Multiple Roots
Not all instruction dependency structures can be realized with a tree of Dependency objects. An example would be a program with an IR that allows for partial Barrier instructions such as the following:
Here, instructions A1, A2 are played on frame A and similarly for B1, B2, C1 & C2. If we say that all A, B, C pulses have durations 100 ns, 150 ns and 50 ns respectively we would expect to realize the following schedule:
A tree wouldn't be possible without grouping instructions C2 and B2 together such that C2 would artificially have to wait for B1 to finish and similarly B2 for C1.
In order to implement this program one must make use of the fact that the Job.EntryPoint Block object takes in a list of instruction-like objects. In all the examples earlier, this list only contained one dependency or pulse, but in the following we realize the program in two different ways to show how dependency graphs with multiple roots can be made.
Program as a flat list of Dependencies
The most straightforward way to implement the program is as a flat list of Dependency objects that cover all the relationships defined in the source. * A1 | A2 * B1 | B2 * C1 | C2 * A1 | B2 * A1 | C2 * B1 | A2 * C1 | A2
Tree format
graph TD
Frame1["Frame"]
Interval1["100 ns"]
Waveform1["ConstantWaveform"]
Waveform1 -- "Duration" --- Interval1
Instruction2["ModulatedPulse"]
Instruction2 -- "Frame" --- Frame1
Instruction2 -- "Envelope" --- Waveform1
Radians2["1 rad"]
Instruction2 -- "PhaseOffset" --- Radians2
Instruction3["ModulatedPulse"]
Instruction3 -- "Frame" --- Frame1
Instruction3 -- "Envelope" --- Waveform1
Radians3["1 rad"]
Instruction3 -- "PhaseOffset" --- Radians3
Instruction4:Alignment["EndToStart"]
Instruction4:Relationship["InstructionRelationship"]
Instruction4:Relationship -- "Alignment" --- Instruction4:Alignment
Instruction4["Dependency"]
Instruction4 -- "Relationship" --- Instruction4:Relationship
Instruction4 -- "Lhs" --- Instruction2
Instruction4 -- "Rhs" --- Instruction3
Frame2["Frame"]
Interval4["150 ns"]
Waveform2["ConstantWaveform"]
Waveform2 -- "Duration" --- Interval4
Instruction6["ModulatedPulse"]
Instruction6 -- "Frame" --- Frame2
Instruction6 -- "Envelope" --- Waveform2
Radians5["2 rad"]
Instruction6 -- "PhaseOffset" --- Radians5
Instruction7["ModulatedPulse"]
Instruction7 -- "Frame" --- Frame2
Instruction7 -- "Envelope" --- Waveform2
Radians6["2 rad"]
Instruction7 -- "PhaseOffset" --- Radians6
Instruction8:Alignment["EndToStart"]
Instruction8:Relationship["InstructionRelationship"]
Instruction8:Relationship -- "Alignment" --- Instruction8:Alignment
Instruction8["Dependency"]
Instruction8 -- "Relationship" --- Instruction8:Relationship
Instruction8 -- "Lhs" --- Instruction6
Instruction8 -- "Rhs" --- Instruction7
Frame3["Frame"]
Interval7["50 ns"]
Waveform3["ConstantWaveform"]
Waveform3 -- "Duration" --- Interval7
Instruction10["ModulatedPulse"]
Instruction10 -- "Frame" --- Frame3
Instruction10 -- "Envelope" --- Waveform3
Radians8["3 rad"]
Instruction10 -- "PhaseOffset" --- Radians8
Instruction11["ModulatedPulse"]
Instruction11 -- "Frame" --- Frame3
Instruction11 -- "Envelope" --- Waveform3
Radians9["3 rad"]
Instruction11 -- "PhaseOffset" --- Radians9
Instruction12:Alignment["EndToStart"]
Instruction12:Relationship["InstructionRelationship"]
Instruction12:Relationship -- "Alignment" --- Instruction12:Alignment
Instruction12["Dependency"]
Instruction12 -- "Relationship" --- Instruction12:Relationship
Instruction12 -- "Lhs" --- Instruction10
Instruction12 -- "Rhs" --- Instruction11
Instruction14["ModulatedPulse"]
Instruction14 -- "Frame" --- Frame1
Instruction14 -- "Envelope" --- Waveform1
Radians10["1 rad"]
Instruction14 -- "PhaseOffset" --- Radians10
Instruction15["ModulatedPulse"]
Instruction15 -- "Frame" --- Frame2
Instruction15 -- "Envelope" --- Waveform2
Radians11["2 rad"]
Instruction15 -- "PhaseOffset" --- Radians11
Instruction16:Alignment["EndToStart"]
Instruction16:Relationship["InstructionRelationship"]
Instruction16:Relationship -- "Alignment" --- Instruction16:Alignment
Instruction16["Dependency"]
Instruction16 -- "Relationship" --- Instruction16:Relationship
Instruction16 -- "Lhs" --- Instruction14
Instruction16 -- "Rhs" --- Instruction15
Instruction18["ModulatedPulse"]
