qiskit.circuit.library.QuadraticForm¶

class QuadraticForm(num_result_qubits=None, quadratic=None, linear=None, offset=None, little_endian=True)[source]¶

Implements a quadratic form on binary variables encoded in qubit registers.

A quadratic form on binary variables is a quadratic function \(Q\) acting on a binary variable of \(n\) bits, \(x = x_0 ... x_{n-1}\). For an integer matrix \(A\), an integer vector \(b\) and an integer \(c\) the function can be written as

\[Q(x) = x^T A x + x^T b + c\]

If \(A\), \(b\) or \(c\) contain scalar values, this circuit computes only an approximation of the quadratic form.

Provided with \(m\) qubits to encode the value, this circuit computes \(Q(x) \mod 2^m\) in [two’s complement](https://stackoverflow.com/questions/1049722/what-is-2s-complement) representation.

\[|x\rangle_n |0\rangle_m \mapsto |x\rangle_n |(Q(x) + 2^m) \mod 2^m \rangle_m\]

Since we use two’s complement e.g. the value of \(Q(x) = 3\) requires 2 bits to represent the value and 1 bit for the sign: 3 = ‘011’ where the first 0 indicates a positive value. On the other hand, \(Q(x) = -3\) would be -3 = ‘101’, where the first 1 indicates a negative value and 01 is the two’s complement of 3.

If the value of \(Q(x)\) is too large to be represented with m qubits, the resulting bitstring is \((Q(x) + 2^m) \mod 2^m)\).

The implementation of this circuit is discussed in [1], Fig. 6.

References

[1]: Gilliam et al., Grover Adaptive Search for Constrained Polynomial Binary Optimization.: arXiv:1912.04088

Parameters

num_result_qubits (Optional[int]) – The number of qubits to encode the result. Called \(m\) in the class documentation.
quadratic (Union[ndarray, List[List[Union[float, ParameterExpression]]], None]) – A matrix containing the quadratic coefficients, \(A\).
linear (Union[ndarray, List[Union[float, ParameterExpression]], None]) – An array containing the linear coefficients, \(b\).
offset (Union[float, ParameterExpression, None]) – A constant offset, \(c\).
little_endian (bool) – Encode the result in little endianness.

Raises

ValueError – If linear and quadratic have mismatching sizes.
ValueError – If num_result_qubits is unspecified but cannot be determined because some values of the quadratic form are parameterized.

__init__(num_result_qubits=None, quadratic=None, linear=None, offset=None, little_endian=True)[source]¶

Parameters

num_result_qubits (Optional[int]) – The number of qubits to encode the result. Called \(m\) in the class documentation.
quadratic (Union[ndarray, List[List[Union[float, ParameterExpression]]], None]) – A matrix containing the quadratic coefficients, \(A\).
linear (Union[ndarray, List[Union[float, ParameterExpression]], None]) – An array containing the linear coefficients, \(b\).
offset (Union[float, ParameterExpression, None]) – A constant offset, \(c\).
little_endian (bool) – Encode the result in little endianness.

Raises

ValueError – If linear and quadratic have mismatching sizes.
ValueError – If num_result_qubits is unspecified but cannot be determined because some values of the quadratic form are parameterized.

