body. Can be specified as either a tuple of a ClassicalRegister to be tested for equality with a given int, or as a tuple of a Clbit to be compared to either a bool or an int.
• true_body (QuantumCircuit) – The circuit body to be run if condition is true.
• false_body (QuantumCircuit) – The circuit to be run if condition is false.
• qubits (Sequence[QubitSpecifier]) – The circuit qubits over which the if/else should be run.
• clbits (Sequence[ClbitSpecifier]) – The circuit clbits over which the if/else should be run.
• label (str(opens in a new tab) | None) – The string label of the instruction in the circuit.

Raises

CircuitError – If the provided condition references Clbits outside the enclosing circuit.

Returns

A handle to the instruction created.

Return type

InstructionSet

if_test(condition: tuple[ClassicalRegister | Clbit, int], true_body: None, qubits: None, clbits: None, *, label: str | None) → qiskit.circuit.controlflow.if_else.IfContext

if_test(condition: tuple[ClassicalRegister | Clbit, int], true_body: QuantumCircuit, qubits: Sequence[Qubit | QuantumRegister | int | slice | Sequence[Qubit | int]], clbits: Sequence[Clbit | ClassicalRegister | int | slice | Sequence[Clbit | int]], *, label: str | None = None) → InstructionSet

Create an if statement on this circuit.

There are two forms for calling this function. If called with all its arguments (with the possible exception of label), it will create a IfElseOp with the given true_body, and there will be no branch for the false condition (see also the if_else() method). However, if true_body (and qubits and clbits) are not passed, then this acts as a context manager, which can be used to build if statements. The return value of the with statement is a chainable context manager, which can be used to create subsequent else blocks. In this form, you do not need to keep track of the qubits or clbits you are using, because the scope will handle it for you.

For example:

from qiskit.circuit import QuantumCircuit, Qubit, Clbit
bits = [Qubit(), Qubit(), Qubit(), Clbit(), Clbit()]
qc = QuantumCircuit(bits)
 
qc.h(0)
qc.cx(0, 1)
qc.measure(0, 0)
qc.h(0)
qc.cx(0, 1)
qc.measure(0, 1)
 
with qc.if_test((bits[3], 0)) as else_:
    qc.x(2)
with else_:
    qc.h(2)
    qc.z(2)

Parameters

• condition (Tuple[Union[ClassicalRegister, Clbit], int(opens in a new tab)]) – A condition to be evaluated at circuit runtime which, if true, will trigger the evaluation of true_body. Can be specified as either a tuple of a ClassicalRegister to be tested for equality with a given int, or as a tuple of a Clbit to be compared to either a bool or an int.
• true_body (Optional[QuantumCircuit]) – The circuit body to be run if condition is true.
• qubits (Optional[Sequence[QubitSpecifier]]) – The circuit qubits over which the if/else should be run.
• clbits (Optional[Sequence[ClbitSpecifier]]) – The circuit clbits over which the if/else should be run.
• label (Optional[str(opens in a new tab)]) – The string label of the instruction in the circuit.

Returns

depending on the call signature, either a context manager for creating the if block (it will automatically be added to the circuit at the end of the block), or an InstructionSet handle to the appended conditional operation.

Return type

InstructionSet or IfContext

Raises

• CircuitError – If the provided condition references Clbits outside the enclosing circuit.
• CircuitError – if an incorrect calling convention is used.

Returns

A handle to the instruction created.

initialize(params, qubits=None, normalize=False)

Initialize qubits in a specific state.

Qubit initialization is done by first resetting the qubits to $|0\rangle$ followed by calling StatePreparation class to prepare the qubits in a specified state. Both these steps are included in the Initialize instruction.

Parameters

• params (Sequence[complex(opens in a new tab)] | str(opens in a new tab) |int(opens in a new tab)) –

  The state to initialize to, can be either of the following.

