QUANTUM COMPUTING

COMPUTATIONAL MODELS

PHYSICAL QUANTUM COMPUTERS

Theory

Quantum Logic Circuits

Decision Diagrams

Analysis and Synthesis of Quantum Circuits by Using Quantum Decision Diagrams(Abdollahi, Pedram; 2006) :

Quantum Logic Synthesis

SIMULATING QUANTUM CIRCUITS ON CONVENTIONAL HARDWARE

FUNDAMENTALS

MATH

QUANTUM MECHANICS

LINEAR ALGEBRA

SUPERPOSITION

ENTANGLEMENT

INTERFERENCE

PROBABILITY

ALGORITHMS

Seminal Algorithms

Grover's

Deutsch's

QDD-based Functional Decomposition

COMPLEX NUMBERS

Shor's

Simulations of Nature

Biology

Chemistry

Physics

Quantum Machine Learning

Conventional

Uncoventional

Weak Simulation

COMPLEXITY

Quantum Factored Forms

Just Like the Real Thing:Fast Weak Simulation of Quantum Computation(Himlich, Markov, Wille; 2018)

Mimicking Actual Quantum Computers

Advanced Weak Simulation

statistically identical output samples through:

Efficient Sampling

Empirical Validation

Quantum Decision Diagrams

Development

General-purpose Quantum Computers

IBM

Google

Quantum Annhealing

Introduction

1

Quantum Logic Synthesis (Background/Context)

Problem: synthesizing a general quantum operation

The paper presents a decision diagram based representation of quantum circuits

quantum operators are represented by a complex unitary matrix

the space of quantum systems is exponentially larger than the space of clasical systems

previous attempts at reversible logic circuit synthesis

exhaustive search

matrix decomposition

local transformations

spectral approaches

Adaptations of EXOR logic decomposition

Reed-Muller representations

why are these insufficient?

The problem: producing an output sample on a conventional computer that is statistically indistinguishable from the outputs of a quantum computer

Decision Diagrams

avoids exponentially expanding matrices