Methods

`__init__`([num_result_qubits, quadratic, …])	type num_result_qubits `Optional`[`int`]
`add_bits`(bits)	Add Bits to the circuit.
`add_calibration`(gate, qubits, schedule[, params])	Register a low-level, custom pulse definition for the given gate.
`add_register`(*regs)	Add registers.
`append`(instruction[, qargs, cargs])	Append one or more instructions to the end of the circuit, modifying the circuit in place.
`assign_parameters`(parameters[, inplace, …])	Assign parameters to new parameters or values.
`barrier`(*qargs)	Apply `Barrier`.
`bind_parameters`(values[, value_dict])	Assign numeric parameters to values yielding a new circuit.
`cast`(value, _type)	Best effort to cast value to type.
`cbit_argument_conversion`(clbit_representation)	Converts several classical bit representations (such as indexes, range, etc.) into a list of classical bits.
`ccx`(control_qubit1, control_qubit2, target_qubit)	Apply `CCXGate`.
`ch`(control_qubit, target_qubit[, label, …])	Apply `CHGate`.
`cls_instances`()	Return the current number of instances of this class, useful for auto naming.
`cls_prefix`()	Return the prefix to use for auto naming.
`cnot`(control_qubit, target_qubit[, label, …])	Apply `CXGate`.
`combine`(rhs)	DEPRECATED - Returns rhs appended to self if self contains compatible registers.
`compose`(other[, qubits, clbits, front, inplace])	Compose circuit with `other` circuit or instruction, optionally permuting wires.
`control`([num_ctrl_qubits, label, ctrl_state])	Control this circuit on `num_ctrl_qubits` qubits.
`copy`([name])	Copy the circuit.
`count_ops`()	Count each operation kind in the circuit.
`cp`(theta, control_qubit, target_qubit[, …])	Apply `CPhaseGate`.
`crx`(theta, control_qubit, target_qubit[, …])	Apply `CRXGate`.
`cry`(theta, control_qubit, target_qubit[, …])	Apply `CRYGate`.
`crz`(theta, control_qubit, target_qubit[, …])	Apply `CRZGate`.
`cswap`(control_qubit, target_qubit1, …[, …])	Apply `CSwapGate`.
`csx`(control_qubit, target_qubit[, label, …])	Apply `CSXGate`.
`cu`(theta, phi, lam, gamma, control_qubit, …)	Apply `CUGate`.
`cu1`(theta, control_qubit, target_qubit[, …])	Apply `CU1Gate`.
`cu3`(theta, phi, lam, control_qubit, target_qubit)	Apply `CU3Gate`.
`cx`(control_qubit, target_qubit[, label, …])	Apply `CXGate`.
`cy`(control_qubit, target_qubit[, label, …])	Apply `CYGate`.
`cz`(control_qubit, target_qubit[, label, …])	Apply `CZGate`.
`dcx`(qubit1, qubit2)	Apply `DCXGate`.
`decompose`()	Call a decomposition pass on this circuit, to decompose one level (shallow decompose).
`delay`(duration[, qarg, unit])	Apply `Delay`.
`depth`()	Return circuit depth (i.e., length of critical path).
`diagonal`(diag, qubit)	Attach a diagonal gate to a circuit.
`draw`([output, scale, filename, style, …])	Draw the quantum circuit.
`ecr`(qubit1, qubit2)	Apply `ECRGate`.
`extend`(rhs)	DEPRECATED - Append QuantumCircuit to the RHS if it contains compatible registers.
`fredkin`(control_qubit, target_qubit1, …)	Apply `CSwapGate`.
`from_qasm_file`(path)	Take in a QASM file and generate a QuantumCircuit object.
`from_qasm_str`(qasm_str)	Take in a QASM string and generate a QuantumCircuit object.
`h`(qubit)	Apply `HGate`.
`hamiltonian`(operator, time, qubits[, label])	Apply hamiltonian evolution to qubits.
`has_register`(register)	Test if this circuit has the register r.
`i`(qubit)	Apply `IGate`.
`id`(qubit)	Apply `IGate`.
`initialize`(params[, qubits])	Initialize qubits in a specific state.
`inverse`()	Invert (take adjoint of) this circuit.
`iso`(isometry, q_input, q_ancillas_for_output)	Attach an arbitrary isometry from m to n qubits to a circuit.
`isometry`(isometry, q_input, …[, …])	Attach an arbitrary isometry from m to n qubits to a circuit.
`iswap`(qubit1, qubit2)	Apply `iSwapGate`.
`mcp`(lam, control_qubits, target_qubit)	Apply `MCPhaseGate`.
`mcrx`(theta, q_controls, q_target[, …])	Apply Multiple-Controlled X rotation gate
`mcry`(theta, q_controls, q_target[, …])	Apply Multiple-Controlled Y rotation gate
`mcrz`(lam, q_controls, q_target[, …])	Apply Multiple-Controlled Z rotation gate
`mct`(control_qubits, target_qubit[, …])	Apply `MCXGate`.
`mcu1`(lam, control_qubits, target_qubit)	Apply `MCU1Gate`.
`mcx`(control_qubits, target_qubit[, …])	Apply `MCXGate`.
`measure`(qubit, cbit)	Measure quantum bit into classical bit (tuples).
`measure_active`([inplace])	Adds measurement to all non-idle qubits.
`measure_all`([inplace])	Adds measurement to all qubits.
`ms`(theta, qubits)	Apply `MSGate`.
`num_connected_components`([unitary_only])	How many non-entangled subcircuits can the circuit be factored to.
`num_nonlocal_gates`()	Return number of non-local gates (i.e.
`num_tensor_factors`()	Computes the number of tensor factors in the unitary (quantum) part of the circuit only.
`num_unitary_factors`()	Computes the number of tensor factors in the unitary (quantum) part of the circuit only.
`p`(theta, qubit)	Apply `PhaseGate`.
`pauli`(pauli_string, qubits)	Apply `PauliGate`.
`power`(power[, matrix_power])	Raise this circuit to the power of `power`.
`qasm`([formatted, filename])	Return OpenQASM string.
`qbit_argument_conversion`(qubit_representation)	Converts several qubit representations (such as indexes, range, etc.) into a list of qubits.
`qubit_duration`(*qubits)	Return the duration between the start and stop time of the first and last instructions, excluding delays, over the supplied qubits.
`qubit_start_time`(*qubits)	Return the start time of the first instruction, excluding delays, over the supplied qubits.
`qubit_stop_time`(*qubits)	Return the stop time of the last instruction, excluding delays, over the supplied qubits.
`r`(theta, phi, qubit)	Apply `RGate`.
`rcccx`(control_qubit1, control_qubit2, …)	Apply `RC3XGate`.
`rccx`(control_qubit1, control_qubit2, …)	Apply `RCCXGate`.
`remove_final_measurements`([inplace])	Removes final measurement on all qubits if they are present.
`repeat`(reps)	Repeat this circuit `reps` times.
`required_result_qubits`(quadratic, linear, offset)	Get the number of required result qubits.
`reset`(qubit)	Reset q.
`reverse_bits`()	Return a circuit with the opposite order of wires.
`reverse_ops`()	Reverse the circuit by reversing the order of instructions.
`rv`(vx, vy, vz, qubit)	Apply `RVGate`.
`rx`(theta, qubit[, label])	Apply `RXGate`.
`rxx`(theta, qubit1, qubit2)	Apply `RXXGate`.
`ry`(theta, qubit[, label])	Apply `RYGate`.
`ryy`(theta, qubit1, qubit2)	Apply `RYYGate`.
`rz`(phi, qubit)	Apply `RZGate`.
`rzx`(theta, qubit1, qubit2)	Apply `RZXGate`.
`rzz`(theta, qubit1, qubit2)	Apply `RZZGate`.
`s`(qubit)	Apply `SGate`.
`save_amplitudes`(params[, label, pershot, …])	Save complex statevector amplitudes.
`save_amplitudes_squared`(params[, label, …])	Save squared statevector amplitudes (probabilities).
`save_density_matrix`([qubits, label, …])	Save the current simulator quantum state as a density matrix.
`save_expectation_value`(operator, qubits[, …])	Save the expectation value of a Hermitian operator.
`save_expectation_value_variance`(operator, qubits)	Save the expectation value of a Hermitian operator.
`save_matrix_product_state`([label, pershot, …])	Save the current simulator quantum state as a matrix product state.
`save_probabilities`([qubits, label, …])	Save measurement outcome probabilities vector.
`save_probabilities_dict`([qubits, label, …])	Save measurement outcome probabilities vector.
`save_stabilizer`([label, pershot, conditional])	Save the current stabilizer simulator quantum state as a Clifford.
`save_state`([label, pershot, conditional])	Save the current simulator quantum state.
`save_statevector`([label, pershot, conditional])	Save the current simulator quantum state as a statevector.
`save_statevector_dict`([label, pershot, …])	Save the current simulator quantum state as a statevector as a dict.
`save_superop`([label, pershot])	Save the current state of the superop simulator.
`save_unitary`([label, pershot])	Save the current state of the unitary simulator.
`sdg`(qubit)	Apply `SdgGate`.
`set_density_matrix`(state)	Set the density matrix state of the simulator.
`set_matrix_product_state`(state)	Set the matrix product state of the simulator.
`set_stabilizer`(state)	Set the Clifford stabilizer state of the simulator.
`set_statevector`(state)	Set the statevector state of the simulator.
`set_superop`(state)	Set the superop state of the simulator.
`set_unitary`(state)	Set the state state of the simulator.
`size`()	Returns total number of gate operations in circuit.
`snapshot`(label[, snapshot_type, qubits, params])	Take a statevector snapshot of the internal simulator representation.
`snapshot_density_matrix`(label[, qubits])	Take a density matrix snapshot of simulator state.
`snapshot_expectation_value`(label, op, qubits)	Take a snapshot of expectation value <O> of an Operator.
`snapshot_probabilities`(label, qubits[, variance])	Take a probability snapshot of the simulator state.
`snapshot_stabilizer`(label)	Take a stabilizer snapshot of the simulator state.
`snapshot_statevector`(label)	Take a statevector snapshot of the simulator state.
`squ`(unitary_matrix, qubit[, mode, …])	Decompose an arbitrary 2*2 unitary into three rotation gates.
`swap`(qubit1, qubit2)	Apply `SwapGate`.
`sx`(qubit)	Apply `SXGate`.
`sxdg`(qubit)	Apply `SXdgGate`.
`t`(qubit)	Apply `TGate`.
`tdg`(qubit)	Apply `TdgGate`.
`tensor`(other[, inplace])	Tensor `self` with `other`.
`to_gate`([parameter_map, label])	Create a Gate out of this circuit.
`to_instruction`([parameter_map])	Create an Instruction out of this circuit.
`toffoli`(control_qubit1, control_qubit2, …)	Apply `CCXGate`.
`u`(theta, phi, lam, qubit)	Apply `UGate`.
`u1`(theta, qubit)	Apply `U1Gate`.
`u2`(phi, lam, qubit)	Apply `U2Gate`.
`u3`(theta, phi, lam, qubit)	Apply `U3Gate`.
`uc`(gate_list, q_controls, q_target[, …])	Attach a uniformly controlled gates (also called multiplexed gates) to a circuit.
`ucrx`(angle_list, q_controls, q_target)	Attach a uniformly controlled (also called multiplexed) Rx rotation gate to a circuit.
`ucry`(angle_list, q_controls, q_target)	Attach a uniformly controlled (also called multiplexed) Ry rotation gate to a circuit.
`ucrz`(angle_list, q_controls, q_target)	Attach a uniformly controlled (also called multiplexed gates) Rz rotation gate to a circuit.
`unitary`(obj, qubits[, label])	Apply unitary gate to q.
`width`()	Return number of qubits plus clbits in circuit.
`x`(qubit[, label])	Apply `XGate`.
`y`(qubit)	Apply `YGate`.
`z`(qubit)	Apply `ZGate`.

