Quantum Fuzzy LogicMOHAMMAED SAED HAJ ALI

KINDA ALTARBOUCH

Agenda

Quantum Membership Function Based Adaptive Neural Fuzzy Inference System

Fuzzy Quantum Circuits to Model Emotional Behaviors of Humanoid Robots

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Quantum Membership Function Based Adaptive Neural Fuzzy Inference System

Introduction

Quantum Membership Function

Hybrid Learning Algorithm for qANFIS

Simulation Results of Robotic Path Planning

Results

Introduction

Adaptive Network based Fuzzy Inference system

ANFISqANFIS

Quantum Membership Function(Multilevel Function )

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

Hybrid Learning Algorithm for qANFI

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

Simulation Results of Robotic Path Planning

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

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Fuzzy Quantum Circuits to Model Emotional Behaviors of Humanoid Robot

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

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Deterministic

Probabilistic

Entangled

Human Behaviors:

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

Hey … What is Bloch Sphere ?!

Bloch Sphere

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)…

Bloch Sphere:

Quantum Sphere of Emotions

Human Behavior Modeling

Human Behavior Modeling

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