This page is from an old version of Qiskit SDK. Go to the latest version.

# TridiagonalToeplitz

class TridiagonalToeplitz(num_state_qubits, main_diag, off_diag, tolerance=0.01, evolution_time=1.0, trotter_steps=1, name='tridi')

GitHub

The deprecated class of tridiagonal Toeplitz symmetric matrices.

Given the main entry, $a$, and the off diagonal entry, $b$, the $4\times 4$ dimensional tridiagonal Toeplitz symmetric matrix is

$\begin{split}\begin{pmatrix} a & b & 0 & 0 \\ b & a & b & 0 \\ 0 & b & a & b \\ 0 & 0 & b & a \end{pmatrix}.\end{split}$

Examples:

import warnings
import numpy as np
from qiskit import QuantumCircuit
from qiskit.algorithms.linear_solvers.matrices import TridiagonalToeplitz

with warnings.catch_warnings():
warnings.simplefilter('ignore')
matrix = TridiagonalToeplitz(2, 1, -1 / 3)
power = 3

# Controlled power (as within QPE)
num_qubits = matrix.num_state_qubits
pow_circ = matrix.power(power).control()
circ_qubits = pow_circ.num_qubits
qc = QuantumCircuit(circ_qubits)
qc.append(matrix.power(power).control(), list(range(circ_qubits)))

Parameters

• num_state_qubits (int) – the number of qubits where the unitary acts.
• main_diag (float) – the main diagonal entry
• off_diag (float) – the off diagonal entry
• tolerance (float) – the accuracy desired for the approximation
• evolution_time (float) – the time of the Hamiltonian simulation
• trotter_steps (int) – the number of Trotter steps
• name (str) – The name of the object.

## Methods

TridiagonalToeplitz.add_bits(bits)

Add Bits to the circuit.

Return type

None

TridiagonalToeplitz.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.

Return type

None

TridiagonalToeplitz.add_register(*regs)

Return type

None

### append

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

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

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

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

Parameters

Returns

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

Return type

qiskit.circuit.InstructionSet

Raises

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

### assign_parameters

TridiagonalToeplitz.assign_parameters(parameters, inplace=False)

Assign parameters to new parameters or values.

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

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

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

Parameters

• parameters (Union[Mapping[Parameter, Union[ParameterExpression, float]], Sequence[Union[ParameterExpression, float]]]) – Either a dictionary or iterable specifying the new parameter values.
• 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 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.

Return type

Optional[QuantumCircuit]

Returns

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

Examples

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

from qiskit.circuit import QuantumCircuit, Parameter

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

Fig. 33 (png, hires.png, pdf)

Fig. 34 (png, hires.png, pdf)

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

from qiskit.circuit import QuantumCircuit, ParameterVector

circuit = QuantumCircuit(2)
params = ParameterVector('P', 2)
circuit.ry(params[0], 0)
circuit.crx(params[1], 0, 1)

bound_circuit = circuit.assign_parameters([1, 2])
bound_circuit.draw('mpl')

circuit.draw('mpl')

Fig. 35 (png, hires.png, pdf)

Fig. 36 (png, hires.png, pdf)

### barrier

TridiagonalToeplitz.barrier(*qargs, label=None)

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

Parameters

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

Returns

handle to the added instructions.

Return type

qiskit.circuit.InstructionSet

### bind_parameters

TridiagonalToeplitz.bind_parameters(values)

Assign numeric parameters to values yielding a new circuit.

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

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

Parameters

values (Union[Mapping[Parameter, float], Sequence[float]]) – {parameter: value, ...} or [value1, value2, ...]

Raises

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

Return type

QuantumCircuit

Returns

Copy of self with assignment substitution.

### break_loop

TridiagonalToeplitz.break_loop()

Apply BreakLoopOp.

Warning

If you are using the context-manager “builder” forms of if_test(), for_loop() or while_loop(), you can only call this method if you are within a loop context, because otherwise the “resource width” of the operation cannot be determined. This would quickly lead to invalid circuits, and so if you are trying to construct a reusable loop body (without the context managers), you must also use the non-context-manager form of if_test() and if_else(). Take care that the BreakLoopOp instruction must span all the resources of its containing loop, not just the immediate scope.

Return type

InstructionSet

Returns

A handle to the instruction created.

Raises

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

### cast

static TridiagonalToeplitz.cast(value, type_)

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

Return type

Union[TypeVar(S), TypeVar(T)]

### cbit_argument_conversion

TridiagonalToeplitz.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

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

Apply CCXGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### ccz

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

Apply CCZGate.