Attributes

`ancillas`	Returns a list of ancilla bits in the order that the registers were added.
`calibrations`	Return calibration dictionary.
`clbits`	Returns a list of classical bits in the order that the registers were added.
`data`	Return the circuit data (instructions and context).
`extension_lib`
`global_phase`	Return the global phase of the circuit in radians.
`header`
`instances`
`metadata`	The user provided metadata associated with the circuit
`num_ancillas`	Return the number of ancilla qubits.
`num_clbits`	Return number of classical bits.
`num_parameters`	Convenience function to get the number of parameter objects in the circuit.
`num_qubits`	Return number of qubits.
`parameters`	Convenience function to get the parameters defined in the parameter table.
`prefix`
`qubits`	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]) – Gate information.
qubits (Union[int, Tuple[int]]) – List of qubits to be measured.
schedule (Schedule) – Schedule information.
params (Optional[List[Union[float, Parameter]]]) – A list of parameters.

Raises

Exception – if the gate is of type string and params is None.

add_register(*regs)¶: Add registers.

property ancillas¶: Returns a list of ancilla bits in the order that the registers were added.

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

Append one or more instructions to the end of the circuit, modifying the circuit in place. Expands qargs and cargs.

Parameters

instruction (qiskit.circuit.Instruction) – Instruction instance to append
qargs (list(argument)) – qubits to attach instruction to
cargs (list(argument)) – clbits to attach instruction to

Returns

a handle to the instruction that was just added

Return type

qiskit.circuit.Instruction

Raises

CircuitError – if object passed is a subclass of Instruction
CircuitError – if object passed is neither subclass nor an instance of Instruction

assign_parameters(parameters, inplace=False, param_dict=None)¶

Assign parameters to new parameters or values.

The keys of the parameter dictionary must be Parameter instances in the current circuit. The values of the dictionary can either be numeric values or new parameter objects. The values can be assigned to the current circuit object or to a copy of it.

Parameters

parameters (dict or iterable) – Either a dictionary or iterable specifying the new parameter values. If a dict, it specifies the mapping from current_parameter to new_parameter, where new_parameter can be a new parameter object or a numeric value. If an iterable, the elements are assigned to the existing parameters in the order they were inserted. You can call QuantumCircuit.parameters to check this order.
inplace (bool) – If False, a copy of the circuit with the bound parameters is returned. If True the circuit instance itself is modified.
param_dict (dict) – Deprecated, use parameters instead.

Raises

CircuitError – If parameters is a dict and contains parameters not present in the circuit.
ValueError – 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 True, otherwise None.

Return type

Optional(QuantumCircuit)

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)

print('Original circuit:')
print(circuit.draw())

circuit.assign_parameters({params[0]: params[2]}, inplace=True)

print('Assigned in-place:')
print(circuit.draw())

Original circuit:
     ┌───────┐         
q_0: ┤ RY(A) ├────■────
     └───────┘┌───┴───┐
q_1: ─────────┤ RX(B) ├
              └───────┘
Assigned in-place:
     ┌───────┐         
q_0: ┤ RY(C) ├────■────
     └───────┘┌───┴───┐
q_1: ─────────┤ RX(B) ├
              └───────┘

Bind the values out-of-place 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({params[0]: 1, params[1]: 2})
print('Bound circuit:')
print(bound_circuit.draw())

print('The original circuit is unchanged:')
print(circuit.draw())

Bound circuit:
     ┌───────┐         
q_0: ┤ RY(1) ├────■────
     └───────┘┌───┴───┐
q_1: ─────────┤ RX(2) ├
              └───────┘
The original circuit is unchanged:
     ┌──────────┐            
q_0: ┤ RY(P[0]) ├─────■──────
     └──────────┘┌────┴─────┐
q_1: ────────────┤ RX(P[1]) ├
                 └──────────┘

barrier(*qargs)¶: Apply Barrier. If qargs is None, applies to all.

bind_parameters(values, value_dict=None)¶

Assign numeric parameters to values yielding a new circuit.

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

Parameters

values (dict or iterable) – {parameter: value, …} or [value1, value2, …]
value_dict (dict) – Deprecated, use values instead.

Raises

CircuitError – If values is a dict and contains parameters not present in the circuit.
TypeError – If values contains a ParameterExpression.

Returns

copy of self with assignment substitution.

Return type

QuantumCircuit

property calibrations¶

Return calibration dictionary.

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

static cast(value, _type)¶: Best effort to cast value to type. Otherwise, returns the value.