  • Statevector or vector of complex amplitudes to initialize to.
  • Labels of basis states of the Pauli eigenstates Z, X, Y. See Statevector.from_label(). Notice the order of the labels is reversed with respect to the qubit index to be applied to. Example label ‘01’ initializes the qubit zero to $|1\rangle$ and the qubit one to $|0\rangle$.
  • An integer that is used as a bitmap indicating which qubits to initialize to $|1\rangle$. Example: setting params to 5 would initialize qubit 0 and qubit 2 to $|1\rangle$ and qubit 1 to $|0\rangle$.

• qubits (Sequence[QubitSpecifier] | None) – Qubits to initialize. If None the initialization is applied to all qubits in the circuit.

• normalize (bool(opens in a new tab)) – Whether to normalize an input array to a unit vector.

Returns

A handle to the instructions created.

Examples

Prepare a qubit in the state $(|0\rangle - |1\rangle) / \sqrt{2}$.

import numpy as np
from qiskit import QuantumCircuit
 
circuit = QuantumCircuit(1)
circuit.initialize([1/np.sqrt(2), -1/np.sqrt(2)], 0)
circuit.draw()

output:

     ┌──────────────────────────────┐
q_0: ┤ Initialize(0.70711,-0.70711) ├
     └──────────────────────────────┘

Initialize from a string two qubits in the state $|10\rangle$. The order of the labels is reversed with respect to qubit index. More information about labels for basis states are in Statevector.from_label().

import numpy as np
from qiskit import QuantumCircuit
 
circuit = QuantumCircuit(2)
circuit.initialize('01', circuit.qubits)
circuit.draw()

output:

     ┌──────────────────┐
q_0: ┤0                 ├
     │  Initialize(0,1) │
q_1: ┤1                 ├
     └──────────────────┘

Initialize two qubits from an array of complex amplitudes.

import numpy as np
from qiskit import QuantumCircuit
 
circuit = QuantumCircuit(2)
circuit.initialize([0, 1/np.sqrt(2), -1.j/np.sqrt(2), 0], circuit.qubits)
circuit.draw()

output:

     ┌────────────────────────────────────┐
q_0: ┤0                                   ├
     │  Initialize(0,0.70711,-0.70711j,0) │
q_1: ┤1                                   ├
     └────────────────────────────────────┘

inverse()

Invert (take adjoint of) this circuit.

This is done by recursively inverting all gates.

Returns

the inverted circuit

Return type

QuantumCircuit

Raises

CircuitError – if the circuit cannot be inverted.

Examples

input:

     ┌───┐
q_0: ┤ H ├─────■──────
     └───┘┌────┴─────┐
q_1: ─────┤ RX(1.57) ├
          └──────────┘

output:

                  ┌───┐
q_0: ──────■──────┤ H ├
     ┌─────┴─────┐└───┘
q_1: ┤ RX(-1.57) ├─────
     └───────────┘

iso(isometry, q_input, q_ancillas_for_output, q_ancillas_zero=None, q_ancillas_dirty=None, epsilon=1e-10)

Attach an arbitrary isometry from m to n qubits to a circuit. In particular, this allows to attach arbitrary unitaries on n qubits (m=n) or to prepare any state on n qubits (m=0). The decomposition used here was introduced by Iten et al. in https://arxiv.org/abs/1501.06911(opens in a new tab).

Parameters

• isometry (ndarray) – an isometry from m to n qubits, i.e., a (complex) ndarray of dimension 2^n×2^m with orthonormal columns (given in the computational basis specified by the order of the ancillas and the input qubits, where the ancillas are considered to be more significant than the input qubits.).
• q_input (QuantumRegister |list(opens in a new tab)[Qubit]) – list of m qubits where the input to the isometry is fed in (empty list for state preparation).
• q_ancillas_for_output (QuantumRegister |list(opens in a new tab)[Qubit]) – list of n-m ancilla qubits that are used for the output of the isometry and which are assumed to start in the zero state. The qubits are listed with increasing significance.
• q_ancillas_zero (QuantumRegister |list(opens in a new tab)[Qubit]) – list of ancilla qubits which are assumed to start in the zero state. Default is q_ancillas_zero = None.
• q_ancillas_dirty (QuantumRegister |list(opens in a new tab)[Qubit]) – list of ancilla qubits which can start in an arbitrary state. Default is q_ancillas_dirty = None.
• epsilon (float(opens in a new tab)) – error tolerance of calculations. Default is epsilon = _EPS.

