Blackbird programming language

Section author: Nathan Killoran <nathan@xanadu.ai>, Josh Izaac <josh@xanadu.ai>

In this section, we provide an overview of the Blackbird quantum programming language. This simple and elegant language breaks down a quantum circuit into a set of instructions detailing the quantum operations we would like to apply, as well as the the subsystems that these operations act on [1].

Operations

Blackbird is a quantum assembly language, capable of representing the basic continuous-variable (CV) states, gates, and measurements outlined in the Introduction. Collectively, these are all considered as Operations. In Blackbird, there are four main types of Operations:

  • State preparation
  • Gate application
  • Measurements
  • Adding and removing subsystems

These all use the following general syntax:

Operation(args) | q

where args represents a list of parameters for the operation, and q is the qumode (or sequence of qumodes) the quantum operation acts upon. In Blackbird code, the symbol | always separates the operation to be applied (on the left) and the subsystem(s) it acts on (on the right).

State preparation

States can be prepared using the state preparation Operators Vacuum, Fock, Coherent, Squeezed, DisplacedSqueezed, and Thermal. By default, all qumode subsystems are assumed initialised in the vacuum state.

# State preparation in Blackbird
Fock(1) | q[0]
Coherent(0.5+2j) | q[1]

In the above example, we have prepared a single photon state in qumode q[0], and a coherent state with \(\alpha=0.5+2i\) in qumode q[1]. Note that we can also construct a state preparation operator with a particular set of parameters, and reuse it repeatedly:

S = Squeezed(1)
S | q[0]
S | q[1]

Gate application

Gates are applied within Blackbird code in the exact same manner as state preparations. Consider the following example:

# Apply the Displacement gate to qumode 0
alpha = 2.0 + 1j
Dgate(alpha) | q[0]

# Apply the Rotation gate
phi = 3.14 / 2
Rgate(phi) | q[0]

# Apply the Squeezing gate
Sgate(2.0, 0.17) | q[0]

# Apply the Beamsplitter gate to qumodes 0 & 1
BSgate(3.14 / 10, 0.223) | (q[0], q[1])

# Apply the Cubic Phase gate (VGate) to qumode 0
gamma = 0.1
Vgate(gamma) | q[0]

Here, we are applying various gates, including the displacement gate (Dgate), rotation gate (Rgate), squeezing gate (Sgate), beamsplitter (BSgate, a two-mode gate), and the cubic phase gate (Vgate). For more details on the gates available, as well as the parameters they take, see Quantum operations.

Note that gate Operations have some subtle differences to state preparation operators:

  • Unlike state preparation operators, some gates (such as the beamsplitter above) can be applied to multiple qumodes.

    Note

    The number of qumodes the gate acts upon and the sequence of qumodes to the right of the | operator must always match – we cannot apply the beamsplitter to a single qumode.

  • We can also apply the Hermitian conjugate of a gate operator; this is specified by appending .H to the operator. For example:

    V = Vgate(gamma)
    V.H | q[0]
    

Note

Operations must be applied in temporal order, from top to bottom.

Measurements

In Blackbird, several CV measurement Operations are available; these include homodyne detection (MeasureHomodyne, as well as the shortcuts MeasureX and MeasureP), heterodyne detection (MeasureHD), and photon detection (Measure). These are applied directly to the qumodes to be measured:

# Homodyne measurement at angle phi
phi = 0.25 * 3.14
MeasureHomodyne(phi) | q[0]

# Special homodyne measurements
MeasureX | q[0]
MeasureP | q[1]

# Heterodyne measurement
MeasureHeterodyne() | q[0]
MeasureHD           | q[1]  # shorthand

# Number state measurements of various qumodes
MeasureFock() | q[0]
MeasureFock() | (q[1], q[2]) # multiple modes
Measure       | q[3]         # shorthand

For more details on measurements, as well as advanced features such as postselection, see the Measurements and post-selection tutorial.

Otherwise, to see how Blackbird programs are used in practice within Strawberry Fields, continue on to the Quantum teleportation tutorial.

Footnotes

[1]Note: the Blackbird syntax is modeled after that of Project Q, but specialized to the CV setting.