# gate_library#

Standard gateset for use with the quantify_scheduler.

## Module Contents#

### Classes#

 Rxy A single qubit rotation around an axis in the equator of the Bloch sphere. X A single qubit rotation of 180 degrees around the X-axis. X90 A single qubit rotation of 90 degrees around the X-axis. Y A single qubit rotation of 180 degrees around the Y-axis. Y90 A single qubit rotation of 90 degrees around the Y-axis. Rz A single qubit rotation about the Z-axis of the Bloch sphere. Z A single qubit rotation of 180 degrees around the Z-axis. Z90 A single qubit rotation of 90 degrees around the Z-axis. H A single qubit Hadamard gate. CNOT Conditional-NOT gate, a common entangling gate. CZ Conditional-phase gate, a common entangling gate. Reset Reset a qubit to the $$|0\rangle$$ state. Measure A projective measurement in the Z-basis.

### Functions#

 _modulo_360_with_mapping(→ float) Maps an input angle theta (in degrees) onto the range ]-180, 180].
class Rxy(theta: float, phi: float, qubit: str)[source]#

A single qubit rotation around an axis in the equator of the Bloch sphere.

This operation can be represented by the following unitary as defined in https://doi.org/10.1109/TQE.2020.2965810:

$\begin{split}\mathsf {R}_{xy} \left(\theta, \varphi\right) = \begin{bmatrix} \textrm {cos}(\theta /2) & -ie^{-i\varphi }\textrm {sin}(\theta /2) \\ -ie^{i\varphi }\textrm {sin}(\theta /2) & \textrm {cos}(\theta /2) \end{bmatrix}\end{split}$
Parameters:
• theta – Rotation angle in degrees, will be casted to the [-180, 180) domain.

• phi – Phase of the rotation axis, will be casted to the [0, 360) domain.

• qubit – The target qubit.

class X(qubit: str)[source]#

Bases: Rxy

A single qubit rotation of 180 degrees around the X-axis.

This operation can be represented by the following unitary:

$\begin{split}X180 = R_{X180} = \begin{bmatrix} 0 & -i \\ -i & 0 \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class X90(qubit: str)[source]#

Bases: Rxy

A single qubit rotation of 90 degrees around the X-axis.

It is identical to the Rxy gate with theta=90 and phi=0

Defined by the unitary:

$\begin{split}X90 = R_{X90} = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & -i \\ -i & 1 \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class Y(qubit: str)[source]#

Bases: Rxy

A single qubit rotation of 180 degrees around the Y-axis.

It is identical to the Rxy gate with theta=180 and phi=90

Defined by the unitary:

$\begin{split}Y180 = R_{Y180} = \begin{bmatrix} 0 & -1 \\ 1 & 0 \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class Y90(qubit: str)[source]#

Bases: Rxy

A single qubit rotation of 90 degrees around the Y-axis.

It is identical to the Rxy gate with theta=90 and phi=90

Defined by the unitary:

$\begin{split}Y90 = R_{Y90} = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & -1 \\ 1 & 1 \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class Rz(theta: float, qubit: str)[source]#

A single qubit rotation about the Z-axis of the Bloch sphere.

This operation can be represented by the following unitary as defined in https://www.quantum-inspire.com/kbase/rz-gate/:

$\begin{split}\mathsf {R}_{z} \left(\theta\right) = \begin{bmatrix} e^{-i\theta/2} & 0 \\ 0 & e^{i\theta/2} \end{bmatrix}\end{split}$
Parameters:
• theta – Rotation angle in degrees, will be cast to the [-180, 180) domain.

• qubit – The target qubit.

class Z(qubit: str)[source]#

Bases: Rz

A single qubit rotation of 180 degrees around the Z-axis.

Note that the gate implements $$R_z(\pi) = -iZ$$, adding a global phase of $$-\pi/2$$. This operation can be represented by the following unitary:

$\begin{split}Z180 = R_{Z180} = -iZ = e^{-\frac{\pi}{2}}Z = \begin{bmatrix} -i & 0 \\ 0 & i \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class Z90(qubit: str)[source]#

Bases: Rz

A single qubit rotation of 90 degrees around the Z-axis.