Instruction18 -- "Frame" --- Frame2
Instruction18 -- "Envelope" --- Waveform2
Radians12["2 rad"]
Instruction18 -- "PhaseOffset" --- Radians12
Instruction19["ModulatedPulse"]
Instruction19 -- "Frame" --- Frame1
Instruction19 -- "Envelope" --- Waveform1
Radians13["1 rad"]
Instruction19 -- "PhaseOffset" --- Radians13
Instruction20:Alignment["EndToStart"]
Instruction20:Relationship["InstructionRelationship"]
Instruction20:Relationship -- "Alignment" --- Instruction20:Alignment
Instruction20["Dependency"]
Instruction20 -- "Relationship" --- Instruction20:Relationship
Instruction20 -- "Lhs" --- Instruction18
Instruction20 -- "Rhs" --- Instruction19
Instruction22["ModulatedPulse"]
Instruction22 -- "Frame" --- Frame1
Instruction22 -- "Envelope" --- Waveform1
Radians14["1 rad"]
Instruction22 -- "PhaseOffset" --- Radians14
Instruction23["ModulatedPulse"]
Instruction23 -- "Frame" --- Frame3
Instruction23 -- "Envelope" --- Waveform3
Radians15["3 rad"]
Instruction23 -- "PhaseOffset" --- Radians15
Instruction24:Alignment["EndToStart"]
Instruction24:Relationship["InstructionRelationship"]
Instruction24:Relationship -- "Alignment" --- Instruction24:Alignment
Instruction24["Dependency"]
Instruction24 -- "Relationship" --- Instruction24:Relationship
Instruction24 -- "Lhs" --- Instruction22
Instruction24 -- "Rhs" --- Instruction23
Instruction26["ModulatedPulse"]
Instruction26 -- "Frame" --- Frame3
Instruction26 -- "Envelope" --- Waveform3
Radians16["3 rad"]
Instruction26 -- "PhaseOffset" --- Radians16
Instruction27["ModulatedPulse"]
Instruction27 -- "Frame" --- Frame1
Instruction27 -- "Envelope" --- Waveform1
Radians17["1 rad"]
Instruction27 -- "PhaseOffset" --- Radians17
Instruction28:Alignment["EndToStart"]
Instruction28:Relationship["InstructionRelationship"]
Instruction28:Relationship -- "Alignment" --- Instruction28:Alignment
Instruction28["Dependency"]
Instruction28 -- "Relationship" --- Instruction28:Relationship
Instruction28 -- "Lhs" --- Instruction26
Instruction28 -- "Rhs" --- Instruction27
Job["Job"]
Job -- "EntryPoint[0]" --- Instruction4
Job -- "EntryPoint[1]" --- Instruction8
Job -- "EntryPoint[2]" --- Instruction12
Job -- "EntryPoint[3]" --- Instruction16
Job -- "EntryPoint[4]" --- Instruction20
Job -- "EntryPoint[5]" --- Instruction24
Job -- "EntryPoint[6]" --- Instruction28JSON format:
Job definition
{
"version": "0.1.0",
"compatible_version": "0.1.0",
"frames": {
"Frame1": {
"port": {
"id": {
"$type": "NumericLiteral",
"value": 1
}
},
"frequency": {
"$type": "NumericLiteral",
"value": 5000000000
},
"phase": {
"$type": "NumericLiteral",
"value": 0
},
"intermediate_frequency": {
"$type": "NumericLiteral",
"value": 10000000
}
},
"Frame2": {
"port": {
"id": {
"$type": "NumericLiteral",
"value": 2
}
},
"frequency": {
"$type": "NumericLiteral",
"value": 5000000000
},
"phase": {
"$type": "NumericLiteral",
"value": 0
},
"intermediate_frequency": {
"$type": "NumericLiteral",
"value": 10000000
}
},
"Frame3": {
"port": {
"id": {
"$type": "NumericLiteral",
"value": 3
}
},
"frequency": {
"$type": "NumericLiteral",
"value": 5000000000
},
"phase": {
"$type": "NumericLiteral",
"value": 0
},
"intermediate_frequency": {
"$type": "NumericLiteral",
"value": 10000000
}
}
},
"waveforms": {
"Waveform1": {
"$type": "ConstantWaveform",
"duration": {
"$type": "NumericLiteral",
"value": 1E-07
}
},
"Waveform2": {
"$type": "ConstantWaveform",
"duration": {
"$type": "NumericLiteral",
"value": 1.5E-07
}
},
"Waveform3": {
"$type": "ConstantWaveform",
"duration": {
"$type": "NumericLiteral",
"value": 5E-08
}
}
},
"instructions": {
"Instruction2": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame1"
},
"envelope": {
"$ref": "Waveform1"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 1
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
},
"Instruction3": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame1"
},
"envelope": {
"$ref": "Waveform1"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 1
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
},
"Instruction5": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame2"
},
"envelope": {
"$ref": "Waveform2"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 2
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
},
"Instruction6": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame2"