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

Parameters

• control_qubit1 (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the first control.
• control_qubit2 (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the second control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘10’). Defaults to controlling on the ‘11’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### ch

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

Apply CHGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

TridiagonalToeplitz.clear()

Clear all instructions in self.

Clearing the circuits will keep the metadata and calibrations.

Return type

None

### cls_instances

classmethod TridiagonalToeplitz.cls_instances()

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

Return type

int

### cls_prefix

classmethod TridiagonalToeplitz.cls_prefix()

Return the prefix to use for auto naming.

Return type

str

### cnot

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

Apply CXGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

QuantumCircuit.cx: the same function with a different name.

### compose

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

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

other can be narrower or of equal width to self.

Parameters

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

Returns

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

Return type

QuantumCircuit

Raises

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

Examples

>>> lhs.compose(rhs, qubits=[3, 2], inplace=True)
            ┌───┐                   ┌─────┐                ┌───┐
lqr_1_0: ───┤ H ├───    rqr_0: ──■──┤ Tdg ├    lqr_1_0: ───┤ H ├───────────────
├───┤              ┌─┴─┐└─────┘                ├───┤
lqr_1_1: ───┤ X ├───    rqr_1: ┤ X ├───────    lqr_1_1: ───┤ X ├───────────────
┌──┴───┴──┐           └───┘                    ┌──┴───┴──┐┌───┐
lqr_1_2: ┤ U1(0.1) ├  +                     =  lqr_1_2: ┤ U1(0.1) ├┤ X ├───────
└─────────┘                                    └─────────┘└─┬─┘┌─────┐
lqr_2_0: ─────■─────                           lqr_2_0: ─────■───────■──┤ Tdg ├
┌─┴─┐                                          ┌─┴─┐        └─────┘
lqr_2_1: ───┤ X ├───                           lqr_2_1: ───┤ X ├───────────────
└───┘                                          └───┘
lcr_0: 0 ═══════════                           lcr_0: 0 ═══════════════════════

lcr_1: 0 ═══════════                           lcr_1: 0 ═══════════════════════

### condition_bounds

TridiagonalToeplitz.condition_bounds()

Return lower and upper bounds on the condition number of the matrix.

Return type

Tuple[float, float]

### continue_loop

TridiagonalToeplitz.continue_loop()

Apply ContinueLoopOp.

Warning

If you are using the context-manager “builder” forms of if_test(), for_loop() or while_loop(), you can only call this method if you are within a loop context, because otherwise the “resource width” of the operation cannot be determined. This would quickly lead to invalid circuits, and so if you are trying to construct a reusable loop body (without the context managers), you must also use the non-context-manager form of if_test() and if_else(). Take care that the ContinueLoopOp instruction must span all the resources of its containing loop, not just the immediate scope.

Return type

InstructionSet

Returns

A handle to the instruction created.

Raises

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

### control

TridiagonalToeplitz.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

TridiagonalToeplitz.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

### copy_empty_like

TridiagonalToeplitz.copy_empty_like(name=None)

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

#### That structure includes:

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

Parameters

name (str) – Name for the copied circuit. If None, then the name stays the same.

Returns

An empty copy of self.

Return type

QuantumCircuit

### count_ops

TridiagonalToeplitz.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

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

Apply CPhaseGate.

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

Parameters

• theta (Union[ParameterExpression, float]) – The angle of the rotation.
• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### crx

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

Apply CRXGate.

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

Parameters

• theta (Union[ParameterExpression, float]) – The angle of the rotation.
• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cry

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

Apply CRYGate.

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

Parameters

• theta (Union[ParameterExpression, float]) – The angle of the rotation.
• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### crz

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

Apply CRZGate.

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

Parameters

• theta (Union[ParameterExpression, float]) – The angle of the rotation.
• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cs

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

Apply CSGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### csdg

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

Apply CSdgGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cswap

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

Apply CSwapGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit1 (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• target_qubit2 (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### csx

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

Apply CSXGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cu

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

Apply CUGate.

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

Parameters

• theta (Union[ParameterExpression, float]) – The $\theta$ rotation angle of the gate.
• phi (Union[ParameterExpression, float]) – The $\phi$ rotation angle of the gate.
• lam (Union[ParameterExpression, float]) – The $\lambda$ rotation angle of the gate.
• gamma (Union[ParameterExpression, float]) – The global phase applied of the U gate, if applied.
• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cx

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

Apply CXGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the control.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cy

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

Apply CYGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the controls.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### cz

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

Apply CZGate.

