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THIS RESEARCH WILL DEVELOP TOOLS FOR ROBUST IMPLEMENTATION OF QUANTUM AND QUANTUM-CLASSICAL PROTOCOLS FOR OPTIMIZATION PROBLEMS RELEVANT TO AERONAUTICS. WE SHALL STUDY THREE SITUATIONS WHERE CONCEPTS FROM QUANTUM ALGORITHMS AND QUANTUM CONTROL THEORY CAN PROVIDE SIGNIFICANT ENHANCEMENT OF OPTIMIZATION IN DIVERSE SETTINGS HAVING APPLICATION TO NETWORK DESIGN AND RESOURCE ALLOCATION/ SCHEDULING. THESE SITUATIONS INCLUDE BOTH THE OPTIMIZATION OF ALGORITHMS WITHIN THE GENERAL CATEGORY OF QUANTUM HEURISTICS AND THE TASK OF VERIFYING QUANTUM OPTIMIZATION PROTOCOLS. WE SHALL USE MACHINE LEARNING TO ASSIST IN DESIGN OF OPTIMAL NOISE MITIGATION PROTOCOLS FOR QUANTUM ENHANCED OPTIMIZATION APPLICABLE TO A WIDE RANGE OF QUADRATIC BINARY OPTIMIZATION PROBLEMS. WE SHALL EXPLORE THE USE OF STOCHASTIC OPTIMIZATION TECHNIQUES TO GENERATE OPTIMAL PROTOCOLS FOR IMPLEMENTATION OF THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM. WE SHALL ADDRESS THE VERIFICATION TASK BY DEVELOPING MACHINE LEARNING QUANTUM STATE TOMOGRAPHY BASED ON CONTINUOUS MEASUREMENTS. SUCH MEASUREMENTS PROVIDE CONSTANT MONITORING WHILE ONLY WEAKLY PERTURBING THE STATE RENDERING THEM USEFUL FOR MONITORING QUANTUM STATES UNDER TIME EVOLUTION DURING ANALOG QUANTUM OPTIMIZATION PROTOCOLS. WE SHALL USE THE PROTOCOLS PRODUCED BY THIS RESEARCH TO EXPLORE APPLICATIONS TO OPTIMIZATION PROBLEMS ARISING IN THE NASA MISSION SPACE INCLUDING COMBINATORIAL OPTIMIZATION PROBLEMS RELATED TO KEY TASKS ARISING IN AERONAUTICS INCLUDING ROBUST NETWORK DESIGN NETWORK FAULT DETECTION RESOURCE ALLOCATION AND JOB SCHEDULING.

$257,014FY2020National Aeronautics and Space AdministrationNASA

Regents Of The University Of California, The

Investigators

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THIS RESEARCH WILL DEVELOP TOOLS FOR ROBUST IMPLEMENTATION OF QUANTUM AND QUANTUM-CLASSICAL PROTOCOLS FOR OPTIMIZATION PROBLEMS RELEVANT TO AERONAUTICS. WE SHALL STUDY THREE SITUATIONS WHERE CONCEPTS FROM QUANTUM ALGORITHMS AND QUANTUM CONTROL THEORY CAN PROVIDE SIGNIFICANT ENHANCEMENT OF OPTIMIZATION IN DIVERSE SETTINGS HAVING APPLICATION TO NETWORK DESIGN AND RESOURCE ALLOCATION/ SCHEDULING. THESE SITUATIONS INCLUDE BOTH THE OPTIMIZATION OF ALGORITHMS WITHIN THE GENERAL CATEGORY OF QUANTUM HEURISTICS AND THE TASK OF VERIFYING QUANTUM OPTIMIZATION PROTOCOLS. WE SHALL USE MACHINE LEARNING TO ASSIST IN DESIGN OF OPTIMAL NOISE MITIGATION PROTOCOLS FOR QUANTUM ENHANCED OPTIMIZATION APPLICABLE TO A WIDE RANGE OF QUADRATIC BINARY OPTIMIZATION PROBLEMS. WE SHALL EXPLORE THE USE OF STOCHASTIC OPTIMIZATION TECHNIQUES TO GENERATE OPTIMAL PROTOCOLS FOR IMPLEMENTATION OF THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM. WE SHALL ADDRESS THE VERIFICATION TASK BY DEVELOPING MACHINE LEARNING QUANTUM STATE TOMOGRAPHY BASED ON CONTINUOUS MEASUREMENTS. SUCH MEASUREMENTS PROVIDE CONSTANT MONITORING WHILE ONLY WEAKLY PERTURBING THE STATE RENDERING THEM USEFUL FOR MONITORING QUANTUM STATES UNDER TIME EVOLUTION DURING ANALOG QUANTUM OPTIMIZATION PROTOCOLS. WE SHALL USE THE PROTOCOLS PRODUCED BY THIS RESEARCH TO EXPLORE APPLICATIONS TO OPTIMIZATION PROBLEMS ARISING IN THE NASA MISSION SPACE INCLUDING COMBINATORIAL OPTIMIZATION PROBLEMS RELATED TO KEY TASKS ARISING IN AERONAUTICS INCLUDING ROBUST NETWORK DESIGN NETWORK FAULT DETECTION RESOURCE ALLOCATION AND JOB SCHEDULING. · GrantIndex