Returns

the isometry is attached to the quantum circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the array is not an isometry of the correct size corresponding to the provided number of qubits.

isometry(isometry, q_input, q_ancillas_for_output, q_ancillas_zero=None, q_ancillas_dirty=None, epsilon=1e-10)

Attach an arbitrary isometry from m to n qubits to a circuit. In particular, this allows to attach arbitrary unitaries on n qubits (m=n) or to prepare any state on n qubits (m=0). The decomposition used here was introduced by Iten et al. in https://arxiv.org/abs/1501.06911(opens in a new tab).

Parameters

• isometry (ndarray) – an isometry from m to n qubits, i.e., a (complex) ndarray of dimension 2^n×2^m with orthonormal columns (given in the computational basis specified by the order of the ancillas and the input qubits, where the ancillas are considered to be more significant than the input qubits.).
• q_input (QuantumRegister |list(opens in a new tab)[Qubit]) – list of m qubits where the input to the isometry is fed in (empty list for state preparation).
• q_ancillas_for_output (QuantumRegister |list(opens in a new tab)[Qubit]) – list of n-m ancilla qubits that are used for the output of the isometry and which are assumed to start in the zero state. The qubits are listed with increasing significance.
• q_ancillas_zero (QuantumRegister |list(opens in a new tab)[Qubit]) – list of ancilla qubits which are assumed to start in the zero state. Default is q_ancillas_zero = None.
• q_ancillas_dirty (QuantumRegister |list(opens in a new tab)[Qubit]) – list of ancilla qubits which can start in an arbitrary state. Default is q_ancillas_dirty = None.
• epsilon (float(opens in a new tab)) – error tolerance of calculations. Default is epsilon = _EPS.

Returns

the isometry is attached to the quantum circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the array is not an isometry of the correct size corresponding to the provided number of qubits.

iswap(qubit1, qubit2)

Apply iSwapGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• qubit1 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubits to apply the gate to.
• qubit2 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubits to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

mcp(lam, control_qubits, target_qubit)

Apply MCPhaseGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• lam (ParameterExpression |float(opens in a new tab)) – The angle of the rotation.
• control_qubits (Sequence(opens in a new tab)[Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]]) – The qubits used as the controls.
• target_qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) targeted by the gate.

Returns

A handle to the instructions created.

Return type

InstructionSet

mcrx(theta, q_controls, q_target, use_basis_gates=False)

Apply Multiple-Controlled X rotation gate

Parameters

• self (QuantumCircuit) – The QuantumCircuit object to apply the mcrx gate on.
• theta (float(opens in a new tab)) – angle theta
• q_controls (QuantumRegister orlist(opens in a new tab)(Qubit)) – The list of control qubits
• q_target (Qubit) – The target qubit
• use_basis_gates (bool(opens in a new tab)) – use p, u, cx

Raises

QiskitError – parameter errors

mcry(theta, q_controls, q_target, q_ancillae=None, mode=None, use_basis_gates=False)

Apply Multiple-Controlled Y rotation gate

Parameters

• self (QuantumCircuit) – The QuantumCircuit object to apply the mcry gate on.
• theta (float(opens in a new tab)) – angle theta
• q_controls (list(opens in a new tab)(Qubit)) – The list of control qubits
• q_target (Qubit) – The target qubit
• q_ancillae (QuantumRegister ortuple(opens in a new tab)(QuantumRegister, int(opens in a new tab))) – The list of ancillary qubits.
• mode (string) – The implementation mode to use
• use_basis_gates (bool(opens in a new tab)) – use p, u, cx

Raises

QiskitError – parameter errors

mcrz(lam, q_controls, q_target, use_basis_gates=False)

Apply Multiple-Controlled Z rotation gate

Parameters

• self (QuantumCircuit) – The QuantumCircuit object to apply the mcrz gate on.
• lam (float(opens in a new tab)) – angle lambda
• q_controls (list(opens in a new tab)(Qubit)) – The list of control qubits
• q_target (Qubit) – The target qubit
• use_basis_gates (bool(opens in a new tab)) – use p, u, cx

Raises

QiskitError – parameter errors

mct(control_qubits, target_qubit, ancilla_qubits=None, mode='noancilla')

Apply MCXGate.

