Quantum 101

Table of Contents Introduction Fundamentals of Photonic Qubits Encoding Information in Photons Single-Photon Sources Photonic Quantum Logic Gates Beam Splitters and Interferometers Phase Shifters and Waveguide Control Measurement-Induced Nonlinearities Linear Optical Quantum Computing...

Table of Contents Introduction Basics of Ion Trapping Paul and Penning Traps Linear RF Traps and Segmented Traps Ion Loading and Initialization Cooling Mechanisms Overview Doppler Cooling Sub-Doppler Techniques: Sisyphus Cooling Sideband Cooling Resolved...

Table of Contents Introduction Overview of Trapped Ion Systems Ion Trapping Mechanisms Internal and Motional States of Ions Qubits in Trapped Ions Quantum Gate Requirements Single-Qubit Gates in Trapped Ions Laser-Based Quantum...

Table of Contents Introduction What Are Quantum Dots? Quantum Confinement and Discrete Energy Levels Types of Quantum Dots Materials Used in Quantum Dot Fabrication Fabrication Methods Colloidal Quantum Dots Epitaxial Self-Assembled Quantum...

Table of Contents Introduction Historical Foundations Spectroscopy of Atomic Transitions Laser Cooling and Trapping Magneto-Optical Traps (MOTs) Optical Dipole Traps and Tweezers Atomic Clocks and Frequency Standards Rydberg Atoms and Strong Interactions Bose-Einstein...

Table of Contents Introduction Historical Background Foundational Experiments in Quantum Mechanics The Double-Slit Experiment Stern-Gerlach and Spin Quantization Bell Test Experiments and Nonlocality Quantum Entanglement: Experimental Realizations Quantum Optics and Photon Experiments Trapped...

Table of Contents Introduction MIP* = RE and Its Impact Quantum PCP Progress and New Approaches QMA-Completeness Results for Hamiltonians Quantum Supremacy: Refinements and Limits Interactive Proofs with Quantum Verifiers Quantum...

Table of Contents Introduction The Landscape of Quantum Complexity Classes BQP and Its Boundaries Quantum Interactive Proofs and MIP* QMA, QIP, and QCMA: Quantum Proof Systems Oracle Separations and Relativized...

Table of Contents Introduction What Is Meta-Complexity? Classical Meta-Complexity: A Recap Meta-Complexity in the Quantum Setting Quantum Kolmogorov Complexity Measuring Descriptions of Quantum States Quantum Circuit Minimization Meta-Computational Complexity Classes Quantum Circuit Lower...

Table of Contents Introduction Classical Advice and Non-uniform Computation Quantum Advice: Definition and Motivation The Class BQP/qpoly Comparison with BQP/poly Quantum Advice States vs Classical Advice Strings Measuring Power of Quantum...

Table of Contents Introduction What Is Property Testing? Classical vs Quantum Property Testing Quantum Query Models Why Property Testing Is Important in Quantum Computing Key Measures: Query Complexity and Distance Property...

Table of Contents Introduction What Are Lattices in Computational Mathematics? Key Lattice Problems: SVP, CVP, SIVP Relevance to Cryptography and Complexity Lattices and Worst-Case to Average-Case Reductions Ajtai’s Theorem and...