Getting Started with QGL

What is QGL

Quantum Gate Language (QGL) is a domain specific programming language embedded in python for specifying gate sequences on quantum processors. It is a low-level language in the sense that users write programs at the level of gates on physical qubits. While the QGL developers pay particular attention to the requirements of superconducting qubit systems, its structure is generic to any qubit system with dipole-coupled qubits in a rotating frame. In such systems, the rotation axis in the X-Y plane is determined by the pulse phase, and Z-axis rotations may be achieved through frame updates.

Dependencies

QGL is embedded in the python programming language. Currently, it is dependent on python versions 3.6+. QGL programming constructs look very similar to python programming constructs.

QGL relies on the concept of a “channel” to represent a qubit. The channel embodies the physical realization of the qubit in an experimental configuration or a simulation configuration. These characteristic can include physical qubit attributes, simulation or equipment mappings, and physical couplings between qubits. This configuration information is specified and maintained in an associated database, bbndb, which is necessary for compiling the QGL program into inputs for physical systems (such as realizable signals/pulses) or simulation inputs (native instruction set).

While QGL is not dependent on Auspex, Auspex is an experiment control framework which greatly facilitates executing QGL programs on laboratory hardware. Auspex provides constructs for abstracting (defining) instruments, connectivity, and post processing to enable “hands off” experimental control of sophiscated experiments on a variety of laboratory equipment including AWGs, digitizers, current sources, etc.

For plotting pulse waveforms within jupyter notebooks, QGL uses the bqplot library (which should be installed automatically when using the methods detailed below) and should not require any additional infrastructure. For Jupyter Lab compatibility additional steps are required:

conda install nodejs
jupyter labextension install @jupyter-widgets/jupyterlab-manager
jupyter labextension install bqplot

Installation

There are a number of ways to obtain QGL:

Directly from the pypi, which will get the most recent master release, e.g. 2019.2:

pip install qgl

QGL can be cloned from GitHub to participate in QGL development:

git clone https://github.com/BBN-Q/qgl.git

Or the source tree can be downloaded from GitHub. For the master branch:

https://github.com/BBN-Q/QGL/archive/master.zip

For downloaded or cloned repositories, one most subsequently install the package using pip:

cd QGL    
pip install -e .

which will automatically fetch and install all of the requirement packages. As typical with package managers, this process will execute the package requirements enumerated in setup.py.

Examples: where to start

QGL comes with a number of example jupyter notebook files that illustrate most of the basic QGL programming concepts (in the QGL/doc directory):

ex1_basic_QGL.ipynb: Basic setup of ‘qubit’ objects, defining sequences of pulses on qubits, and visualizing these pulse sequences.
ex2_single_qubit_sequences.ipynb: Simple spectroscopy and coherence experiments on a single qubit.
ex3_two_qubit_sequences.ipynb: Examples of two-qubit sequences, including CR gates.

Note that running Ex1 will generate a channel library database, example.sqlite. Ex2 and Ex3 rely on this database, so Ex1 must be run before Ex2 and Ex3. If the database schema changes, example.sqlite must be regenerated. So, make sure to remove example.sqlite whenever updating QGL versions.

In addition to these example notebooks for manipulating qubits, channel_libriary.ipynb provides a basic Channel Library that is used by ex2_single_qubit_sequences and ex3_two_qubit_sequences example notebooks.

Channels and Qubits

Many quantum processors require non-uniform control parameters to achieve high-fidelity gates across all qubits in the device. To support this need, QGL provides a number of channel objects to store the individual parameters needed to control or measure particular qubits.

Gates in QGL operate on resources known as logical channels. For control, these channels are either Qubits or Edges. The qubit channels encode properties specific to manipulating individual qubits in quantum processor, while Edges encode the connectivity of the device. Since some 2-qubit gates have a preferred directionality due to the physical parameters of the device, edges correspond to a directed edge in the qubit connectivity graph. Qubit measurements instead act upon a third logical channel type which is the measurement channel. A final logical resource type is the logical marker channel which is used to carry ancillary pulse information for things such as event triggers.

All logical channels are associated with physical channels through a Channel Library database in order for the QGL compiler to produce pulse files for the target hardware. The setup of this mapping is briefly described in the QGL example notebooks in this folder and a more detailed description is provide with the Auspex tools.

While setup of these channels is important for final sequence compilation, QGL programs typically refer only to Qubit channels. Actions on other channel types may be implied by the operation. For example, to create a Qubit object in QGL, one can write:

cl = ChannelLibrary(":memory:")
q1 = cl.new_qubit("q1")

where the Channel Library contains the “physical” information for the logical “qubit” channel.

