# Syntax and grammar¶

Note

The Blackbird used directly inside a Strawberry Fields Engine context is a superset of the Blackbird quantum assembly language described here, as it is embedded in a Python environment.

You can think of it as ‘Python-enhanced Blackbird’, as Python functions and constructs, can be used, even if they are not ‘officially’ part of the Blackbird spec.

## Introduction¶

In this section, we define the structure, syntax, and grammar of Blackbird code.

### Philosophy¶

Blackbird was designed from the ground up, adhering to the following philosophies:

Encapsulate any universal photonic quantum computation.

Be clear, concise, and simple to read and follow. This simplicity should allow for both

• Human readability - operations and expressions should correspond to existing conventions, and allude to common notation in quantum computing
• Hardware execution - code should be unambiguous, with one quantum operation per line

Be easy to learn, using constructs and operators familiar in scientific computation.

A Blackbird script should contain only one quantum algorithm or simulation, making it an ideal format for saving and loading photonic quantum computing algorithms.

### Similarity to Python¶

To satisfy points 2 and 3, Blackbird is deliberately Python-like, inheriting the following:

• Case sensitivity.
• # for line comments.
• Newlines indicate the end of a statement.
• Operators and literals are similar to their Python equivalents.
• The | operator is used to apply intrinsic quantum operations to quantum registers.
• After measurement, quantum modes are automatically and implicitly converted into classical registers.
• The resulting output is implicitly determined by the presence of measurement statements.

### Differences to Python¶

Contrary to Python, however, we also introduce the following restrictions, to enable Blackbird to function as a quantum assembly language across a wide array of quantum hardware:

• Statically typed - you must declare the variable type, and variables and arguments of conflicting types are not automatically cast to the correct type.
• Array variables may be declared, but Blackbird does not support array manipulation.

All Blackbird programs must begin with a required metadata block as follows:

name progam_name
version 1.0


The name and the version keywords must be given in the order above and are mandatory. The name simply specifies the name of your Blackbird program, while the version number is the version number of the Blackbird spec it is written for.

In addition, you may specify an optional target keyword:

target chip0


This indicates the device or simulator the Blackbird program targets — that is, you are specifying that the contained Blackbird code is compiled for the targeted device/simulator.

The target keyword also accepts keyword options, using the syntax (option1=0.32, option2=40). For example:

target chip0 (shots=100)


## Variable declarations¶

Variable may be optionally defined on any new line in the blackbird script.

The syntax for defining variables is as follows:

type name = expression


with the following types supported:

• int: 0, 1, 5
• float: 8.0, 0.43, -0.123, 89.23e-10
• complex: 0+5j, 8.1-1j, 0.54+0.21j
• bool: True, False
• str: any ASCII string surrounded by double quotation marks, "hello world"

Note

• When using a float, you must provide the full decimal. I.e., 8 and 8. are not valid floats, but 8.0 is.
• When using a complex, you must provide both real and imaginary parts. I.e., 8 and 2j are not valid complex literals, but 8+0j is.

Examples:

int n = +5
int k = n

float m = -0.5432
float alpha = 0.5432
float x = 0.5+0.1
float Delta = 0.543

complex beta = 5.21
complex y = -0.43e-4+0.912j
complex z = +0.43e-4-0.912j

bool flag = True
str name = "program1"


Warning

All variable names are allowed, except those consisting of a single ‘q’ followed by an integer, for example q0, q1, q2, etc. These are reserved for quantum register references.

### Operators¶

Blackbird allows expressions using the following operators:

• +: addition, unary positive
• -: subtraction, unary negation
• *: multiplication
• /: division
• **: right-associative exponentiation.

### Functions¶

Blackbird also supports the intrinsic functions

• sqrt()
• exp(), log
• sin(), cos(), tan()
• arcsin(), arccos(), arctan()
• sinh(), cosh(), tanh()
• arcsinh(), arccosh(), arctanh()

and the intrinsic constant

• pi

You can also use previously defined variable names in your expressions:

float gamma = 2.0*cos(alpha*pi)
float test = n**2.0


### Arrays¶

To define arrays, specify 'array' after the variable type. Each row of the array is then defined on an indented line, with columns separated by commas.

float array A =
-1.0, 2.0
-0.1, 0.2

complex array U[3, 3] =
-0.23191638+0.17828953j,  0.58457815+0.41415933j, -0.05795454-0.46965132j
+0.42259383+0.56368926j, -0.42219920+0.04735544j, -0.18902308-0.01590913j
-0.02396850+0.64301446j,  0.09918161+0.36797446j,  0.26993055+0.30341975j


Note

For additional array validation, you can specify the shape of the array using square brackets directly after the variable name (i.e., U[3, 3]) but this is optional.