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

Parameters

• control_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) used as the controls.
• target_qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) targeted by the gate.
• label (Optional[str]) – The string label of the gate in the circuit.
• ctrl_state (Union[str, int, None]) – The control state in decimal, or as a bitstring (e.g. ‘1’). Defaults to controlling on the ‘1’ state.

Return type

InstructionSet

Returns

A handle to the instructions created.

### dcx

TridiagonalToeplitz.dcx(qubit1, qubit2)

Apply DCXGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### decompose

TridiagonalToeplitz.decompose(gates_to_decompose=None, reps=1)

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

Parameters

• gates_to_decompose (str or list(str)) – optional subset of gates to decompose. Defaults to all gates in circuit.
• reps (int) – Optional number of times the circuit should be decomposed. For instance, reps=2 equals calling circuit.decompose().decompose(). can decompose specific gates specific time

Returns

a circuit one level decomposed

Return type

QuantumCircuit

### delay

TridiagonalToeplitz.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 or ParameterExpression) – 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

handle to the added instructions.

Return type

qiskit.circuit.InstructionSet

Raises

CircuitError – if arguments have bad format.

### depth

TridiagonalToeplitz.depth(*args, **kwargs)

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

Parameters

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

Returns

Depth of circuit.

Return type

int

Notes

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

### diagonal

TridiagonalToeplitz.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

TridiagonalToeplitz.draw(*args, **kwargs)

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

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

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

latex: high-quality images compiled via latex.

latex_source: raw uncompiled latex output.

Parameters

• output (str) – 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 or latex output type. If style is a str, it is used as the path to a json file which contains a style dict. The file will be opened, parsed, and then any style elements in the dict will replace the default values in the input dict. A file to be loaded must end in .json, but the name entered here can omit .json. For example, style='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 unless the user config file (usually ~/.qiskit/settings.conf) has an alternative value set. For example, circuit_reverse_bits = True.
• 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, except for when output is set to "text".
• wire_order (list) – Optional. A list of integers used to reorder the display of the bits. The list must have an entry for every bit with the bits in the range 0 to (num_qubits + num_clbits).

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

### ecr

TridiagonalToeplitz.ecr(qubit1, qubit2)

Apply ECRGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### eigs_bounds

TridiagonalToeplitz.eigs_bounds()

Return lower and upper bounds on the absolute eigenvalues of the matrix.

Return type

Tuple[float, float]

### find_bit

TridiagonalToeplitz.find_bit(bit)

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

Parameters

bit (Bit) – The bit to locate.

Returns

A 2-tuple. The first element (index)

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

Return type

namedtuple(int, List[Tuple(Register, int)])

Notes

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

Raises

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

### for_loop

TridiagonalToeplitz.for_loop(indexset, loop_parameter=None, body=None, qubits=None, clbits=None, *, label=None)

Create a for loop on this circuit.

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

For example:

from qiskit import QuantumCircuit
qc = QuantumCircuit(2, 1)

with qc.for_loop(range(5)) as i:
qc.h(0)
qc.cx(0, 1)
qc.measure(0, 0)
qc.break_loop().c_if(0, True)

Parameters

• indexset (Iterable[int]) – A collection of integers to loop over. Always necessary.

• loop_parameter (Optional[Parameter]) –

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

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

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

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

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

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

Returns

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

Return type

InstructionSet or ForLoopContext

Raises

CircuitError – if an incorrect calling convention is used.

### fredkin

TridiagonalToeplitz.fredkin(control_qubit, target_qubit1, target_qubit2)

Apply CSwapGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

QuantumCircuit.cswap: the same function with a different name.

### from_instructions

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

Construct a circuit from an iterable of CircuitInstructions.

Parameters

• instructions – The instructions to add to the circuit.
• qubits – Any qubits to add to the circuit. This argument can be used, for example, to enforce a particular ordering of qubits.
• clbits – Any classical bits to add to the circuit. This argument can be used, for example, to enforce a particular ordering of classical bits.
• name – The name of the circuit.
• global_phase – The global phase of the circuit in radians.
• metadata – Arbitrary key value metadata to associate with the circuit.

Returns

The quantum circuit.

### from_qasm_file

static TridiagonalToeplitz.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

### from_qasm_str

static TridiagonalToeplitz.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

### get_instructions

TridiagonalToeplitz.get_instructions(name)

Get instructions matching name.

Parameters

name (str) – The name of instruction to.

Returns

list of (instruction, qargs, cargs).

Return type

list(tuple)

### h

TridiagonalToeplitz.h(qubit)

Apply HGate.

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

Parameters

qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) to apply the gate to.

Return type

InstructionSet

Returns

A handle to the instructions created.