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)

ccx(control_qubit1, control_qubit2, target_qubit)¶: Apply CCXGate.

ch(control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CHGate.

property clbits¶: Returns a list of classical bits in the order that the registers were added.

classmethod cls_instances()¶: Return the current number of instances of this class, useful for auto naming.

classmethod cls_prefix()¶: Return the prefix to use for auto naming.

cnot(control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CXGate.

combine(rhs)¶

DEPRECATED - Returns rhs appended to self if self contains compatible registers.

Two circuits are compatible if they contain the same registers or if they contain different registers with unique names. The returned circuit will contain all unique registers between both circuits.

Return self + rhs as a new object.

Parameters: rhs (QuantumCircuit) – The quantum circuit to append to the right hand side.
Returns: Returns a new QuantumCircuit object
Return type: QuantumCircuit
Raises: QiskitError – if the rhs circuit is not compatible

compose(other, qubits=None, clbits=None, front=False, inplace=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 or QuantumCircuit or BaseOperator) – (sub)circuit to compose onto self.
qubits (list[Qubit|int]) – qubits of self to compose onto.
clbits (list[Clbit|int]) – clbits of self to compose onto.
front (bool) – If True, front composition will be performed (not implemented yet).
inplace (bool) – If True, modify the object. Otherwise return composed circuit.

Returns

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

Return type

QuantumCircuit

Raises

CircuitError – if composing on the front.
QiskitError – if other is wider or there are duplicate edge mappings.

Examples:

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

.. parsed-literal::

                ┌───┐                   ┌─────┐                ┌───┐
    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 ═══════════════════════

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

Control this circuit on num_ctrl_qubits qubits.

Parameters

num_ctrl_qubits (int) – The number of control qubits.
label (str) – An optional label to give the controlled operation for visualization.
ctrl_state (str or int) – 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) – 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

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.

crx(theta, control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CRXGate.

cry(theta, control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CRYGate.

crz(theta, control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CRZGate.

cswap(control_qubit, target_qubit1, target_qubit2, label=None, ctrl_state=None)¶: Apply CSwapGate.

csx(control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CSXGate.

cu(theta, phi, lam, gamma, control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CUGate.

cu1(theta, control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CU1Gate.

cu3(theta, phi, lam, control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CU3Gate.

cx(control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CXGate.

cy(control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CYGate.

cz(control_qubit, target_qubit, label=None, ctrl_state=None)¶: Apply CZGate.

property data¶

Return the circuit data (instructions and context).

Returns

a list-like object containing the tuples for the circuit’s data.

Each tuple is in the format (instruction, qargs, cargs), where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.

Return type

QuantumCircuitData

dcx(qubit1, qubit2)¶: Apply DCXGate.

decompose()¶

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

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 or float) – duration of the delay.
qarg (Object) – qubit argument to apply this delay.
unit (str) – unit of the duration. Supported units: ‘s’, ‘ms’, ‘us’, ‘ns’, ‘ps’, ‘dt’. Default is dt, i.e. integer time unit depending on the target backend.

Returns

the attached delay instruction.

Return type

qiskit.Instruction

Raises

CircuitError – if arguments have bad format.

depth()¶

Return circuit depth (i.e., length of critical path). This does not include compiler or simulator directives such as ‘barrier’ or ‘snapshot’.

Returns: Depth of circuit.
Return type: int

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).

Parameters

diag (list) – list of the 2^k diagonal entries (for a diagonal gate on k qubits). Must contain at least two entries
qubit (QuantumRegister|list) – 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=False, justify=None, vertical_compression='medium', idle_wires=True, with_layout=True, fold=None, ax=None, initial_state=False, cregbundle=True)¶

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

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

matplotlib: images with color rendered purely in Python.

latex: high-quality images compiled via latex.

latex_source: raw uncompiled latex output.

Parameters

output (str) – 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) – 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) – file path to save image to. Defaults to None.
style (dict or str) – dictionary of style or file name of style json file. This option is only used by the mpl 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='iqx.json' or style='iqx'. 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': 'iqx'}. 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 = iqx. If none of these are set, the default 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) – 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) – when set to True, reverse the bit order inside registers for the output visualization. Defaults to False.
plot_barriers (bool) – 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) – include idle wires (wires with no circuit elements) in output visualization. Default is True.
with_layout (bool) – include layout information, with labels on the physical layout. Default is True.
fold (int) – 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) – 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) – optional. Adds |0> in the beginning of the wire. Default is False.
cregbundle (bool) – optional. If set True, bundle classical registers. Default is True.

Returns

TextDrawing or matplotlib.figure or PIL.Image or str:

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 – when the output methods requires non-installed libraries.

Example

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

../_images/qiskit.circuit.library.QuadraticForm_2_0.png

ecr(qubit1, qubit2)¶: Apply ECRGate.

extend(rhs)¶

DEPRECATED - Append QuantumCircuit to the RHS if it contains compatible registers.

Two circuits are compatible if they contain the same registers or if they contain different registers with unique names. The returned circuit will contain all unique registers between both circuits.

Modify and return self.

Parameters: rhs (QuantumCircuit) – The quantum circuit to append to the right hand side.
Returns: Returns this QuantumCircuit object (which has been modified)
Return type: QuantumCircuit
Raises: QiskitError – if the rhs circuit is not compatible

fredkin(control_qubit, target_qubit1, target_qubit2)¶: Apply CSwapGate.

static from_qasm_file(path)¶

Take in a QASM file and generate a QuantumCircuit object.

Parameters: path (str) – Path to the file for a QASM program
Returns: The QuantumCircuit object for the input QASM
Return type: QuantumCircuit

static from_qasm_str(qasm_str)¶

Take in a QASM string and generate a QuantumCircuit object.

Parameters: qasm_str (str) – A QASM program string
Returns: The QuantumCircuit object for the input QASM
Return type: QuantumCircuit

property global_phase¶: Return the global phase of the circuit in radians.

h(qubit)¶: Apply HGate.

hamiltonian(operator, time, qubits, label=None)¶: Apply hamiltonian evolution to qubits.

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

i(qubit)¶: Apply IGate.

id(qubit)¶: Apply IGate.

initialize(params, qubits=None)¶

Initialize qubits in a specific state.

Qubit initialization is done by first resetting the qubits to \(|0\rangle\) followed by an state preparing unitary. Both these steps are included in the Initialize instruction.

Parameters

params (str or list or int) –
- str: labels of basis states of the Pauli eigenstates Z, X, Y. See
  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> and the qubit one to |0>.
- list: vector of complex amplitudes to initialize to.
- int: an integer that is used as a bitmap indicating which qubits to initialize
  to |1>. Example: setting params to 5 would initialize qubit 0 and qubit 2 to |1> and qubit 1 to |0>.
qubits (QuantumRegister or int) –
- QuantumRegister: A list of qubits to be initialized [Default: None].
- int: Index of qubit to initialized [Default: None].