## Quantum program¶

The | operator is used to apply intrinsic quantum operations to quantum registers.

For example:

# Statements have the following form:
Operation(parameters) | modes

# Depending on the operation, parameters may be optional
# Parameters can be variables of literals or expressions
complex alpha = 0.5+0.2
float delta = 0.5423
Coherent(alpha**2, Delta*sqrt(pi)) | 0

# Multiple modes are specified by comma separated integers
Interferometer(U) | [0, 1, 2, 3]

# Finish with measurements
MeasureFock() | 0


Currently, the device always accepts keyword arguments, and operations always accept positional arguments.

To pass measured mode values to successive gate arguments, you may use the reserved variables qX, where X is an integer representing mode X, as parameters:

S2gate(0.43, 0.12) | [0, 1]
MeasureX | 0
MeasureP | 1
Xgate(sqrt(2)*q0+q1) | 2


After running a Blackbird program, the user should expect to receive the results as an array:

• each column is a measurement result, corresponding to the measurements in the order they appear in the blackbird program
• each row represents a shot/run

## Templates¶

A Blackbird template is simply a Blackbird script that contains template parameters.

Template parameters use the syntax {parameter_name}, and can be placed within any numeric expression.

For example, consider the following state teleportation template:

name StateTeleportation
version 1.0

# state to be teleported:
Coherent({alpha}) | 0

# teleportation algorithm
Squeezed(-{sq}) | 1
Squeezed({sq}) | 2
BSgate(pi/4, 0) | (1, 2)
BSgate(pi/4, 0) | (0, 1)
MeasureX | 0
MeasureP | 1
Xgate(sqrt(2)*q0) | 2
Zgate(sqrt(2)*q1) | 2


Here, the initial state preparation uses a template parameter {alpha}, while the squeezed resource states have magnitude given by parameter {sq}.

The advantage of Blackbird templates is that a Blackbird script can encapsulate a photonic quantum circuit with free parameters. A library that makes use of the Blackbird quantum assembly language (such as Strawberry Fields) can dynamically update template parameters without needing to recompile the program.

## Including subroutines¶

There may be the case where you have a Blackbird program or template representing a circuit primitive that you may want to re-use across multiple Blackbird programs.

This is possible using the include statement. This has the following syntax:

include "path/to/filename.xbb"


where the file path is relative to the location of the current Blackbird script. A Blackbird script may have multiple includes, and they must all be placed after the metadata block, and before the quantum program/variables are defined.

The include statement allows the external Blackbird program to be used as a subroutine within the existing script. This quantum subroutine is called via the name of the included Blackbird script. For example, consider a state teleportation template, state_teleportation.xbb:

name StateTeleportation
version 1.0

# maximally entangled states
Squeezed(-{sq}) | 1
Squeezed({sq}) | 2
BSgate(pi/4, 0) | (1, 2)

# Alice performs the joint measurement
# in the maximally entangled basis
BSgate(pi/4, 0) | (0, 1)
MeasureX | 0
MeasureP | 1

# Bob conditionally displaces his mode
# based on Alice's measurement result
Xgate(sqrt(2)*q0) | 2
Zgate(sqrt(2)*q1) | 2


This template accepts the parameter sq (the squeezing magnitude of the resource states), and acts on three modes, teleporting the state in mode 0 to mode 2.

Now, consider another file, example_include.xbb, which includes the above StateTeleportation operation imported from the state_teleportation.xbb template:

name ExampleInclude
version 1.0
target gaussian (shots=10)

include "state_teleportation.xbb"

float alpha = 0.3423

Coherent(a=alpha) | 0
Coherent(a=alpha) | 1
StateTeleportation(sq=1) | [0, 2, 3]
MeasureHeterodyne() | 3


We can now call the StateTeleportation subroutine, with sq=1, and apply it to modes 0, 2, and 3.

Note

Make sure to avoid circular includes when using the include statement.