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
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