This operation can be represented by the following unitary:

$\begin{split}Z90 = R_{Z90} = e^{-\frac{\pi/2}{2}}S = e^{-\frac{\pi/2}{2}}\sqrt{Z} = \frac{1}{\sqrt{2}}\begin{bmatrix} 1-i & 0 \\ 0 & 1+i \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class H(*qubits: str)[source]#

Note that the gate uses $$R_z(\pi) = -iZ$$, adding a global phase of $$-\pi/2$$. This operation can be represented by the following unitary:

$\begin{split}H = Y90 \cdot Z = \frac{-i}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \\ \end{bmatrix}\end{split}$
Parameters:

qubit – The target qubit.

class CNOT(qC: str, qT: str)[source]#

Conditional-NOT gate, a common entangling gate.

Performs an X gate on the target qubit qT conditional on the state of the control qubit qC.

This operation can be represented by the following unitary:

$\begin{split}\mathrm{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ \end{bmatrix}\end{split}$
Parameters:
• qC – The control qubit.

• qT – The target qubit

class CZ(qC: str, qT: str)[source]#

Conditional-phase gate, a common entangling gate.

Performs a Z gate on the target qubit qT conditional on the state of the control qubit qC.

This operation can be represented by the following unitary:

$\begin{split}\mathrm{CZ} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \\ \end{bmatrix}\end{split}$
Parameters:
• qC – The control qubit.

• qT – The target qubit

class Reset(*qubits: str)[source]#

Reset a qubit to the $$|0\rangle$$ state.

The Reset gate is an idle operation that is used to initialize one or more qubits.

Note

Strictly speaking this is not a gate as it can not be described by a unitary.

Examples

The operation can be used in several ways:

from quantify_scheduler.operations.gate_library import Reset

reset_1 = Reset("q0")
reset_2 = Reset("q1", "q2")
reset_3 = Reset(*[f"q{i}" for i in range(3, 6)])

Parameters:

qubits – The qubit(s) to reset. NB one or more qubits can be specified, e.g., Reset("q0"), Reset("q0", "q1", "q2"), etc..

class Measure(*qubits: str, acq_channel: Hashable | None = None, acq_index: Tuple[int, Ellipsis] | int | None = None, acq_protocol: Literal[SSBIntegrationComplex, Trace, TriggerCount, NumericalSeparatedWeightedIntegration, NumericalWeightedIntegration, ThresholdedAcquisition] | None = None, bin_mode: = None, feedback_trigger_label: = None)[source]#

A projective measurement in the Z-basis.

The measurement is compiled according to the type of acquisition specified in the device configuration.

Note

Strictly speaking this is not a gate as it can not be described by a unitary.

Parameters:
• qubits – The qubits you want to measure.

• acq_channel – Only for special use cases. By default (if None): the acquisition channel specified in the device element is used. If set, this acquisition channel is used for this measurement.

• acq_index – Index of the register where the measurement is stored. If None specified, this defaults to writing the result of all qubits to acq_index 0. By default None.

• acq_protocol ("SSBIntegrationComplex" | "Trace" | "TriggerCount" | "NumericalSeparatedWeightedIntegration" | "NumericalWeightedIntegration" | None, optional) – Acquisition protocols that are supported. If None is specified, the default protocol is chosen based on the device and backend configuration. By default None.

• bin_mode – The binning mode that is to be used. If not None, it will overwrite the binning mode used for Measurements in the circuit-to-device compilation step. By default None.

• feedback_trigger_label (str) – The label corresponding to the feedback trigger, which is mapped by the compiler to a feedback trigger address on hardware, by default None.

_modulo_360_with_mapping(theta: float) [source]#

Maps an input angle theta (in degrees) onto the range ]-180, 180].

By mapping the input angle to the range ]-180, 180] (where -180 is excluded), it ensures that the output amplitude is always minimized on the hardware. This mapping should not have an effect on the qubit in general.

-180 degrees is excluded to ensure positive amplitudes in the gates like X180 and Z180.

Note that an input of -180 degrees is remapped to 180 degrees to maintain the positive amplitude constraint.

Parameters:

theta (float) – The rotation angle in degrees. This angle will be mapped to the interval ]-180, 180].

Returns:

The mapped angle in degrees, which will be in the range ]-180, 180]. This mapping ensures the output amplitude is always minimized for transmon operations.

Return type:

float

Example

 >>> _modulo_360_with_mapping(360) 0.0 >>> _modulo_360_with_mapping(-180) 180.0 >>> _modulo_360_with_mapping(270) -90.0