The new_qubit method returns a Qubit object with the properties defined by the name q1 if found in the channel library. If the name is not found, then the users gets a Qubit object with the default properties.

Gate Primitives

The underlying representation of all QGL operations is a Pulse object. However, users are not expected to create Pulses directly, but instead interact with various pre-defined one- and two-qubit primitives.

Single-Qubit Operations

QGL provides the following single-qubit gates:

# generic rotation angle and phase
Utheta(q, angle, phase)

# generic rotations about a specific axis (phase)
Xtheta(q, angle)
Ytheta(q, angle)
Ztheta(q, angle)

# generic rotations of a specific angle
U(q, phase)
U90(q, phase)

# rotations of particular angle and phase
# X (phase = 0)
X(q)    # rotates by pi (180 degrees)
X90(q)  # rotates by +pi/2
X90m(q) # rotates by -pi/2

# Y (phase = pi/2)
Y(q)
Y90(q)
Y90m(q)

# just frame-updates
Z(q)
Z90(q)
Z90m(q)

# identity (delay or no-op)
Id(q, length) # length parameter is optional

# measurement
MEAS(q)

Due to the utility of Clifford-group operations in characterizing gate performance, QGL also directly provides a primitive to implement the 24-element single-qubit Clifford group:

# atomic Clifford operation on 1-qubit
AC(q, n)

This method is “atomic” because it implements the full 1-qubit Clifford group with one pulse per element, as opposed to requiring a sequence of the primitives already given above. We known of no canonical way to specify the elements of the Clifford group; consequently, AC identifies which Clifford by a numerical index (0-23). See the definition of AC in PulsePrimitives.py or the definition of C1 in Cliffords.py to find our enumeration of the group.

Two-qubit Operations

QGL provides only one high-level two-qubit primitive, CNOT. The implementation of CNOT may be chosen by specifying the cnot_implementation key in QGL’s config.py file.

# high-level primitives
CNOT(q1, q2)

# mid-level primitives
CNOT_simple(q1, q2) # a single-pulse gate on Edge(q1, q2)
CNOT_CR(q1, q2)     # an "echoed" cross-resonance CNOT gate on Edge(q1, q2)
ZX90_CR(q1, q2)     # a ZX90 on Edge(q1, q2) implemented with "echoed"
                    # cross-resonance pulses

# lowest-level primitives
echoCR(q1, q2)  # A "echoed" cross-resonance pulse

Composite Pulses

Occasionally one wants to construct a sequence of pulses and treat them as if the entire sequence were a single pulse. For this, QGL allows pulses to be joined with the + operator. This allows, for example, us to define

def hadamard(q):
    return Y90(q) + X(q)

and then use hadamard(q) just like any other pulse primitive, even though it is composed of a sequence of two pulses.

Additional Pulse Parameters

All QGL pulse primitives accept an arbitrary number of additional keyword arguments. In particular, any QGL primitive accepts a length keyword to modify the length of the resulting operation. These additional parameters are passed to the shape function when the QGL compiler constructs waveforms from Pulse objects.

Sequences and Concurrent Operations

Programs in QGL are specified using python lists. For example,
seq = [[X90(q1), X(q1), Y(q1), X90(q1), MEAS(q1)]]

The elements of the list provide a time-ordered sequence of pulses to execute. Using the python list to describe sequences allows for the use of python’s powerful list comprehension syntax to describe sequence variations. For instance, you can concisely write a scan over a rotation angle or delay in a list comprehension such as:

seq = [[X90(q1), Id(q1, length=d), X90(q1), MEAS(q1)] for d in np.linspace(0, 10e-6, 11)]

QGL’s compiler assumes that such lists of lists represent a series of related experiments and schedules them to occur sequentially in the AWG output.

Users express concurrent operation in QGL using the * operator. For instance,

q1 = cl.new_qubit("q1")
q2 = cl.new_qubit("q2")
seq = [[X90(q1)*X90(q2), MEAS(q1)*MEAS(q2)]]

would execute the same sequence on Qubits q1 and q2. If the gate durations differ between q1 and q2, the QGL compiler injects delays to create aligned PulseBlocks. By default, simultaneous pulses are “left-aligned”, meaning that the leading pulse edges are aligned and padding delays are injected on the trailing edge. However, the user may change this behavior with the align method:

seq = [[align(X90(q1)*X90(q2)), align(MEAS(q1)*MEAS(q2), mode="right")][

align takes a mode argument (“left”, “right”, or default “center”) to specify a particular pulse alignment within a PulseBlock.