### hamiltonian

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

Apply hamiltonian evolution to qubits.

### has_calibration_for

TridiagonalToeplitz.has_calibration_for(instr_context)

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

### has_register

TridiagonalToeplitz.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

TridiagonalToeplitz.i(qubit)

Apply IGate.

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

Parameters

qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) to apply the gate to.

Return type

InstructionSet

Returns

A handle to the instructions created.

### id

TridiagonalToeplitz.id(qubit)

Apply IGate.

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

Parameters

qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) to apply the gate to.

Return type

InstructionSet

Returns

A handle to the instructions created.

QuantumCircuit.i: the same function.

### if_else

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

Apply IfElseOp.

Note

This method does not have an associated context-manager form, because it is already handled by the if_test() method. You can use the else part of that with something such as:

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

Parameters

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

Raises

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

Return type

InstructionSet

Returns

A handle to the instruction created.

### if_test

TridiagonalToeplitz.if_test(condition, true_body=None, qubits=None, clbits=None, *, label=None)

Create an if statement on this circuit.

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

For example:

from qiskit.circuit import QuantumCircuit, Qubit, Clbit
bits = [Qubit(), Qubit(), Qubit(), Clbit(), Clbit()]
qc = QuantumCircuit(bits)

qc.h(0)
qc.cx(0, 1)
qc.measure(0, 0)
qc.h(0)
qc.cx(0, 1)
qc.measure(0, 1)

with qc.if_test((bits[3], 0)) as else_:
qc.x(2)
with else_:
qc.h(2)
qc.z(2)

Parameters

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

Returns

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

Return type

InstructionSet or IfContext

Raises

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

Returns

A handle to the instruction created.

### initialize

TridiagonalToeplitz.initialize(params, qubits=None)

Initialize qubits in a specific state.

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

Parameters

• params (str or list or int) –

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

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

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()

output:

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

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

import numpy as np
from qiskit import QuantumCircuit

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

output:

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

Initialize two qubits from an array of complex amplitudes.

import numpy as np
from qiskit import QuantumCircuit

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

output:

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

### inverse

TridiagonalToeplitz.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

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

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

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.
• epsilon (float) – error tolerance of calculations. Default is epsilon = _EPS.

Returns

the isometry is attached to the quantum circuit.

Return type

QuantumCircuit

Raises

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

### isometry

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

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

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.
• epsilon (float) – error tolerance of calculations. Default is epsilon = _EPS.

Returns

the isometry is attached to the quantum circuit.

Return type

QuantumCircuit

Raises

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

### iswap

TridiagonalToeplitz.iswap(qubit1, qubit2)

Apply iSwapGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### mcp

TridiagonalToeplitz.mcp(lam, control_qubits, target_qubit)

Apply MCPhaseGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### mcrx

TridiagonalToeplitz.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 (QuantumRegister or 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

TridiagonalToeplitz.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

TridiagonalToeplitz.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

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

Apply MCXGate.

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

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

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

Raises

• ValueError – if the given mode is not known, or if too few ancilla qubits are passed.
• AttributeError – if no ancilla qubits are passed, but some are needed.

QuantumCircuit.mcx: the same gate with a different name.

### mcx

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

Apply MCXGate.

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

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

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

Raises

• ValueError – if the given mode is not known, or if too few ancilla qubits are passed.
• AttributeError – if no ancilla qubits are passed, but some are needed.

### measure

TridiagonalToeplitz.measure(qubit, cbit)

Measure quantum bit into classical bit (tuples).

Parameters

Returns

handle to the added instructions.

Return type

qiskit.circuit.InstructionSet

Raises

CircuitError – if arguments have bad format.

### measure_active

TridiagonalToeplitz.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

TridiagonalToeplitz.measure_all(inplace=True, add_bits=True)

Adds measurement to all qubits.

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

Returns a new circuit with measurements if inplace=False.

Parameters

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

Returns

Returns circuit with measurements when inplace=False.

Return type

QuantumCircuit

Raises

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

### ms

TridiagonalToeplitz.ms(theta, qubits)

Apply MSGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### num_connected_components

TridiagonalToeplitz.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

TridiagonalToeplitz.num_nonlocal_gates()

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

Conditional nonlocal gates are also included.

### num_tensor_factors

TridiagonalToeplitz.num_tensor_factors()

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

Notes

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

Return type

int

### num_unitary_factors

TridiagonalToeplitz.num_unitary_factors()

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

Return type

int

### p

TridiagonalToeplitz.p(theta, qubit)

Apply PhaseGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### pauli

TridiagonalToeplitz.pauli(pauli_string, qubits)

Apply PauliGate.