The multi-cX gate can be implemented using different techniques, which use different numbers of ancilla qubits and have varying circuit depth. These modes are:

• 'noancilla': Requires 0 ancilla qubits.
• 'recursion': Requires 1 ancilla qubit if more than 4 controls are used, otherwise 0.
• 'v-chain': Requires 2 less ancillas than the number of control qubits.
• 'v-chain-dirty': Same as for the clean ancillas (but the circuit will be longer).

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubits (Sequence[QubitSpecifier]) – The qubits used as the controls.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• ancilla_qubits (QubitSpecifier | Sequence[QubitSpecifier] | None) – The qubits used as the ancillae, if the mode requires them.
• mode (str(opens in a new tab)) – The choice of mode, explained further above.

Returns

A handle to the instructions created.

Raises

• ValueError(opens in a new tab) – if the given mode is not known, or if too few ancilla qubits are passed.
• AttributeError(opens in a new tab) – if no ancilla qubits are passed, but some are needed.

Return type

InstructionSet

mcx(control_qubits, target_qubit, ancilla_qubits=None, mode='noancilla')

Apply MCXGate.

The multi-cX gate can be implemented using different techniques, which use different numbers of ancilla qubits and have varying circuit depth. These modes are:

• 'noancilla': Requires 0 ancilla qubits.
• 'recursion': Requires 1 ancilla qubit if more than 4 controls are used, otherwise 0.
• 'v-chain': Requires 2 less ancillas than the number of control qubits.
• 'v-chain-dirty': Same as for the clean ancillas (but the circuit will be longer).

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubits (Sequence[QubitSpecifier]) – The qubits used as the controls.
• target_qubit (QubitSpecifier) – The qubit(s) targeted by the gate.
• ancilla_qubits (QubitSpecifier | Sequence[QubitSpecifier] | None) – The qubits used as the ancillae, if the mode requires them.
• mode (str(opens in a new tab)) – The choice of mode, explained further above.

Returns

A handle to the instructions created.

Raises

• ValueError(opens in a new tab) – if the given mode is not known, or if too few ancilla qubits are passed.
• AttributeError(opens in a new tab) – if no ancilla qubits are passed, but some are needed.

Return type

InstructionSet

measure(qubit, cbit)

Measure a quantum bit (qubit) in the Z basis into a classical bit (cbit).

When a quantum state is measured, a qubit is projected in the computational (Pauli Z) basis to either $\lvert 0 \rangle$ or $\lvert 1 \rangle$. The classical bit cbit indicates the result of that projection as a 0 or a 1 respectively. This operation is non-reversible.

Parameters

• qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – qubit(s) to measure.
• cbit (Clbit |ClassicalRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Clbit |int(opens in a new tab)]) – classical bit(s) to place the measurement result(s) in.

Returns

handle to the added instructions.

Return type

qiskit.circuit.InstructionSet

Raises

CircuitError – if arguments have bad format.

Examples

In this example, a qubit is measured and the result of that measurement is stored in the classical bit (usually expressed in diagrams as a double line):

from qiskit import QuantumCircuit
circuit = QuantumCircuit(1, 1)
circuit.h(0)
circuit.measure(0, 0)
circuit.draw()

     ┌───┐┌─┐
  q: ┤ H ├┤M├
     └───┘└╥┘
c: 1/══════╩═
           0

It is possible to call measure with lists of qubits and cbits as a shortcut for one-to-one measurement. These two forms produce identical results:

circuit = QuantumCircuit(2, 2)
circuit.measure([0,1], [0,1])

circuit = QuantumCircuit(2, 2)
circuit.measure(0, 0)
circuit.measure(1, 1)

Instead of lists, you can use QuantumRegister and ClassicalRegister under the same logic.

from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
qreg = QuantumRegister(2, "qreg")
creg = ClassicalRegister(2, "creg")
circuit = QuantumCircuit(qreg, creg)
circuit.measure(qreg, creg)

This is equivalent to:

circuit = QuantumCircuit(qreg, creg)
circuit.measure(qreg[0], creg[0])
circuit.measure(qreg[1], creg[1])

measure_active(inplace=True)

Adds measurement to all non-idle qubits. Creates a new ClassicalRegister with a size equal to the number of non-idle qubits being measured.

