# qiskit.circuit.library.HiddenLinearFunction¶

class HiddenLinearFunction(adjacency_matrix)[source]

Circuit to solve the hidden linear function problem.

The 2D Hidden Linear Function problem is determined by a 2D adjacency matrix A, where only elements that are nearest-neighbor on a grid have non-zero entries. Each row/column corresponds to one binary variable $$x_i$$.

The hidden linear function problem is as follows:

$q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4)$

and restrict $$q(x)$$ onto the nullspace of A. This results in a linear function.

$2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4) \forall x \in \mathrm{Ker}(A)$

and the goal is to recover this linear function (equivalently a vector $$[z_0, ..., z_{n-1}]$$). There can be multiple solutions.

In [1] it is shown that the present circuit solves this problem on a quantum computer in constant depth, whereas any corresponding solution on a classical computer would require circuits that grow logarithmically with $$n$$. Thus this circuit is an example of quantum advantage with shallow circuits.

Reference Circuit:

Reference:

[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. arXiv:1704.00690

Create new HLF circuit.

Parameters

adjacency_matrix (Union[List[List[int]], ndarray]) – a symmetric n-by-n list of 0-1 lists. n will be the number of qubits.

Raises

CircuitError – If A is not symmetric.

__init__(adjacency_matrix)[source]

Create new HLF circuit.

Parameters

adjacency_matrix (Union[List[List[int]], ndarray]) – a symmetric n-by-n list of 0-1 lists. n will be the number of qubits.

Raises

CircuitError – If A is not symmetric.

Methods

 __init__(adjacency_matrix) Create new HLF 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(param_dict[, inplace]) Assign parameters to new parameters or values. barrier(*qargs) Apply Barrier. bind_parameters(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. Return the current number of instances of this class, useful for auto naming. Return the prefix to use for auto naming. cnot(control_qubit, target_qubit[, label, …]) Apply CXGate. combine(rhs) Append rhs 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 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. Call a decomposition pass on this circuit, to decompose one level (shallow decompose). delay(duration[, qarg, unit]) Apply Delay. Return circuit depth (i.e., length of critical path). diag_gate(diag, qubit) Deprecated version of QuantumCircuit.diagonal. diagonal(diag, qubit) Attach a diagonal gate to a circuit. draw([output, scale, filename, style, …]) Draw the quantum circuit. extend(rhs) Append QuantumCircuit to the right hand side 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 to qubits. has_register(register) Test if this circuit has the register r. i(qubit) Apply IGate. id(qubit) Apply IGate. initialize(params, qubits) Apply initialize to circuit. 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. mcmt(gate, control_qubits, target_qubits[, …]) Apply a multi-control, multi-target using a generic gate. 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, q_ancillae) 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. DEPRECATED: use circuit.reverse_ops(). ms(theta, qubits) Apply MSGate. num_connected_components([unitary_only]) How many non-entangled subcircuits can the circuit be factored to. Return number of non-local gates (i.e. Computes the number of tensor factors in the unitary (quantum) part of the circuit only. Computes the number of tensor factors in the unitary (quantum) part of the circuit only. p(theta, qubit) Apply PhaseGate. 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. reset(qubit) Reset q. Return a circuit with the opposite order of wires. Reverse the circuit by reversing the order of instructions. 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. sdg(qubit) Apply SdgGate. 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 of an Operator. snapshot_probabilities(label, qubits[, variance]) Take a probability snapshot of the simulator state. Take a stabilizer snapshot of the simulator state. 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. 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. 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 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_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)

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(param_dict, inplace=False)

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
• param_dict (dict) – A dictionary specifying the mapping from current_parameter to new_parameter, where new_parameter can be a new parameter object or a numeric value.

• inplace (bool) – If False, a copy of the circuit with the bound parameters is returned. If True the circuit instance itself is modified.