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.initialize([1/np.sqrt(2), -1/np.sqrt(2)], 0)
circuit.draw()

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

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

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

import numpy as np
from qiskit import QuantumCircuit

circuit = QuantumCircuit(2)
circuit.initialize('01', circuit.qubits)
circuit.draw()

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

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

Initialize two qubits from an array of complex amplitudes .. jupyter-execute:

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)¶

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.

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[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[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[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[Qubit]) – list of ancilla qubits which can start in an arbitrary state. Default is q_ancillas_dirty = None.

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)¶

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.

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[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[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[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[Qubit]) – list of ancilla qubits which can start in an arbitrary state. Default is q_ancillas_dirty = None.

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.

mcp(lam, control_qubits, target_qubit)¶: Apply MCPhaseGate.

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) – angle theta
q_controls (list(Qubit)) – The list of control qubits
q_target (Qubit) – The target qubit
use_basis_gates (bool) – 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) – angle theta
q_controls (list(Qubit)) – The list of control qubits
q_target (Qubit) – The target qubit
q_ancillae (QuantumRegister or tuple(QuantumRegister, int)) – The list of ancillary qubits.
mode (string) – The implementation mode to use
use_basis_gates (bool) – 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) – angle lambda
q_controls (list(Qubit)) – The list of control qubits
q_target (Qubit) – The target qubit
use_basis_gates (bool) – use p, u, cx

Raises

QiskitError – parameter errors

mct(control_qubits, target_qubit, ancilla_qubits=None, mode='noancilla')¶: Apply MCXGate.

mcu1(lam, control_qubits, target_qubit)¶: Apply MCU1Gate.

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).

measure(qubit, cbit)¶

Measure quantum bit into classical bit (tuples).

Parameters

qubit (QuantumRegister|list|tuple) – quantum register
cbit (ClassicalRegister|list|tuple) – classical register

Returns

the attached measure instruction.

Return type

qiskit.Instruction

Raises

CircuitError – if qubit is not in this circuit or bad format; if cbit is not in this circuit or not creg.

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) – All measurements inplace or return new circuit.
Returns: Returns circuit with measurements when inplace = False.
Return type: QuantumCircuit

measure_all(inplace=True)¶

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

Returns a new circuit with measurements if inplace=False.

Parameters: inplace (bool) – All measurements inplace or return new circuit.
Returns: Returns circuit with measurements when inplace = False.
Return type: QuantumCircuit

property metadata¶

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.

ms(theta, qubits)¶: Apply MSGate.

property num_ancillas¶: Return the number of ancilla qubits.

property num_clbits¶: Return number of classical bits.

num_connected_components(unitary_only=False)¶

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

Parameters: unitary_only (bool) – Compute only unitary part of graph.
Returns: Number of connected components in circuit.
Return type: int

num_nonlocal_gates()¶

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

Conditional nonlocal gates are also included.

property num_parameters¶: Convenience function to get the number of parameter objects in the circuit.

property num_qubits¶: Return number of qubits.

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.

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

p(theta, qubit)¶: Apply PhaseGate.

property parameters¶: Convenience function to get the parameters defined in the parameter table.

pauli(pauli_string, qubits)¶: Apply PauliGate.

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 (int) – The power to raise this circuit to.
matrix_power (bool) – 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

qasm(formatted=False, filename=None)¶

Return OpenQASM string.

Parameters

formatted (bool) – Return formatted Qasm string.
filename (str) – Save Qasm to file with name ‘filename’.

Returns

If formatted=False.

Return type

str

Raises

ImportError – If pygments is not installed and formatted is True.
QasmError – If circuit has free parameters.

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: Where each tuple is a qubit.
Return type: List(tuple)

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 – Qubits within self to include.
Return type: Union[int, float]
Returns: Return the duration between the first start and last stop time of non-delay instructions

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 – Qubits within self to include. Integers are allowed for qubits, indicating
of self.qubits. (indices) –

Return type

Union[int, float]

Returns

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

Raises

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

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 – Qubits within self to include. Integers are allowed for qubits, indicating
of self.qubits. (indices) –

Return type

Union[int, float]

Returns

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

Raises

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

property qubits¶: Returns a list of quantum bits in the order that the registers were added.

r(theta, phi, qubit)¶: Apply RGate.

rcccx(control_qubit1, control_qubit2, control_qubit3, target_qubit)¶: Apply RC3XGate.

rccx(control_qubit1, control_qubit2, target_qubit)¶: Apply RCCXGate.

remove_final_measurements(inplace=True)¶

Removes final measurement on all qubits if they are present. Deletes the ClassicalRegister that was used to store the values from these measurements if it is idle.

Returns a new circuit without measurements if inplace=False.

Parameters: inplace (bool) – All measurements removed inplace or return new circuit.
Returns: Returns circuit with measurements removed when inplace = False.
Return type: QuantumCircuit

repeat(reps)¶

Repeat this circuit reps times.

Parameters: reps (int) – How often this circuit should be repeated.
Returns: A circuit containing reps repetitions of this circuit.
Return type: QuantumCircuit

static required_result_qubits(quadratic, linear, offset)[source]¶

Get the number of required result qubits.

Parameters

quadratic (Union[ndarray, List[List[float]]]) – A matrix containing the quadratic coefficients.
linear (Union[ndarray, List[float]]) – An array containing the linear coefficients.
offset (float) – A constant offset.

Return type

int

Returns

The number of qubits needed to represent the value of the quadratic form in twos complement.

reset(qubit)¶: Reset q.

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

reverse_ops()¶

Reverse the circuit by reversing the order of instructions.

This is done by recursively reversing all instructions. It does not invert (adjoint) any gate.

Returns: the reversed circuit.
Return type: QuantumCircuit

Examples

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

rv(vx, vy, vz, qubit)¶: Apply RVGate.

rx(theta, qubit, label=None)¶: Apply RXGate.

rxx(theta, qubit1, qubit2)¶: Apply RXXGate.

ry(theta, qubit, label=None)¶: Apply RYGate.

ryy(theta, qubit1, qubit2)¶: Apply RYYGate.

rz(phi, qubit)¶: Apply RZGate.

rzx(theta, qubit1, qubit2)¶: Apply RZXGate.

rzz(theta, qubit1, qubit2)¶: Apply RZZGate.

s(qubit)¶: Apply SGate.

save_amplitudes(params, label='amplitudes', pershot=False, conditional=False)¶

Save complex statevector amplitudes.

