1. Quantum-Classical Hybrid Machine Learning for Gene Regulatory Pathways
Radhakrishnan Balu , CISD-ARL
CEM II, 04/03/2018, West Point, NY

2. Outline of the Talk
A Brief introduction to the Science problem
Review of Bayesian Networks
Adiabatic Quantum Computation
Probabilistic Logic Programming (ML)
Solution Architecture and Results

3. Bio Signaling Pathways
A Bayesian Network based Causal Relationship Elucidation
Sachs, K.; Perez, O.; Pe’er, D.; Laughenburger, A. D.; Nolan, P. G. Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data. Science 2005, 308.

4. Bayesian Networks BN is a pair (Bs, Bp).
Bs is directed acyclic graph representing the model
Bp is the set of conditional probabilities
Xi state of node – gene is activated or not
Probability of Xi conditioned on the joint state of its parents πi(BS)
Parents: Arcs in the structure to Xi
Coin Toss
Weather
Visit Zoo
Spend Money

5. Bayesian Networks
Proteomics data from flow cytometry Concentrations of proteins as probabilities
Bayesian networks for hypothetical proteins X, Y, Z, and W. In this model, X influences Y, which, in turn, influences both Z and W.

6. Acyclic directed graphs
Bayesian Networks
Acyclic directed graphs
Biological pathways may contain cycles
May miss some dependencies

7. Quantum Annealing 2000 qubit processor
Restricted class of optimization problems
Quadratic Unconstrained Binary Optimization (QUBO)
O’Gorman, B. A., Perdomo-Ortiz, A., Babbush, R., Aspuru-Guzik, A. & Smelyanskiy, V. Bayesian network structure learning using quantum annealing. European Physics Journal Special Topics 224, 163–188 (2015)

8. D-Wave Two (Vesuvius) D-Wave II Processor
503/512 functional qubits with “Chimera graph” couplings
8x8 unit cells comprising 512 qubits
equivalence in the sense of minor embedding

9. Quantum Annealing Intuition
It is a simple physical process of thermaliztion
Very difficult to simulate on classical computers
Quantum annealers are suitable for such tasks
Map the problem to energy minimization
Radhakrishnan Balu, Dale Shires, and Raju Namburu, “A quantum algorithm for uniform sampling of models of propositional logic based on quantum probability,” J. Defense Modeling and Simulation (2016).

10. A special-purpose optimizer
Designed to find the ground state of classical Ising spin models:

11. Designed to implement QA
(special case of adiabatic quantum computation, at finite T)
17mK

12. First-Order Probabilistic Logic
(3 = 5) Pope(X)
X is Albert Einstein
X is Francis
X is DiNardo (probable)
X is Parolin (more or less probable)

13. Entanglement Semantics
Non-commutative Probability
Quantum Probability Space
Attach Probability Amplitudes to H-interpretations
Projections of H
ρ - State
Denotational Semantics
Distribution Semantics
Entanglement Semantics Ω
H-I
Radhakrishnan Balu: Quantum probabilistic logic programming, Proc. SPIE-DSS, quantum information and computation, Baltimore MD (2015)

14. Current Implementation
Number of nodes of BN = 8
Number of parents allowed = 3
Number of logical qubits = 230
Number of Physical qubits 2000 14

15. Hybrid Architecture D-Wave Suprvised Learning Proteomics BN
PRISM (MLE)
Proteomics BN
Unsuprvised Learning
Nand Kishore, Radhakrishnan Balu, and Shashi P. Karna, “Modeling Genetic Regulatory Networks Using First-Order Probabilistic Logic”, ARL-TR-6354, 2013.
PRISM (MAP)

16. ORIGINAL vs PRISM SCORE
Legend :
Black arcs : Correct edges (True Positives)
Dotted arcs : Missed edges (False Negatives)
Red arcs : Wrong edges (False Positives)
Green arcs : Reversed edges (False Positive + False Negative)
TRUE POSITIVE : 12
FALSE POSITIVES : 2
FALSE NEGATIVES : 2

17. R vs PRISM TRUE POSITIVE : 12 TRUE POSITIVE : 11 FALSE POSITIVES : 2
Legend :
Black arcs : Correct edges (True Positives)
Dotted arcs : Missed edges (False Negatives)
Red arcs : Wrong edges (False Positives)
Green arcs : Reversed edges (False Positive + False Negative)
TRUE POSITIVE : 12
FALSE POSITIVES : 2
FALSE NEGATIVES : 2
TRUE POSITIVE : 11
FALSE POSITIVES : 2
FALSE NEGATIVES : 3

18. ORIGINAL vs R SCORE TRUE POSITIVE : 11 FALSE POSITIVES : 2
Legend :
Black arcs : Correct edges (True Positives)
Dotted arcs : Missed edges (False Negatives)
Red arcs : Wrong edges (False Positives)
Green arcs : Reversed edges (False Positive + False Negative)
TRUE POSITIVE : 11
FALSE POSITIVES : 2
FALSE NEGATIVES : 3

19. Future Plans Applications beyond GRN
Learning within Quantum processing
Error correction for robustness
Scalability beyond 8-nodes BN
Development on 4000 qubit processor
Bayesian Neural Networks 19

20. Thank you for your attention20