Returns a new circuit with measurements if inplace=False.

Parameters

inplace (bool(opens in a new tab)) – All measurements inplace or return new circuit.

Returns

Returns circuit with measurements when inplace = False.

Return type

QuantumCircuit

measure_all(inplace=True, add_bits=True)

Adds measurement to all qubits.

By default, adds new classical bits in a ClassicalRegister to store these measurements. If add_bits=False, the results of the measurements will instead be stored in the already existing classical bits, with qubit n being measured into classical bit n.

Returns a new circuit with measurements if inplace=False.

Parameters

• inplace (bool(opens in a new tab)) – All measurements inplace or return new circuit.
• add_bits (bool(opens in a new tab)) – Whether to add new bits to store the results.

Returns

Returns circuit with measurements when inplace=False.

Return type

QuantumCircuit

Raises

CircuitError – if add_bits=False but there are not enough classical bits.

ms(theta, qubits)

Apply MSGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterExpression |float(opens in a new tab)) – The angle of the rotation.
• qubits (Sequence(opens in a new tab)[Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]]) – The qubits to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

num_connected_components(unitary_only=False)

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

Parameters

unitary_only (bool(opens in a new tab)) – Compute only unitary part of graph.

Returns

Number of connected components in circuit.

Return type

int(opens in a new tab)

num_nonlocal_gates()

Return number of non-local gates (i.e. involving 2+ qubits).

Conditional nonlocal gates are also included.

Return type

int(opens in a new tab)

num_tensor_factors()

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

Notes

This is here for backwards compatibility, and will be removed in a future release of Qiskit. You should call num_unitary_factors instead.

Return type

int(opens in a new tab)

num_unitary_factors()

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

Return type

int(opens in a new tab)

p(theta, qubit)

Apply PhaseGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterExpression |float(opens in a new tab)) – THe angle of the rotation.
• qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

pauli(pauli_string, qubits)

Apply PauliGate.

Parameters

• pauli_string (str(opens in a new tab)) – A string representing the Pauli operator to apply, e.g. ‘XX’.
• qubits (Sequence(opens in a new tab)[Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]]) – The qubits to apply this gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

power(power, matrix_power=False)

Raise this circuit to the power of power.

If power is a positive integer and matrix_power is False, this implementation defaults to calling repeat. Otherwise, if the circuit is unitary, the matrix is computed to calculate the matrix power.

Parameters

• power (float(opens in a new tab)) – The power to raise this circuit to.
• matrix_power (bool(opens in a new tab)) – If True, the circuit is converted to a matrix and then the matrix power is computed. If False, and power is a positive integer, the implementation defaults to repeat.

Raises

CircuitError – If the circuit needs to be converted to a gate but it is not unitary.

Returns

A circuit implementing this circuit raised to the power of power.

Return type

QuantumCircuit

prepare_state(state, qubits=None, label=None, normalize=False)

Prepare qubits in a specific state.

This class implements a state preparing unitary. Unlike Initialize it does not reset the qubits first.

Parameters

• state (str(opens in a new tab) orlist(opens in a new tab) orint(opens in a new tab) orStatevector) –

  • Statevector: Statevector to initialize to.
  • str: labels of basis states of the Pauli eigenstates Z, X, Y. See Statevector.from_label(). Notice the order of the labels is reversed with respect to the qubit index to be applied to. Example label ‘01’ initializes the qubit zero to $|1\rangle$ and the qubit one to $|0\rangle$.
  • list: vector of complex amplitudes to initialize to.
  • int: an integer that is used as a bitmap indicating which qubits to initialize to $|1\rangle$. Example: setting params to 5 would initialize qubit 0 and qubit 2 to $|1\rangle$ and qubit 1 to $|0\rangle$.

