SLIDE 1
PyZX: Quantum circuit optimization using the ZX-calculus
Aleks Kissinger
aleks@cs.ru.nl
John van de Wetering
john@vdwetering.name
Institute for Computing and Information Sciences Radboud University Nijmegen
February 3, 2019
PyZX: Quantum circuit optimization using the ZX-calculus Aleks - - PowerPoint PPT Presentation
PyZX: Quantum circuit optimization using the ZX-calculus Aleks - - PowerPoint PPT Presentation
PyZX: Quantum circuit optimization using the ZX-calculus Aleks Kissinger aleks@cs.ru.nl John van de Wetering john@vdwetering.name Institute for Computing and Information Sciences Radboud University Nijmegen February 3, 2019 Quantum
SLIDE 2
SLIDE 3
Quantum computation
§ Quantum computation is done by quantum circuits.
SLIDE 4
Quantum computation
§ Quantum computation is done by quantum circuits. § A quantum circuit consists of quantum gates.
SLIDE 5
Quantum computation
§ Quantum computation is done by quantum circuits. § A quantum circuit consists of quantum gates. § Single qubit gates: NOT, S, T, H.
SLIDE 6
Quantum computation
§ Quantum computation is done by quantum circuits. § A quantum circuit consists of quantum gates. § Single qubit gates: NOT, S, T, H. NOT S = H ? NOT H H(adamard) T = ? S
SLIDE 7
Quantum computation
§ Quantum computation is done by quantum circuits. § A quantum circuit consists of quantum gates. § Single qubit gates: NOT, S, T, H. NOT S = H ? NOT H H(adamard) T = ? S § Two qubit gate: CNOT (controlled NOT)
SLIDE 8
Quantum computation
§ Quantum computation is done by quantum circuits. § A quantum circuit consists of quantum gates. § Single qubit gates: NOT, S, T, H. NOT S = H ? NOT H H(adamard) T = ? S § Two qubit gate: CNOT (controlled NOT) § These are all the gates you need.
SLIDE 9
Quantum computation
§ Quantum computation is done by quantum circuits. § A quantum circuit consists of quantum gates. § Single qubit gates: NOT, S, T, H. NOT S = H ? NOT H H(adamard) T = ? S § Two qubit gate: CNOT (controlled NOT) § These are all the gates you need. § Our objective is to minimize number of gates needed. § Specifically T-gates.
SLIDE 10
Circuit diagrams
NOT =
+
CNOT =
+
SLIDE 11
Circuit diagrams
NOT =
+
CNOT =
+
An example quantum circuit:
T
` `
H
`
S S
SLIDE 12
Circuit identities
+ +
=
H H
=
T T
=
S T: T
=
SLIDE 13
Gate commutation
=
+ + + +
T
=
+
T
+
T
=
+ +
T T
+ +
T
SLIDE 14
More circuit equalities
SLIDE 15
And more circuit equalities
SLIDE 16
And even more circuit equalities
SLIDE 17
Things get messy because circuits are very rigid
SLIDE 18
Things get messy because circuits are very rigid Enter ZX-diagrams
SLIDE 19
ZX-diagrams
What gates are to circuits, spiders are to ZX-diagrams.
SLIDE 20
ZX-diagrams
What gates are to circuits, spiders are to ZX-diagrams. Z-spiders:
α
... ... X-spiders:
α
... ... (α P r0, 2πs)
SLIDE 21
ZX-diagrams
What gates are to circuits, spiders are to ZX-diagrams. Z-spiders:
α
... ... X-spiders:
α
... ... (α P r0, 2πs) Spiders can be wired in any way:
α
π 2 3π 2
β π
SLIDE 22
ZX-diagrams
What gates are to circuits, spiders are to ZX-diagrams. Z-spiders:
α
... ... X-spiders:
α
... ... (α P r0, 2πs) Spiders can be wired in any way:
α
π 2 3π 2
β π
Note: “Only connectivity matters”
SLIDE 23
Quantum gates as ZX-diagrams
Every quantum gate can be written as a ZX-diagram: S “
π 2
T “
π 4
H “ :=
π 2 π 2 π 2
CNOT “
SLIDE 24
Quantum gates as ZX-diagrams
Every quantum gate can be written as a ZX-diagram: S “
π 2
T “
π 4
H “ :=
π 2 π 2 π 2
CNOT “
Theorem
Any linear map between qubits can be represented as a ZX-diagram.
SLIDE 25
Rules for ZX-diagrams: The ZX-calculus
β
... ...
α
... ... “ ... ... ...
α`β p-1qaα
“
aπ aπ aπ α
... ...
aπ aπ
...
aπ α
“ ...
aπ aπ α
... “
α
... “ “ “ α, β P r0, 2πs, a P t0, 1u
SLIDE 26
Completeness of the ZX-calculus
Theorem
If two ZX-diagrams represent the same computation, then they can be transformed into one another using the previous rules (and one additional one).
SLIDE 27
Completeness of the ZX-calculus
Theorem
If two ZX-diagrams represent the same computation, then they can be transformed into one another using the previous rules (and one additional one). So instead of dozens of circuit equalities, we just have a few simple rules.
SLIDE 28
PyZX
§ PyZX is an open-source Python library. § github.com/Quantomatic/pyzx
SLIDE 29
PyZX
§ PyZX is an open-source Python library. § github.com/Quantomatic/pyzx § Its goal is to allow easy manipulation of large ZX-diagrams.
SLIDE 30
PyZX
§ PyZX is an open-source Python library. § github.com/Quantomatic/pyzx § Its goal is to allow easy manipulation of large ZX-diagrams. § Visualisation: Jupyter and Matplotlib. § Documentation: Sphinx § Numpy for various things.
SLIDE 31
PyZX and optimization
§ Recall: we want to minimize T-count.
SLIDE 32
PyZX and optimization
§ Recall: we want to minimize T-count. § So how well does PyZX do this?
SLIDE 33
PyZX and optimization
§ Recall: we want to minimize T-count. § So how well does PyZX do this? § For every circuit tested matches or beats the state-of-the-art.
SLIDE 34
PyZX and optimization
§ Recall: we want to minimize T-count. § So how well does PyZX do this? § For every circuit tested matches or beats the state-of-the-art.
(Usually performs similarly, but goes up to 50% better than previous best)
SLIDE 35
PyZX and optimization
§ Recall: we want to minimize T-count. § So how well does PyZX do this? § For every circuit tested matches or beats the state-of-the-art.
(Usually performs similarly, but goes up to 50% better than previous best)
§ What about other metrics: gate count/depth?
SLIDE 36
PyZX and optimization
§ Recall: we want to minimize T-count. § So how well does PyZX do this? § For every circuit tested matches or beats the state-of-the-art.
(Usually performs similarly, but goes up to 50% better than previous best)
§ What about other metrics: gate count/depth? § Work in progress.
SLIDE 37
Demonstration time
SLIDE 38
Future work
§ Allow routing for restricted architectures.
SLIDE 39
Future work
§ Allow routing for restricted architectures. § Optimize for different metrics.
SLIDE 40
Future work
§ Allow routing for restricted architectures. § Optimize for different metrics. § Allow ancillae.
SLIDE 41
Future work
§ Allow routing for restricted architectures. § Optimize for different metrics. § Allow ancillae. § Closer integration with other frameworks/libraries.
SLIDE 42