efficiently embedding qubo problems on adiabatic quantum … · 2018. 10. 11. · efficiently...
TRANSCRIPT
Efficiently Embedding QUBO Problems on Adiabatic Quantum Computers
Prasanna Datehttps://prasannadate.github.io
PhD CandidateDepartment of Computer Science
Rensselaer Polytechnic Institute (RPI)Advisor: Prof. Chris Carothers
ASTRO Intern (Jan-Aug, 2018)Computational Data Analytics (CDA) Group
Oak Ridge National Laboratory (ORNL)Mentor: Dr. Robert Patton
Quantum Computing with D-Wave
Prasanna Date | [email protected] | prasannadate.github.io 2
End of Moore’s Law
Rise of Machine Learning and Deep Learning
Neuromorphic Computing
Quantum Computing
Universal Quantum
Computing
Adiabatic Quantum
Computing
Quantum Computing with D-Wave
Prasanna Date | [email protected] | prasannadate.github.io 3
End of Moore’s Law
Rise of Machine Learning and Deep Learning
Neuromorphic Computing
Quantum Computing
Universal Quantum
Computing
Adiabatic Quantum
Computing
Can quantum computers be used for machine learning?
Quantum Computing with D-Wave
Prasanna Date | [email protected] | prasannadate.github.io 4
End of Moore’s Law
Rise of Machine Learning and Deep Learning
Neuromorphic Computing
Quantum Computing
Universal Quantum
Computing
Adiabatic Quantum
Computing
Can quantum computers be used for machine learning?
What can the D-Wave do?
The QUBO Problem
Prasanna Date | [email protected] | prasannadate.github.io 5
min$ ∈ {'(,*(},
-./- + -.1 + 2
QUBO = Quadratic Unconstrained Binary Optimization
The QUBO Problem
Prasanna Date | [email protected] | prasannadate.github.io 6
min$ ∈ {'(,*(},
-./- + -.1 + 2
QUBO = Quadratic Unconstrained Binary Optimization
NP Hard !!!
What is Embedding?
Prasanna Date | [email protected] | prasannadate.github.io 8
Traveling Salesman Problem (TSP)
Airline Scheduling Problem
Protein Folding Problem
Node Packing Problem
⋮
Any NP Hard Problem
QUBO Problem D-Wave Hardware
min% ∈ {(),+)}-
./0. + ./2 + 3
EMBEDDING
What is Embedding?
Prasanna Date | [email protected] | prasannadate.github.io 9
QUBO Problem D-Wave Hardware
min$ ∈ {'(,*(},
-./- + -.1 + 2
EMBEDDING
NP Hard Problem
REDUCTION
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 12
0 120 0
0 120 0
1321
0 0 0
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 13
0 120 0
0 120 0
1321
0 0 0
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 14
0 120 0
0 120 0
1321
0 0 0
0 120 0
13 1423 24
0 00 0
0 340 0
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 15
0 120 0
0 120 0
1321
0 0 0
0 120 0
13 1423 24
0 00 0
0 340 0
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 16
0 120 0
0 120 0
1321
0 0 0
0 120 0
13 1423 24
0 00 0
0 340 0
0 12 130 0 230 0 0
14 1524 2534 35
0 0 00 0 0
0 450 0
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 17
0 120 0
0 120 0
1321
0 0 0
0 120 0
13 1423 24
0 00 0
0 340 0
0 12 130 0 230 0 0
14 1524 2534 35
0 0 00 0 0
0 450 0
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 18
!" !# !$ !% !& !'
( =
0 12 130 0 230 0 0
14 15 1624 25 2634 35 36
0 0 00 0 00 0 0
0 45 460 0 560 0 0
!"!#!$!%!&!'
Why is Embedding hard?
Prasanna Date | [email protected] | prasannadate.github.io 19
!" !# !$ !% !& !'
( =
0 12 130 0 230 0 0
14 15 1624 25 2634 35 36
0 0 00 0 00 0 0
0 45 460 0 560 0 0
!"!#!$!%!&!'
What makes a GOOD Embedding Algorithm?
• Time: Should run as fast as possible• Qubit Footprint: Should as few qubits as possible• Accuracy: Should get the objective function value as close to the
global minima as possible
Prasanna Date | [email protected] | prasannadate.github.io 20
Embedding Algorithm Comparison
• Compared my algorithm to D-Wave’s algorithm• Criteria for comparison:• Embedding Time• Qubit Footprint• Accuracy
• Generated problems synthetically, while ensuring at least one global minima
Prasanna Date | [email protected] | prasannadate.github.io 21
Embedding Algorithm Comparison: Time
Prasanna Date | [email protected] | prasannadate.github.io 22
QUBO Problem:
min$ ∈ {'(,*(},
-./- + -.1 + 2
Embedding Algorithm Comparison: Qubit Footprint
Prasanna Date | [email protected] | prasannadate.github.io 23
QUBO Problem:
min$ ∈ {'(,*(},
-./- + -.1 + 2
30% Less Qubits!!!
Embedding Algorithm Comparison: Accuracy
Prasanna Date | [email protected] | prasannadate.github.io 24
QUBO Problem:
min$ ∈ {'(,*(},
-./- + -.1 + 2
Other Metrics
• Longest qubit chain length• Number of bit flips from
globally optimal solution
Prasanna Date | [email protected] | prasannadate.github.io 25
Conclusion
• Quantum Computing with D-Wave• Efficient Embedding Algorithm for D-Wave• Other Work: Quantum Machine Learning
Prasanna Date | [email protected] | prasannadate.github.io 26
Thank You!Prasanna Date
https://prasannadate.github.io
PhD CandidateDepartment of Computer Science
Rensselaer Polytechnic Institute (RPI)[email protected]
ASTRO Intern (Jan-Aug, 2018)Computational Data Analytics (CDA) Group
Oak Ridge National Laboratory (ORNL)[email protected]