Parameters

params (List[int] or List[str]) – the basis states to return amplitudes for.
label (str) – the key for retrieving saved data from results.
pershot (bool) – if True save a list of amplitudes vectors for each shot of the simulation rather than the a single amplitude vector [Default: False].
conditional (bool) – if True save the amplitudes vector conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if params is invalid for the specified number of qubits.

save_amplitudes_squared(params, label='amplitudes_squared', unnormalized=False, pershot=False, conditional=False)¶

Save squared statevector amplitudes (probabilities).

Parameters

params (List[int] or List[str]) – the basis states to return amplitudes for.
label (str) – the key for retrieving saved data from results.
unnormalized (bool) – If True return save the unnormalized accumulated probabilities over all shots [Default: False].
pershot (bool) – if True save a list of probability vectors for each shot of the simulation rather than the a single amplitude vector [Default: False].
conditional (bool) – if True save the probability vector conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if params is invalid for the specified number of qubits.

save_density_matrix(qubits=None, label='density_matrix', unnormalized=False, pershot=False, conditional=False)¶

Save the current simulator quantum state as a density matrix.

Parameters

qubits (list or None) – the qubits to save reduced density matrix on. If None the full density matrix of qubits will be saved [Default: None].
label (str) – the key for retrieving saved data from results.
unnormalized (bool) – If True return save the unnormalized accumulated or conditional accumulated density matrix over all shots [Default: False].
pershot (bool) – if True save a list of density matrices for each shot of the simulation rather than the average over all shots [Default: False].
conditional (bool) – if True save the average or pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

save_expectation_value(operator, qubits, label='expectation_value', unnormalized=False, pershot=False, conditional=False)¶

Save the expectation value of a Hermitian operator.

Parameters

operator (Pauli or SparsePauliOp or Operator) – a Hermitian operator.
qubits (list) – circuit qubits to apply instruction.
label (str) – the key for retrieving saved data from results.
unnormalized (bool) – If True return save the unnormalized accumulated or conditional accumulated expectation value over all shot [Default: False].
pershot (bool) – if True save a list of expectation values for each shot of the simulation rather than the average over all shots [Default: False].
conditional (bool) – if True save the average or pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if the input operator is invalid or not Hermitian.

Note

This method appends a SaveExpectationValue instruction to the quantum circuit.

save_expectation_value_variance(operator, qubits, label='expectation_value_variance', unnormalized=False, pershot=False, conditional=False)¶

Save the expectation value of a Hermitian operator.

Parameters

operator (Pauli or SparsePauliOp or Operator) – a Hermitian operator.
qubits (list) – circuit qubits to apply instruction.
label (str) – the key for retrieving saved data from results.
unnormalized (bool) – If True return save the unnormalized accumulated or conditional accumulated expectation value and variance over all shot [Default: False].
pershot (bool) – if True save a list of expectation values and variances for each shot of the simulation rather than the average over all shots [Default: False].
conditional (bool) – if True save the data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if the input operator is invalid or not Hermitian.

Note

This method appends a SaveExpectationValueVariance instruction to the quantum circuit.

save_matrix_product_state(label='matrix_product_state', pershot=False, conditional=False)¶

Save the current simulator quantum state as a matrix product state.

Parameters

label (str) – the key for retrieving saved data from results.
pershot (bool) – if True save the mps for each shot of the simulation [Default: False].
conditional (bool) – if True save pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

save_probabilities(qubits=None, label='probabilities', unnormalized=False, pershot=False, conditional=False)¶

Save measurement outcome probabilities vector.

Parameters

qubits (list or None) – the qubits to apply snapshot to. If None all qubits will be snapshot [Default: None].
label (str) – the key for retrieving saved data from results.
unnormalized (bool) – If True return save the unnormalized accumulated probabilities over all shots [Default: False].
pershot (bool) – if True save a list of probabilities for each shot of the simulation rather than the average over all shots [Default: False].
conditional (bool) – if True save the probabilities data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

save_probabilities_dict(qubits=None, label='probabilities', unnormalized=False, pershot=False, conditional=False)¶

Save measurement outcome probabilities vector.

Parameters

qubits (list or None) – the qubits to apply snapshot to. If None all qubits will be snapshot [Default: None].
label (str) – the key for retrieving saved data from results.
unnormalized (bool) – If True return save the unnormalized accumulated probabilities over all shots [Default: False].
pershot (bool) – if True save a list of probabilities for each shot of the simulation rather than the average over all shots [Default: False].
conditional (bool) – if True save the probabilities data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

save_stabilizer(label='stabilizer', pershot=False, conditional=False)¶

Save the current stabilizer simulator quantum state as a Clifford.

Parameters

label (str) – the key for retrieving saved data from results.
pershot (bool) – if True save a list of Cliffords for each shot of the simulation [Default: False].
conditional (bool) – if True save pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Note

This instruction is always defined across all qubits in a circuit.

save_state(label=None, pershot=False, conditional=False)¶

Save the current simulator quantum state.

Parameters

label (str or None) – Optional, the key for retrieving saved data from results. If None the key will be the state type of the simulator.
pershot (bool) – if True save a list of statevectors for each shot of the simulation [Default: False].
conditional (bool) – if True save pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

save_statevector(label='statevector', pershot=False, conditional=False)¶

Save the current simulator quantum state as a statevector.

Parameters

pershot (bool) – if True save a list of statevectors for each shot of the simulation [Default: False].
label (str) – the key for retrieving saved data from results.
conditional (bool) – if True save pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Note

This instruction is always defined across all qubits in a circuit.

save_statevector_dict(label='statevector', pershot=False, conditional=False)¶

Save the current simulator quantum state as a statevector as a dict.

Parameters

label (str) – the key for retrieving saved data from results.
pershot (bool) – if True save a list of statevectors for each shot of the simulation [Default: False].
conditional (bool) – if True save pershot data conditional on the current classical register values [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Note

This instruction is always defined across all qubits in a circuit.

save_superop(label='superop', pershot=False)¶

Save the current state of the superop simulator.

Parameters

label (str) – the key for retrieving saved data from results.
pershot (bool) – if True save a list of SuperOp matrices for each shot of the simulation [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Note

This instruction is always defined across all qubits in a circuit.

save_unitary(label='unitary', pershot=False)¶

Save the current state of the unitary simulator.

Parameters

label (str) – the key for retrieving saved data from results.
pershot (bool) – if True save a list of unitaries for each shot of the simulation [Default: False].

Returns

with attached instruction.

Return type

QuantumCircuit

Note

This instruction is always defined across all qubits in a circuit.

sdg(qubit)¶: Apply SdgGate.

set_density_matrix(state)¶

Set the density matrix state of the simulator.

Parameters: state (DensityMatrix) – a density matrix.
Returns: with attached instruction.
Return type: QuantumCircuit
Raises: ExtensionError – If the density matrix is the incorrect size for the current circuit.

set_matrix_product_state(state)¶

Set the matrix product state of the simulator.

Parameters: state (Tuple[List[Tuple[np.array[complex_t]]]], List[List[float]]) – A matrix_product_state.
Returns: with attached instruction.
Return type: QuantumCircuit
Raises: ExtensionError – If the structure of the state is incorrect

set_stabilizer(state)¶

Set the Clifford stabilizer state of the simulator.

Parameters: state (Clifford) – A clifford operator.
Returns: with attached instruction.
Return type: QuantumCircuit
Raises: ExtensionError – If the state is the incorrect size for the current circuit.

set_statevector(state)¶

Set the statevector state of the simulator.

Parameters: state (Statevector) – A state matrix.
Returns: with attached instruction.
Return type: QuantumCircuit
Raises: ExtensionError – If the state is the incorrect size for the current circuit.

set_superop(state)¶

Set the superop state of the simulator.

Parameters

state (QuantumChannel) – A CPTP quantum channel.

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – If the state is the incorrect size for the current circuit.
ExtensionError – if the input QuantumChannel is not CPTP.

set_unitary(state)¶

Set the state state of the simulator.

Parameters

state (Operator) – A state matrix.

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – If the state is the incorrect size for the current circuit.
ExtensionError – if the input matrix is not unitary.

size()¶

Returns total number of gate operations in circuit.

Returns: Total number of gate operations.
Return type: int

snapshot(label, snapshot_type='statevector', qubits=None, params=None)¶

Take a statevector snapshot of the internal simulator representation. Works on all qubits, and prevents reordering (like barrier). :param label: a snapshot label to report the result :type label: str :param snapshot_type: the type of the snapshot. :type snapshot_type: str :param qubits: the qubits to apply snapshot to [Default: None]. :type qubits: list or None :param params: the parameters for snapshot_type [Default: None]. :type params: list or None

Returns: with attached command
Return type: QuantumCircuit
Raises: ExtensionError – malformed command

snapshot_density_matrix(label, qubits=None)¶

Take a density matrix snapshot of simulator state.

Parameters

label (str) – a snapshot label to report the result
qubits (list or None) – the qubits to apply snapshot to. If None all qubits will be snapshot [Default: None].

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if snapshot is invalid.

Note

This method will be deprecated after the qiskit-aer 0.8 release. It has been superseded by the qiskit.providers.aer.library.save_density_matrix() circuit method.

snapshot_expectation_value(label, op, qubits, single_shot=False, variance=False)¶

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

Parameters

label (str) – a snapshot label to report the result
op (Operator) – operator to snapshot
qubits (list) – the qubits to snapshot.
single_shot (bool) – return list for each shot rather than average [Default: False]
variance (bool) – compute variance of values [Default: False]

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if snapshot is invalid.

Note

This method will be deprecated after the qiskit-aer 0.8 release. It has been superseded by the qiskit.providers.aer.library.save_expectation_value() and qiskit.providers.aer.library.save_expectation_value_variance() circuit methods.

snapshot_probabilities(label, qubits, variance=False)¶

Take a probability snapshot of the simulator state.

Parameters

label (str) – a snapshot label to report the result
qubits (list) – the qubits to snapshot.
variance (bool) – compute variance of probabilities [Default: False]

Returns

with attached instruction.

Return type

QuantumCircuit

Raises

ExtensionError – if snapshot is invalid.

Note

This method will be deprecated after the qiskit-aer 0.8 release. It has been superseded by the qiskit.providers.aer.library.save_probabilities() and qiskit.providers.aer.library.save_probabilities_dict() circuit methods.

snapshot_stabilizer(label)¶

Take a stabilizer snapshot of the simulator state.

Parameters: label (str) – a snapshot label to report the result.
Returns: with attached instruction.
Return type: QuantumCircuit
Raises: ExtensionError – if snapshot is invalid.

Additional Information:: This snapshot is always performed on all qubits in a circuit. The number of qubits parameter specifies the size of the instruction as a barrier and should be set to the number of qubits in the circuit.

Note

This method will be deprecated after the qiskit-aer 0.8 release. It has been superseded by the qiskit.providers.aer.library.save_stabilizer() circuit method.

snapshot_statevector(label)¶

Take a statevector snapshot of the simulator state.

Parameters: label (str) – a snapshot label to report the result.
Returns: with attached instruction.
Return type: QuantumCircuit
Raises: ExtensionError – if snapshot is invalid.

Additional Information:: This snapshot is always performed on all qubits in a circuit. The number of qubits parameter specifies the size of the instruction as a barrier and should be set to the number of qubits in the circuit.

Note

This method will be deprecated after the qiskit-aer 0.8 release. It has been superseded by the qiskit.providers.aer.library.save_statevector() circuit method.

squ(unitary_matrix, qubit, mode='ZYZ', up_to_diagonal=False, *, u=None)¶

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

Note that the decomposition is up to a global phase shift. (This is a well known decomposition, which can be found for example in Nielsen and Chuang’s book “Quantum computation and quantum information”.)

Parameters

unitary_matrix (ndarray) – 2*2 unitary (given as a (complex) ndarray).
qubit (QuantumRegister | Qubit) – The qubit which the gate is acting on.
mode (string) – determines the used decomposition by providing the rotation axes. The allowed modes are: “ZYZ” (default)
up_to_diagonal (bool) – if set to True, the single-qubit unitary is decomposed up to a diagonal matrix, i.e. a unitary u’ is implemented such that there exists a 2*2 diagonal gate d with u = d.dot(u’)
u (ndarray) – Deprecated, use unitary_matrix instead.

Returns

The single-qubit unitary instruction attached to the circuit.

Return type

InstructionSet

Raises

QiskitError – if the format is wrong; if the array u is not unitary

swap(qubit1, qubit2)¶: Apply SwapGate.

sx(qubit)¶: Apply SXGate.

sxdg(qubit)¶: Apply SXdgGate.

t(qubit)¶: Apply TGate.

tdg(qubit)¶: Apply TdgGate.

tensor(other, inplace=False)¶

Tensor self with other.

Remember that in the little-endian convention the leftmost operation will be at the bottom of the circuit. See also [the docs](qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html) for more information.