Parameters

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

Return type

InstructionSet

Returns

A handle to the instructions created.

### power

TridiagonalToeplitz.power(power, matrix_power=False)

Build powers of the circuit.

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.

Return type

QuantumCircuit

Returns

The quantum circuit implementing powers of the unitary.

### prepare_state

TridiagonalToeplitz.prepare_state(state, qubits=None, label=None)

Prepare qubits in a specific state.

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

Parameters

• state (str or list or int or Statevector) –

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

• QuantumRegister: A list of qubits to be initialized [Default: None].
• Qubit: Single qubit to be initialized [Default: None].
• int: Index of qubit to be initialized [Default: None].
• list: Indexes of qubits to be initialized [Default: None].
• label (str) – An optional label for the gate

Returns

a handle to the instruction that was just initialized

Return type

qiskit.circuit.Instruction

Examples

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

import numpy as np
from qiskit import QuantumCircuit

circuit = QuantumCircuit(1)
circuit.prepare_state([1/np.sqrt(2), -1/np.sqrt(2)], 0)
circuit.draw()

output:

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

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

import numpy as np
from qiskit import QuantumCircuit

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

output:

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

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

import numpy as np
from qiskit import QuantumCircuit

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

output:

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

### qasm

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

Return OpenQASM string.

Parameters

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

Returns

If formatted=False.

Return type

str

Raises

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

### qbit_argument_conversion

TridiagonalToeplitz.qbit_argument_conversion(qubit_representation)

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

Parameters

qubit_representation (Object) – representation to expand

Returns

the resolved instances of the qubits.

Return type

List(Qubit)

### qubit_duration

TridiagonalToeplitz.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

float

Returns

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

### qubit_start_time

TridiagonalToeplitz.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
• self.qubits. (indices of) –

Return type

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

TridiagonalToeplitz.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
• self.qubits. (indices of) –

Return type

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.

### r

TridiagonalToeplitz.r(theta, phi, qubit)

Apply RGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rcccx

TridiagonalToeplitz.rcccx(control_qubit1, control_qubit2, control_qubit3, target_qubit)

Apply RC3XGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rccx

TridiagonalToeplitz.rccx(control_qubit1, control_qubit2, target_qubit)

Apply RCCXGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### remove_final_measurements

TridiagonalToeplitz.remove_final_measurements(inplace=True)

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

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

Parameters

inplace (bool) – All measurements removed inplace or return new circuit.

Returns

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

Return type

QuantumCircuit

### repeat

TridiagonalToeplitz.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

TridiagonalToeplitz.reset(qubit)

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

Parameters

qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – qubit(s) to reset.

Returns

handle to the added instruction.

Return type

qiskit.circuit.InstructionSet

### reverse_bits

TridiagonalToeplitz.reverse_bits()

Return a circuit with the opposite order of wires.

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

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

Returns

the circuit with reversed bit order.

Return type

QuantumCircuit

Examples

input:

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

output:

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

### reverse_ops

TridiagonalToeplitz.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

TridiagonalToeplitz.rv(vx, vy, vz, qubit)

Apply RVGate.

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

Rotation around an arbitrary rotation axis $v$, where $|v|$ is the angle of rotation in radians.

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rx

TridiagonalToeplitz.rx(theta, qubit, label=None)

Apply RXGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rxx

TridiagonalToeplitz.rxx(theta, qubit1, qubit2)

Apply RXXGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### ry

TridiagonalToeplitz.ry(theta, qubit, label=None)

Apply RYGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### ryy

TridiagonalToeplitz.ryy(theta, qubit1, qubit2)

Apply RYYGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rz

TridiagonalToeplitz.rz(phi, qubit)

Apply RZGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rzx

TridiagonalToeplitz.rzx(theta, qubit1, qubit2)

Apply RZXGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### rzz

TridiagonalToeplitz.rzz(theta, qubit1, qubit2)

Apply RZZGate.

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

Parameters

Return type

InstructionSet

Returns

A handle to the instructions created.

### s

TridiagonalToeplitz.s(qubit)

Apply SGate.

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

Parameters

qubit (Union[Qubit, QuantumRegister, int, slice, Sequence[Union[Qubit, int]]]) – The qubit(s) to apply the gate to.

Return type

InstructionSet

Returns

A handle to the instructions created.

### save_amplitudes

TridiagonalToeplitz.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

TridiagonalToeplitz.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_clifford

TridiagonalToeplitz.save_clifford(label='clifford', pershot=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].

Returns

with attached instruction.

Return type

QuantumCircuit

Note

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