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

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

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.

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

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.

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

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)

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

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).

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

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

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)

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)

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

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)

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

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

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

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

Thank you for your attention 20