     ┌────────┐        ┌─────┐          ┌─────┐
q_0: ┤ bottom ├ ⊗ q_0: ┤ top ├  = q_0: ─┤ top ├──
     └────────┘        └─────┘         ┌┴─────┴─┐
                                  q_1: ┤ bottom ├
                                       └────────┘

Parameters

other (QuantumCircuit) – The other circuit to tensor this circuit with.
inplace (bool) – If True, modify the object. Otherwise return composed circuit.

Examples

from qiskit import QuantumCircuit
top = QuantumCircuit(1)
top.x(0);
bottom = QuantumCircuit(2)
bottom.cry(0.2, 0, 1);
tensored = bottom.tensor(top)
print(tensored.draw())

        ┌───┐   
q_0: ───┤ X ├───
        └───┘   
q_1: ─────■─────
     ┌────┴────┐
q_2: ┤ RY(0.2) ├
     └─────────┘

Returns: The tensored circuit (returns None if inplace==True).
Return type: QuantumCircuit

to_gate(parameter_map=None, label=None)¶

Create a Gate out of this circuit.

Parameters

parameter_map (dict) – For parameterized circuits, a mapping from parameters in the circuit to parameters to be used in the gate. If None, existing circuit parameters will also parameterize the gate.
label (str) – Optional gate label.

Returns

a composite gate encapsulating this circuit (can be decomposed back)

Return type

Gate

to_instruction(parameter_map=None)¶

Create an Instruction out of this circuit.

Parameters: parameter_map (dict) – For parameterized circuits, a mapping from parameters in the circuit to parameters to be used in the instruction. If None, existing circuit parameters will also parameterize the instruction.
Returns: a composite instruction encapsulating this circuit (can be decomposed back)
Return type: qiskit.circuit.Instruction

toffoli(control_qubit1, control_qubit2, target_qubit)¶: Apply CCXGate.

u(theta, phi, lam, qubit)¶: Apply UGate.

u1(theta, qubit)¶: Apply U1Gate.

u2(phi, lam, qubit)¶: Apply U2Gate.

u3(theta, phi, lam, qubit)¶: Apply U3Gate.

uc(gate_list, q_controls, q_target, up_to_diagonal=False)¶

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

The decomposition was introduced by Bergholm et al. in https://arxiv.org/pdf/quant-ph/0410066.pdf.

Parameters

gate_list (list[ndarray]) – list of two qubit unitaries [U_0,…,U_{2^k-1}], where each single-qubit unitary U_i is a given as a 2*2 array
q_controls (QuantumRegister|list[(QuantumRegister,int)]) – list of k control qubits. The qubits are ordered according to their significance in the computational basis. For example if q_controls=[q[1],q[2]] (with q = QuantumRegister(2)), the unitary U_0 is performed if q[1] and q[2] are in the state zero, U_1 is performed if q[2] is in the state zero and q[1] is in the state one, and so on
q_target (QuantumRegister|(QuantumRegister,int)) – target qubit, where we act on with the single-qubit gates.
up_to_diagonal (bool) – If set to True, the uniformly controlled gate is decomposed up to a diagonal gate, i.e. a unitary u’ is implemented such that there exists a diagonal gate d with u = d.dot(u’), where the unitary u describes the uniformly controlled gate

Returns

the uniformly controlled gate is attached to the circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the list number of control qubits does not correspond to the provided number of single-qubit unitaries; if an input is of the wrong type

ucrx(angle_list, q_controls, q_target)¶

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

The decomposition is base on https://arxiv.org/pdf/quant-ph/0406176.pdf by Shende et al.

Parameters

angle_list (list) – list of (real) rotation angles \([a_0,...,a_{2^k-1}]\)
q_controls (QuantumRegister|list) – list of k control qubits (or empty list if no controls). The control qubits are ordered according to their significance in increasing order: For example if q_controls=[q[0],q[1]] (with q = QuantumRegister(2)), the rotation Rx(a_0) is performed if q[0] and q[1] are in the state zero, the rotation Rx(a_1) is performed if q[0] is in the state one and q[1] is in the state zero, and so on
q_target (QuantumRegister|Qubit) – target qubit, where we act on with the single-qubit rotation gates

Returns

the uniformly controlled rotation gate is attached to the circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the list number of control qubits does not correspond to the provided number of single-qubit unitaries; if an input is of the wrong type

ucry(angle_list, q_controls, q_target)¶

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

The decomposition is base on https://arxiv.org/pdf/quant-ph/0406176.pdf by Shende et al.

Parameters

angle_list (list[numbers) – list of (real) rotation angles \([a_0,...,a_{2^k-1}]\)
q_controls (QuantumRegister|list[Qubit]) – list of k control qubits (or empty list if no controls). The control qubits are ordered according to their significance in increasing order: For example if q_controls=[q[0],q[1]] (with q = QuantumRegister(2)), the rotation Ry(a_0) is performed if q[0] and q[1] are in the state zero, the rotation Ry(a_1) is performed if q[0] is in the state one and q[1] is in the state zero, and so on
q_target (QuantumRegister|Qubit) – target qubit, where we act on with the single-qubit rotation gates

Returns

the uniformly controlled rotation gate is attached to the circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the list number of control qubits does not correspond to the provided number of single-qubit unitaries; if an input is of the wrong type

ucrz(angle_list, q_controls, q_target)¶

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

The decomposition is base on https://arxiv.org/pdf/quant-ph/0406176.pdf by Shende et al.

Parameters

angle_list (list[numbers) – list of (real) rotation angles [a_0,…,a_{2^k-1}]
q_controls (QuantumRegister|list[Qubit]) – list of k control qubits (or empty list if no controls). The control qubits are ordered according to their significance in increasing order: For example if q_controls=[q[1],q[2]] (with q = QuantumRegister(2)), the rotation Rz(a_0)is performed if q[1] and q[2] are in the state zero, the rotation Rz(a_1) is performed if q[1] is in the state one and q[2] is in the state zero, and so on
q_target (QuantumRegister|Qubit) – target qubit, where we act on with the single-qubit rotation gates

Returns

the uniformly controlled rotation gate is attached to the circuit.

Return type

QuantumCircuit

Raises

QiskitError – if the list number of control qubits does not correspond to the provided number of single-qubit unitaries; if an input is of the wrong type

unitary(obj, qubits, label=None)¶: Apply unitary gate to q.

width()¶

Return number of qubits plus clbits in circuit.

Returns: Width of circuit.
Return type: int

x(qubit, label=None)¶: Apply XGate.

y(qubit)¶: Apply YGate.

z(qubit)¶: Apply ZGate.