Raises

CircuitError – If param_dict contains parameters not present in the circuit

Returns

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

Return type

Optional(QuantumCircuit)

Examples

>>> 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()
┌───────┐
q_0: |0>┤ Ry(A) ├────■────
└───────┘┌───┴───┐
q_1: |0>─────────┤ Rx(B) ├
└───────┘
>>> circuit.assign_parameters({params[0]: params[2]}, inplace=True)
>>> circuit.draw()
┌───────┐
q_0: |0>┤ Ry(C) ├────■────
└───────┘┌───┴───┐
q_1: |0>─────────┤ Rx(B) ├
└───────┘
>>> bound_circuit = circuit.assign_parameters({params[1]: 1, params[2]: 2})
>>> bound_circuit.draw()
┌───────┐
q_0: |0>┤ Ry(2) ├────■────
└───────┘┌───┴───┐
q_1: |0>─────────┤ Rx(1) ├
└───────┘
>>> bound_circuit.parameters  # this one has no free parameters anymore
set()
>>> circuit.parameters  # the original one is still parameterized
{Parameter(A), Parameter(C)}

barrier(*qargs)

Apply Barrier. If qargs is None, applies to all.

bind_parameters(value_dict)

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

value_dict (dict) – {parameter: value, …}

Raises
• CircuitError – If value_dict contains parameters not present in the circuit

• TypeError – If value_dict contains a ParameterExpression in the values.

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)

Append rhs 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)

            ┌───┐                   ┌─────┐                ┌───┐
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.

diag_gate(diag, qubit)

Deprecated version of QuantumCircuit.diagonal.

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.

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

latex: high-quality images compiled via LaTeX.

latex_source: raw uncompiled LaTeX output.

matplotlib: images with color rendered purely in Python.

Parameters
• output (str) – Select the output method to use for drawing the circuit. Valid choices are text, latex, latex_source, or mpl. By default the ‘text’ drawer is used unless a user config file has an alternative backend set as the default. If the output kwarg is set, that backend will always be used over the default in a user config file.

• scale (float) – scale of image to draw (shrink if < 1)

• filename (str) – file path to save image to

• style (dict or str) – dictionary of style or file name of style file. This option is only used by the mpl output type. If a str is passed in that is the path to a json file which contains a dictionary of style, then that will be opened, parsed, and used as the input dict. See: Style Dict Doc for more information on the contents.

• interactive (bool) – when set 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.

• reverse_bits (bool) – When set to True, reverse the bit order inside registers for the output visualization.

• 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 is the number of (visual) layers before folding. Default is 25.

• ax (matplotlib.axes.Axes) – 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. This is only used when the output kwarg is set to use the mpl backend. It will be silently ignored with all other outputs.

• initial_state (bool) – Optional. Adds |0> in the beginning of the wire. Only used by the text, latex and latex_source outputs. Default: False.

• cregbundle (bool) – Optional. If set True bundle classical registers. Not used by the matplotlib output. Default: True.

Returns

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

• PIL.Image (output=’latex’)

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

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

a matplotlib figure object for the circuit diagram.

• str (output=’latex_source’)

The LaTeX source code for visualizing the circuit diagram.

• TextDrawing (output=’text’)

A drawing that can be printed as ASCII art.

Raises
• VisualizationError – when an invalid output method is selected

• ImportError – when the output methods require non-installed libraries

Style Dict Details

The style dict kwarg contains numerous options that define the style of the output circuit visualization. The style dict is only used by the mpl output. The options available in the style dict are defined below:

Parameters
• name (str) – The name of the style. The name can be set to ‘iqx’, ‘bw’, or ‘default’. This overrides the setting in the ‘~/.qiskit/settings.conf’ file.

• textcolor (str) – The color code to use for text. Defaults to ‘#000000’

• subtextcolor (str) – The color code to use for subtext. Defaults to ‘#000000’

• linecolor (str) – The color code to use for lines. Defaults to ‘#000000’

• creglinecolor (str) – The color code to use for classical register lines. Defaults to ‘#778899’

• gatetextcolor (str) – The color code to use for gate text. Defaults to ‘#000000’

• gatefacecolor (str) – The color code to use for gates. Defaults to ‘#ffffff’

• barrierfacecolor (str) – The color code to use for barriers. Defaults to ‘#bdbdbd’

• backgroundcolor (str) – The color code to use for the background. Defaults to ‘#ffffff’

• fontsize (int) – The font size to use for text. Defaults to 13.

• subfontsize (int) – The font size to use for subtext. Defaults to 8.