• qubits (QuantumRegister orQubit orint(opens in a new tab)) –

  • QuantumRegister: A list of qubits to be initialized [Default: None].
  • Qubit: Single qubit to be initialized [Default: None].
  • int: Index of qubit to be initialized [Default: None].
  • list: Indexes of qubits to be initialized [Default: None].

• label (str(opens in a new tab)) – An optional label for the gate

• normalize (bool(opens in a new tab)) – Whether to normalize an input array to a unit vector.

Returns

a handle to the instruction that was just initialized

Return type

qiskit.circuit.Instruction

Examples

Prepare a qubit in the state $(|0\rangle - |1\rangle) / \sqrt{2}$.

import numpy as np
from qiskit import QuantumCircuit
 
circuit = QuantumCircuit(1)
circuit.prepare_state([1/np.sqrt(2), -1/np.sqrt(2)], 0)
circuit.draw()

output:

     ┌─────────────────────────────────────┐
q_0: ┤ State Preparation(0.70711,-0.70711) ├
     └─────────────────────────────────────┘

Prepare from a string two qubits in the state $|10\rangle$. The order of the labels is reversed with respect to qubit index. More information about labels for basis states are in Statevector.from_label().

import numpy as np
from qiskit import QuantumCircuit
 
circuit = QuantumCircuit(2)
circuit.prepare_state('01', circuit.qubits)
circuit.draw()

output:

     ┌─────────────────────────┐
q_0: ┤0                        ├
     │  State Preparation(0,1) │
q_1: ┤1                        ├
     └─────────────────────────┘

Initialize two qubits from an array of complex amplitudes .. code-block:

import numpy as np
from qiskit import QuantumCircuit
 
circuit = QuantumCircuit(2)
circuit.prepare_state([0, 1/np.sqrt(2), -1.j/np.sqrt(2), 0], circuit.qubits)
circuit.draw()

output:

     ┌───────────────────────────────────────────┐
q_0: ┤0                                          ├
     │  State Preparation(0,0.70711,-0.70711j,0) │
q_1: ┤1                                          ├
     └───────────────────────────────────────────┘

qasm(formatted=False, filename=None, encoding=None)

Return OpenQASM 2.0 string.

Parameters

• formatted (bool(opens in a new tab)) – Return formatted OpenQASM 2.0 string.
• filename (str(opens in a new tab)) – Save OpenQASM 2.0 to file with name ‘filename’.
• encoding (str(opens in a new tab)) – Optionally specify the encoding to use for the output file if filename is specified. By default this is set to the system’s default encoding (ie whatever locale.getpreferredencoding() returns) and can be set to any valid codec or alias from stdlib’s codec module(opens in a new tab)

Returns

If formatted=False.

Return type

str(opens in a new tab)

Raises

• MissingOptionalLibraryError – If pygments is not installed and formatted is True.
• QASM2ExportError – If circuit has free parameters.
• QASM2ExportError – If an operation that has no OpenQASM 2 representation is encountered.

qbit_argument_conversion(qubit_representation)

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

Parameters

qubit_representation (Object) – representation to expand

Returns

the resolved instances of the qubits.

Return type

List(Qubit)

qubit_duration(*qubits)

Return the duration between the start and stop time of the first and last instructions, excluding delays, over the supplied qubits. Its time unit is self.unit.

Parameters

*qubits (Qubit |int(opens in a new tab)) – Qubits within self to include.

Returns

Return the duration between the first start and last stop time of non-delay instructions

Return type

float(opens in a new tab)

qubit_start_time(*qubits)

Return the start time of the first instruction, excluding delays, over the supplied qubits. Its time unit is self.unit.

Return 0 if there are no instructions over qubits

Parameters

• *qubits (Qubit |int(opens in a new tab)) – Qubits within self to include. Integers are allowed for qubits, indicating
• self.qubits. (indices of) –

Returns

Return the start time of the first instruction, excluding delays, over the qubits

Raises

CircuitError – if self is a not-yet scheduled circuit.