},
"envelope": {
"$ref": "Waveform2"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 2
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
},
"Instruction8": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame3"
},
"envelope": {
"$ref": "Waveform3"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 3
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
},
"Instruction9": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame3"
},
"envelope": {
"$ref": "Waveform3"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 3
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
}
},
"entry_point": [
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction2"
},
"rhs": {
"$ref": "Instruction3"
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction5"
},
"rhs": {
"$ref": "Instruction6"
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction8"
},
"rhs": {
"$ref": "Instruction9"
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction2"
},
"rhs": {
"$ref": "Instruction6"
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction5"
},
"rhs": {
"$ref": "Instruction3"
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction2"
},
"rhs": {
"$ref": "Instruction9"
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$ref": "Instruction8"
},
"rhs": {
"$ref": "Instruction3"
}
}
]
}
Program as a two-rooted graph
It's possible and neater to implement the same program above with just two root nodes in EntryPoint, which results in fewer explicits statements and aligns to the symmetry of the program. * (A1 / B1) | (A2 / B2) * (A1 / C1) | (A2 / B2)
Tree format
graph TD
Frame1["Frame"]
Interval1["100 ns"]
Waveform1["ConstantWaveform"]
Waveform1 -- "Duration" --- Interval1
Instruction3["ModulatedPulse"]
Instruction3 -- "Frame" --- Frame1
Instruction3 -- "Envelope" --- Waveform1
Radians2["1 rad"]
Instruction3 -- "PhaseOffset" --- Radians2
Frame2["Frame"]
Interval3["150 ns"]
Waveform2["ConstantWaveform"]
Waveform2 -- "Duration" --- Interval3
Instruction4["ModulatedPulse"]
Instruction4 -- "Frame" --- Frame2
Instruction4 -- "Envelope" --- Waveform2
Radians4["2 rad"]
Instruction4 -- "PhaseOffset" --- Radians4
Instruction5:Alignment["StartToStart"]
Instruction5:Relationship["InstructionRelationship"]
Instruction5:Relationship -- "Alignment" --- Instruction5:Alignment
Instruction5["Dependency"]
Instruction5 -- "Relationship" --- Instruction5:Relationship
Instruction5 -- "Lhs" --- Instruction3
Instruction5 -- "Rhs" --- Instruction4
Instruction7["ModulatedPulse"]
Instruction7 -- "Frame" --- Frame1
Instruction7 -- "Envelope" --- Waveform1
Radians5["1 rad"]
Instruction7 -- "PhaseOffset" --- Radians5
Instruction8["ModulatedPulse"]
Instruction8 -- "Frame" --- Frame2
Instruction8 -- "Envelope" --- Waveform2
Radians6["2 rad"]
Instruction8 -- "PhaseOffset" --- Radians6
Instruction9:Alignment["StartToStart"]
Instruction9:Relationship["InstructionRelationship"]
Instruction9:Relationship -- "Alignment" --- Instruction9:Alignment
Instruction9["Dependency"]
Instruction9 -- "Relationship" --- Instruction9:Relationship
Instruction9 -- "Lhs" --- Instruction7
Instruction9 -- "Rhs" --- Instruction8
Instruction10:Alignment["EndToStart"]
Instruction10:Relationship["InstructionRelationship"]
Instruction10:Relationship -- "Alignment" --- Instruction10:Alignment
Instruction10["Dependency"]
Instruction10 -- "Relationship" --- Instruction10:Relationship
Instruction10 -- "Lhs" --- Instruction5
Instruction10 -- "Rhs" --- Instruction9
Instruction13["ModulatedPulse"]
Instruction13 -- "Frame" --- Frame1
Instruction13 -- "Envelope" --- Waveform1
Radians7["1 rad"]
Instruction13 -- "PhaseOffset" --- Radians7
Frame3["Frame"]
Interval8["50 ns"]
Waveform3["ConstantWaveform"]
Waveform3 -- "Duration" --- Interval8
Instruction14["ModulatedPulse"]
Instruction14 -- "Frame" --- Frame3
Instruction14 -- "Envelope" --- Waveform3
Radians9["3 rad"]
Instruction14 -- "PhaseOffset" --- Radians9
Instruction15:Alignment["StartToStart"]
Instruction15:Relationship["InstructionRelationship"]
Instruction15:Relationship -- "Alignment" --- Instruction15:Alignment
Instruction15["Dependency"]
Instruction15 -- "Relationship" --- Instruction15:Relationship
Instruction15 -- "Lhs" --- Instruction13
Instruction15 -- "Rhs" --- Instruction14
