quantumfuzzylogic
TRANSCRIPT
Agenda
Quantum Membership Function Based Adaptive Neural Fuzzy Inference System
Fuzzy Quantum Circuits to Model Emotional Behaviors of Humanoid Robots
Introduction
Quantum Membership Function
Hybrid Learning Algorithm for qANFIS
Simulation Results of Robotic Path Planning
Results
Quantum Membership Function(Multilevel Function )
Example of quantum membership function: The number of levels ns = 3the center c = 0the slope factor β = 2and the quantum intervals Θ=[5, 15, 25]
For nodei, ci is the center of qMF,βi is the slope factor,nsi denotes the number of levels in the qMF, and θ is the αth quantum internal
Hybrid Learning Algorithm for qANFI
tGA LSE approach
GD or qPSO RMSE
tGA : Trimming-Operator-Based Genetic Algorithm
LSE approach : Least Squares Estimate method
GD : Gradient Descent
qPSO : quantum-inspired particle swarm optimization methods
RMSE : root mean square error
Simulation Results of Robotic Path Planning
we apply qANFIS to the robotic path planning problem. To control the robot moving to the target
The qANFIS models have two types: (1) GD-qANFIS whose qMFs are updated by GD approach and
(2) qPSO-qANFIS whose qMFs are adjusted by qPSO approach
Input Output
d : distanceΦ : angle between the robot and target
Θ : is the steering angle of the robot
Simulation Results of Robotic Path Planning
Case 1 Case 2
Smallest RMSE GD - qANFIS qPSO - qANFIS
Steps qPSO – qANFIS = 96 stepsGD – ANFIS = 101 steps
GD – ANFIS = 97 stepsANFIS = 97 steps
qPSO – qANFIS = 98 steps
Quantum Computer Benefits:
Solve Constraint Satisfaction Problems(CSP) extremely quickly.
Quantum Computer are able to model Boolean, Multiple-valued, continuous and fuzzy logic.
Quantum Computer Benefits:
Solve Constraint Satisfaction Problems(CSP) extremely quickly.
Quantum Computer are able to model Boolean, Multiple-valued, continuous and fuzzy logic.
butCan one create a concept combined Benefits of Fuzzy Logic and Quantum
Circuits
Quantum Circuits:
is a model for quantum computation in which a computation is a sequence of quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register. This analogous structure is referred to as an n-qubit.
Represented as Matrices:
single Qubit:
two Qubits:
Quantum Circuits:
Hadamard Gate:
maps: to & to
represents rotation of about the axis
Matrix:
Where: H * H’ = I -- > H is “ Unitary Matrix ”
Quantum Circuits:
Commonly Used Gates:
Pauli-X Gate, Pauli-Y Gate, Pauli-Z Gate
Phase Shift Gates
Toffoli Gate
From Fuzzy Circuits to Fuzzy Quantum Circuits:
Single Qubit & Many Qubit Operators represented by
“Unitary Matrix ”.
and play another role to change phases of points on the Bloch’s sphere.
Fuzzy Logic Fuzzy Quantum Logic
Minimum operator Conjunction operator
Maximum operator Disjunction operator
Not operator Complement operator
Member Function Single Qubit operator
Bloch Sphere to represent Logic States: One meridian of the bloch’s sphere
is mapped to the [0,1] interval of Fuzzy
sets.
Using Complex number whish is
similarity to Complex Fuzzy Logic.
External observed (measured)…