Return type

float(opens in a new tab)

qubit_stop_time(*qubits)

Return the stop time of the last instruction, excluding delays, over the supplied qubits. Its time unit is self.unit.

Return 0 if there are no instructions over qubits

Parameters

• *qubits (Qubit |int(opens in a new tab)) – Qubits within self to include. Integers are allowed for qubits, indicating
• self.qubits. (indices of) –

Returns

Return the stop time of the last instruction, excluding delays, over the qubits

Raises

CircuitError – if self is a not-yet scheduled circuit.

Return type

float(opens in a new tab)

r(theta, phi, qubit)

Apply RGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• theta (ParameterExpression |float(opens in a new tab)) – The angle of the rotation.
• phi (ParameterExpression |float(opens in a new tab)) – The angle of the axis of rotation in the x-y plane.
• qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) to apply the gate to.

Returns

A handle to the instructions created.

Return type

InstructionSet

rcccx(control_qubit1, control_qubit2, control_qubit3, target_qubit)

Apply RC3XGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit1 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) used as the first control.
• control_qubit2 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) used as the second control.
• control_qubit3 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) used as the third control.
• target_qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) targeted by the gate.

Returns

A handle to the instructions created.

Return type

InstructionSet

rccx(control_qubit1, control_qubit2, target_qubit)

Apply RCCXGate.

For the full matrix form of this gate, see the underlying gate documentation.

Parameters

• control_qubit1 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) used as the first control.
• control_qubit2 (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) used as the second control.
• target_qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – The qubit(s) targeted by the gate.

Returns

A handle to the instructions created.

Return type

InstructionSet

remove_final_measurements(inplace=True)

Removes final measurements and barriers on all qubits if they are present. Deletes the classical registers that were used to store the values from these measurements that become idle as a result of this operation, and deletes classical bits that are referenced only by removed registers, or that aren’t referenced at all but have become idle as a result of this operation.

Measurements and barriers are considered final if they are followed by no other operations (aside from other measurements or barriers.)

Parameters

inplace (bool(opens in a new tab)) – All measurements removed inplace or return new circuit.

Returns

Returns the resulting circuit when inplace=False, else None.

Return type

QuantumCircuit

repeat(reps)

Repeat this circuit reps times.

Parameters

reps (int(opens in a new tab)) – How often this circuit should be repeated.

Returns

A circuit containing reps repetitions of this circuit.

Return type

QuantumCircuit

reset(qubit)

Reset the quantum bit(s) to their default state.

Parameters

qubit (Qubit |QuantumRegister |int(opens in a new tab) |slice(opens in a new tab) |Sequence(opens in a new tab)[Qubit |int(opens in a new tab)]) – qubit(s) to reset.

Returns

handle to the added instruction.

Return type

qiskit.circuit.InstructionSet

reverse_bits()

Return a circuit with the opposite order of wires.

The circuit is “vertically” flipped. If a circuit is defined over multiple registers, the resulting circuit will have the same registers but with their order flipped.

This method is useful for converting a circuit written in little-endian convention to the big-endian equivalent, and vice versa.

Returns

the circuit with reversed bit order.

Return type

QuantumCircuit

Examples

input:

     ┌───┐
a_0: ┤ H ├──■─────────────────
     └───┘┌─┴─┐
a_1: ─────┤ X ├──■────────────
          └───┘┌─┴─┐
a_2: ──────────┤ X ├──■───────
               └───┘┌─┴─┐
b_0: ───────────────┤ X ├──■──
                    └───┘┌─┴─┐
b_1: ────────────────────┤ X ├
                         └───┘

output:

                         ┌───┐
b_0: ────────────────────┤ X ├
                    ┌───┐└─┬─┘
b_1: ───────────────┤ X ├──■──
               ┌───┐└─┬─┘
a_0: ──────────┤ X ├──■───────
          ┌───┐└─┬─┘
a_1: ─────┤ X ├──■────────────
     ┌───┐└─┬─┘
a_2: ┤ H ├──■─────────────────
     └───┘