Instruction17["ModulatedPulse"]
Instruction17 -- "Frame" --- Frame1
Instruction17 -- "Envelope" --- Waveform1
Radians10["1 rad"]
Instruction17 -- "PhaseOffset" --- Radians10
Instruction18["ModulatedPulse"]
Instruction18 -- "Frame" --- Frame3
Instruction18 -- "Envelope" --- Waveform3
Radians11["3 rad"]
Instruction18 -- "PhaseOffset" --- Radians11
Instruction19:Alignment["StartToStart"]
Instruction19:Relationship["InstructionRelationship"]
Instruction19:Relationship -- "Alignment" --- Instruction19:Alignment
Instruction19["Dependency"]
Instruction19 -- "Relationship" --- Instruction19:Relationship
Instruction19 -- "Lhs" --- Instruction17
Instruction19 -- "Rhs" --- Instruction18
Instruction20:Alignment["EndToStart"]
Instruction20:Relationship["InstructionRelationship"]
Instruction20:Relationship -- "Alignment" --- Instruction20:Alignment
Instruction20["Dependency"]
Instruction20 -- "Relationship" --- Instruction20:Relationship
Instruction20 -- "Lhs" --- Instruction15
Instruction20 -- "Rhs" --- Instruction19
Job["Job"]
Job -- "EntryPoint[0]" --- Instruction10
Job -- "EntryPoint[1]" --- Instruction20JSON format:
Job definition
{
"version": "0.1.0",
"compatible_version": "0.1.0",
"frames": {
"Frame1": {
"port": {
"id": {
"$type": "NumericLiteral",
"value": 1
}
},
"frequency": {
"$type": "NumericLiteral",
"value": 5000000000
},
"phase": {
"$type": "NumericLiteral",
"value": 0
},
"intermediate_frequency": {
"$type": "NumericLiteral",
"value": 10000000
}
},
"Frame2": {
"port": {
"id": {
"$type": "NumericLiteral",
"value": 2
}
},
"frequency": {
"$type": "NumericLiteral",
"value": 5000000000
},
"phase": {
"$type": "NumericLiteral",
"value": 0
},
"intermediate_frequency": {
"$type": "NumericLiteral",
"value": 10000000
}
},
"Frame3": {
"port": {
"id": {
"$type": "NumericLiteral",
"value": 3
}
},
"frequency": {
"$type": "NumericLiteral",
"value": 5000000000
},
"phase": {
"$type": "NumericLiteral",
"value": 0
},
"intermediate_frequency": {
"$type": "NumericLiteral",
"value": 10000000
}
}
},
"waveforms": {
"Waveform1": {
"$type": "ConstantWaveform",
"duration": {
"$type": "NumericLiteral",
"value": 1E-07
}
},
"Waveform2": {
"$type": "ConstantWaveform",
"duration": {
"$type": "NumericLiteral",
"value": 1.5E-07
}
},
"Waveform3": {
"$type": "ConstantWaveform",
"duration": {
"$type": "NumericLiteral",
"value": 5E-08
}
}
},
"instructions": {
"Instruction3": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame1"
},
"envelope": {
"$ref": "Waveform1"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 1
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
},
"Instruction6": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame1"
},
"envelope": {
"$ref": "Waveform1"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 1
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
}
},
"entry_point": [
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$type": "Dependency",
"relationship": {
"alignment": "StartToStart"
},
"lhs": {
"$ref": "Instruction3"
},
"rhs": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame2"
},
"envelope": {
"$ref": "Waveform2"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 2
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
}
},
"rhs": {
"$type": "Dependency",
"relationship": {
"alignment": "StartToStart"
},
"lhs": {
"$ref": "Instruction6"
},
"rhs": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame2"
},
"envelope": {
"$ref": "Waveform2"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 2
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
}
}
},
{
"$type": "Dependency",
"relationship": {},
"lhs": {
"$type": "Dependency",
"relationship": {
"alignment": "StartToStart"
},
"lhs": {
"$ref": "Instruction3"
},
"rhs": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame3"
},
"envelope": {
"$ref": "Waveform3"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 3
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
}
},
"rhs": {
"$type": "Dependency",
"relationship": {
"alignment": "StartToStart"
},
"lhs": {
"$ref": "Instruction6"
},
"rhs": {
"$type": "ModulatedPulse",
"frame": {
"$ref": "Frame3"
},
"envelope": {
"$ref": "Waveform3"
},
"phase_offset": {
"$type": "NumericLiteral",
"value": 3
},
"amplitude": {
"$type": "NumericLiteral",
"value": 1
}
}
}
}
]
}