Pulse Shapes and Waveforms

The QGL compiler constructs waveforms to implement the desired quantum operations. To do this, each pulse has a shape_fun (shape function) that is called with its shapeParams. A number of commonly used shapes are defined in the PulseShapes module including:

constant - i.e. a “square” pulse with constant amplitude
tanh - essentially a square pulse with rounded edges
gaussian - a truncated Gaussian shape
drag - the DRAG pulse gives a Gaussian shape with its derivative on the opposite quadrature.
gaussOn - the first half of a truncated Gaussian shape
gaussOff - the second half of a truncated Gaussian shape

The default pulse shape is determined by properties in the Channel Library. However, the QGL programmer may override the default shape with a keyword argument. For example, to force the use of square pulse shape we may write:

seq = [[X(q1, shape_fun=PulseShapes.constant), MEAS(q1)]]

One common use case for specifying a shape function is in the construction of composite pulses. For instance, you may want a square pulse shape with Gaussian edges rather than those given by the tanh function. To do this you might write:

seq = [[X(q1, shape_fun=PulseShapes.gaussOn) +\
       X(q1, shape_fun=PulseShapes.constant) +\
       X(q1, shape_fun=PulseShapes.gaussOff),
       MEAS(q1)]]

Shape functions can be an arbitrary piece of python code that returns a NumPy array of complex values. Shape functions must accept all of their arguments as keyword arguments. The only arguments that are guaranteed to exist are sampling_rate and length. The pulse length is always assumed to be in units of seconds; it is up to the shape function to use the passed sampling rate to convert from time into number of points/samples. As an example, we could define a ramp shape with

def ramp(length=0, sampling_rate=1e9, **kwargs):
    numPts = int(np.round(length * sampling_rate))
    return np.linspace(0, 1, numPts)

Then use it with any pulse primitive, e.g.:

seq = [[X(q1, shape_fun=ramp)]]

If your custom shape function requires additional arguments, you must either arrange for these parameters to exist in the LogicalChannel‘s shapeParams dictionary, or pass them at the call site. For instance,

def foo(length=0, sampling_rate=1e9, bar=1, **kwargs):
    numPts = int(np.round(length * sampling_rate))
    # something involving bar...

seq = [[X(q1, bar=0.5, shape_fun=foo)]] # bar is passed as a keyword arg

See the PulseShapes module for further examples.

Compiling and Plotting

To compile the QGL gate and pulse primitives to waveform and AWG vendor-specific hardware instructions, use the compile_to_hardware() method, e.g.:

seq = [[X90(q1), Id(q1, length=d), X90(q1), MEAS(q1)] for d in np.linspace(0, 10e-6, 11)]
meta_info = compile_to_hardware(seq, 'test/ramsey')

This code snippet will create a folder called test inside [AWGDir] (if defined) or a temp directory and produce sequence files for each AWG targeted by the PhysicalChannels associated with the QGL program. For instance, if the q1 channel targeted an AWG named APS1 and the M-q1 channel targeted APS2, then the above call to compile_to_hardware would produce two files: ramsey-APS1.aps2 and ramsey-APS2.aps2 in the test folder. It would also produce a meta information file ramsey-meta.json which contains data about the QGL program that may be useful for executing the program in an instrument control platform such as Auspex. compile_to_hardware returns the path to this “meta info” file.

The plot_pulse_files() creates a visual representation of the pulse sequence created by a QGL program. For example,

plot_pulse_files(meta_info)

will create an interactive plot where each line represents a physical output channel of an AWG referenced by the QGL program.

Built-in Basic Sequences

QGL provides many pre-defined methods for sequences commonly used to characterize a quantum device. These methods are defined in QGL’s BasicSequences package and include:
• RabiAmp
• RabiWidth
• PulsedSpec
• InversionRecovery
• Ramsey
• HahnEcho
• CPMG
• SingleQubitRB
• TwoQubitRB

Usage of each is defined in its respective doc string. For instance, at an ipython prompt, you may type ?RabiAmp to learn about the RabiAmp function. This will return information on the function usage and return types as illustrated below:

Signature: RabiAmp(qubit, amps, phase=0, showPlot=False)
Docstring:
Variable amplitude Rabi nutation experiment.

Parameters
----------
qubit : logical channel to implement sequence (LogicalChannel)
amps : pulse amplitudes to sweep over (iterable)
phase : phase of the pulse (radians)
showPlot : whether to plot (boolean)

Returns
-------
plotHandle : handle to plot window to prevent destruction
File:      ~/Repos/QGL/QGL/BasicSequences/Rabi.py
Type:      function

We encourage users to peruse the methods defined in BasicSequences for templates that may be useful in writing their own QGL programs.

For additional information into QGL settings and compiler customizations (such as type of 2-qubit gate), please reveiw config.py.