1. Magic-State Functional Units
Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures
OCT 24, 2018
Ding, Y., Holmes, A., Javadi-Abhari, A., Franklin, D., Martonosi, M., & Chong, F. T. 
ArXiv:
DOI: /MICRO

2. Background Our Techniques Results OUTLINE 1
Magic-State Distillation and Braiding 2
Our Techniques
Concatenation and Force-directed Annealing 3
Results

3. Operations on Error-Corrected Quantum Computers
FAULT-TOLERANT QC
Operations on Error-Corrected Quantum Computers
Easy single-qubit gates:
Difficult 2-qubit gate: CNOT gate H X Z
Expensive to implement: requires braiding
Difficult single-qubit gate: T gate
|𝜓⟩ T
T|𝜓⟩
|𝑇⟩
Useful applications contain
a significant number of T gates.
Consume: 1 magic state
Expensive to implement: requires magic state distillation

4. MAGIC-STATE DISTILLATION
Magic State Distillation is Expensive
Quantum Chemistry
*Ising Model of spin chain with size 500.
Ising Model
QFT
Operations spent on magic state distillation: 99.4%
Operations spent on distillation (percentage)
Common Kernel
*Quantum Fourier Transform with size 100.
Operations spent on magic state distillation: 99.8%
T-gate Percentage

5. MAGIC-STATE DISTILLATION
Block Code Distillation Factory T T p2 T p T T
“Distillation Factory” T

6. COMMUNICATION VIA BRAIDING
Distance does not matter.

7. COMMUNICATION VIA BRAIDING
Crossing is prohibited.

8. COMMUNICATION VIA BRAIDING
Fewer crossings?

9. OBJECTIVE
Mapping

10. Our Techniques for Congestion Minimization

11. TECHNIQUES
Mapping

12. Concatenate and Arrange
TECHNIQUES
Concatenate and Arrange
Cost of Permutation Step
78%
66%
48%
48%
28%

13. Force-Directed Annealing
TECHNIQUES
Force-Directed Annealing 1
Vertex-Vertex Attraction 2
Edge-Edge Repulsion 3
Magnetic Dipole
Source:

14. Vertex-Vertex Attraction

15. FORCE-DIRECTED ANNEALING
Vertex-Vertex Attraction
Calculated with
cycle-by-cycle simulation

16. Edge-Edge Repulsion

17. FORCE-DIRECTED ANNEALING
Edge-Edge Repulsion

18. Magnetic Dipole + + - - - + -

19. FORCE-DIRECTED ANNEALING
Magnetic Dipole Rotation

20. FORCE-DIRECTED ANNEALING
Valiant-Style Routing
Intermediate hops

21. Multi-Level Factories
RESULTS
Multi-Level Factories
5.6x overhead reduction

22. Conclusion
Magic-state distillation extremely dominates most applications’ workloads.
Surface code braiding circuits are difficult to execute.
Circuit latency and edge crossings are strongly correlated.
Force-directed annealing heuristics generate low-latency qubit mappings.
Hierarchical stitching optimizes multi-level circuits

23. Thank you!
Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures.
Ding, Y., Holmes, A., Javadi-Abhari, A., Franklin, D., Martonosi, M., & Chong, F. T. (2018). 
arXiv preprint arXiv: