Efficiently Embedding QUBO Problems on Adiabatic Quantum … · 2018. 10. 11. · Efficiently Embedding QUBO Problems on Adiabatic Quantum Computers Prasanna Date PhD Candidate Department

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

datep@rpi.edu

ASTRO Intern (Jan-Aug, 2018)Computational Data Analytics (CDA) Group

Oak Ridge National Laboratory (ORNL)Mentor: Dr. Robert Patton

datep@ornl.gov

Quantum Computing with D-Wave

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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 | datep@rpi.edu | 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 | datep@rpi.edu | 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

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min$ ∈ {'(,*(},

-./- + -.1 + 2

QUBO = Quadratic Unconstrained Binary Optimization

The QUBO Problem

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min$ ∈ {'(,*(},

-./- + -.1 + 2

QUBO = Quadratic Unconstrained Binary Optimization

NP Hard !!!

Embedding

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What is Embedding?

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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?

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QUBO Problem D-Wave Hardware

min$ ∈ {'(,*(},

-./- + -.1 + 2

EMBEDDING

NP Hard Problem

REDUCTION

Why is Embedding hard?

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0 120 0

Why is Embedding hard?

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0 120 0

Why is Embedding hard?

Prasanna Date | datep@rpi.edu | prasannadate.github.io 12

0 120 0

0 120 0

1321

0 0 0

Why is Embedding hard?

Prasanna Date | datep@rpi.edu | prasannadate.github.io 13

0 120 0

0 120 0

1321

0 0 0

Why is Embedding hard?

Prasanna Date | datep@rpi.edu | 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 | datep@rpi.edu | 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 | datep@rpi.edu | 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 | datep@rpi.edu | 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 | datep@rpi.edu | 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 | datep@rpi.edu | 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

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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

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Embedding Algorithm Comparison: Time

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QUBO Problem:

min$ ∈ {'(,*(},

-./- + -.1 + 2

Embedding Algorithm Comparison: Qubit Footprint

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QUBO Problem:

min$ ∈ {'(,*(},

-./- + -.1 + 2

30% Less Qubits!!!

Embedding Algorithm Comparison: Accuracy

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QUBO Problem:

min$ ∈ {'(,*(},

-./- + -.1 + 2

Other Metrics

• Longest qubit chain length• Number of bit flips from

globally optimal solution

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Conclusion

• Quantum Computing with D-Wave• Efficient Embedding Algorithm for D-Wave• Other Work: Quantum Machine Learning

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Thank You!Prasanna Date

https://prasannadate.github.io

PhD CandidateDepartment of Computer Science

Rensselaer Polytechnic Institute (RPI)datep@rpi.edu

ASTRO Intern (Jan-Aug, 2018)Computational Data Analytics (CDA) Group

Oak Ridge National Laboratory (ORNL)datep@ornl.gov