• displaytext (dict) –

A dictionary of the text to use for each element type in the output visualization. The default values are:

{
'id': 'id',
'u0': 'U_0',
'u1': 'U_1',
'u2': 'U_2',
'u3': 'U_3',
'x': 'X',
'y': 'Y',
'z': 'Z',
'h': 'H',
's': 'S',
'sdg': 'S^\dagger',
't': 'T',
'tdg': 'T^\dagger',
'rx': 'R_x',
'ry': 'R_y',
'rz': 'R_z',
'reset': '\left|0\right\rangle'
}


You must specify all the necessary values if using this. There is no provision for passing an incomplete dict in.

• displaycolor (dict) –

The color codes to use for each circuit element in the form (gate_color, text_color). The default values are:

{
'u1': ('#FA74A6', '#000000'),
'u2': ('#FA74A6', '#000000'),
'u3': ('#FA74A6', '#000000'),
'id': ('#05BAB6', '#000000'),
'x': ('#05BAB6', '#000000'),
'y': ('#05BAB6', '#000000'),
'z': ('#05BAB6', '#000000'),
'h': ('#6FA4FF', '#000000'),
'cx': ('#6FA4FF', '#000000'),
'cy': ('#6FA4FF', '#000000'),
'cz': ('#6FA4FF', '#000000'),
'swap': ('#6FA4FF', '#000000'),
's': ('#6FA4FF', '#000000'),
'sdg': ('#6FA4FF', '#000000'),
'dcx': ('#6FA4FF', '#000000'),
'iswap': ('#6FA4FF', '#000000'),
't': ('#BB8BFF', '#000000'),
'tdg': ('#BB8BFF', '#000000'),
'r': ('#BB8BFF', '#000000'),
'rx': ('#BB8BFF', '#000000'),
'ry': ('#BB8BFF', '#000000'),
'rz': ('#BB8BFF', '#000000'),
'rxx': ('#BB8BFF', '#000000'),
'ryy': ('#BB8BFF', '#000000'),
'rzx': ('#BB8BFF', '#000000'),
'reset': ('#000000', #FFFFFF'),
'target': ('#FFFFFF, '#FFFFFF'),
'measure': ('#000000', '#FFFFFF'),
'ccx': ('#BB8BFF', '#000000'),
'cdcx': ('#BB8BFF', '#000000'),
'ccdcx': ('#BB8BFF', '#000000'),
'cswap': ('#BB8BFF', '#000000'),
'ccswap': ('#BB8BFF', '#000000'),
'mcx': ('#BB8BFF', '#000000'),
'mcx_gray': ('#BB8BFF', '#000000),
'u': ('#BB8BFF', '#000000'),
'p': ('#BB8BFF', '#000000'),
'sx': ('#BB8BFF', '#000000'),
'sxdg': ('#BB8BFF', '#000000')
}


Colors can also be entered without the text color, such as ‘u1’: ‘#FA74A6’, in which case the text color will always be ‘gatetextcolor’. The ‘displaycolor’ dict can contain any number of elements from one to the entire dict above.

• latexdrawerstyle (bool) – When set to True, enable LaTeX mode, which will draw gates like the latex output modes.

• usepiformat (bool) – When set to True, use radians for output.

• fold (int) – The number of circuit elements to fold the circuit at. Defaults to 20.

• cregbundle (bool) – If set True, bundle classical registers

• showindex (bool) – If set True, draw an index.

• compress (bool) – If set True, draw a compressed circuit.

• figwidth (int) – The maximum width (in inches) for the output figure.

• dpi (int) – The DPI to use for the output image. Defaults to 150.

• margin (list) – A list of margin values to adjust spacing around output image. Takes a list of 4 ints: [x left, x right, y bottom, y top].

• creglinestyle (str) – The style of line to use for classical registers. Choices are ‘solid’, ‘doublet’, or any valid matplotlib linestyle kwarg value. Defaults to doublet

extend(rhs)

Append QuantumCircuit to the right hand side 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 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)

Apply initialize to circuit.

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.

mcmt(gate, control_qubits, target_qubits, ancilla_qubits=None, mode='noancilla', *, single_control_gate_fun=None, q_controls=None, q_ancillae=None, q_targets=None)

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

This can also be used to implement a generic multi-control gate, as the target could also be of length 1.

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, 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: - ‘no-ancilla’: 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

mirror()

DEPRECATED: use circuit.reverse_ops().

Returns

the reversed circuit.

Return type

QuantumCircuit

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.

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.

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

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) ├─────

└──────────┘

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.

sdg(qubit)

Apply SdgGate.

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.

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.

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.

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.

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.

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.

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.

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.

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.