Quantum 101

Table of Contents Introduction Classical Background: NP and MA From MA to QMA: A Quantum Leap Formal Definition of QMA The Role of the Quantum Witness Completeness and Soundness in...

Table of Contents Introduction Understanding QMA Understanding QCMA The Key Difference: Quantum vs Classical Witness Formal Definitions of QMA and QCMA Verifier’s Role in Both Models Complexity and Verification Power Relationship Between...

Table of Contents Introduction Defining Randomness Classical Randomness: Pseudorandomness and Entropy Quantum Randomness: Intrinsic and Fundamental Sources of Classical Randomness Sources of Quantum Randomness Determinism in Classical Mechanics Indeterminism in Quantum Mechanics Random...

Table of Contents Introduction What Is an Oracle? Purpose of Oracle Constructions Oracle Turing Machines Oracle Separations: Classical vs Quantum Relativized Complexity Classes Oracle Separations in Classical Complexity Oracle Results in Quantum...

Table of Contents Introduction Complexity Classes at a Glance What Is BQP? What Is P? What Is NP? What Is PP? The Inclusion Chain: P ⊆ BPP ⊆ BQP ⊆ PP BQP...

Table of Contents Introduction What Is BQP? Formal Definition of BQP The Quantum Turing Machine Model The Quantum Circuit Model How BQP Differs from P and NP BQP vs BPP Key Properties...

Table of Contents Introduction What Is Quantum Complexity Theory? Classical vs Quantum Models of Computation Why Quantum Complexity Matters The Quantum Turing Machine Quantum Circuits and Uniform Families Basic Quantum Complexity...

Table of Contents Introduction What Are Complexity Classes? Deterministic vs Non-Deterministic Models Class P (Polynomial Time) Class NP (Nondeterministic Polynomial Time) Relationship Between P and NP NP-Complete Problems Reductions and Hardness Class PSPACE...

Table of Contents Introduction What Is Computational Complexity? Importance in Computer Science and Physics Time and Space Complexity Big O Notation Worst, Average, and Best-Case Complexity Complexity Classes Overview P: Polynomial Time NP:...

Table of Contents Introduction What Are Quantum Dots? Quantum Confinement and Artificial Atoms Types of Quantum Dot Qubits Electron Spin Qubits Singlet-Triplet Qubits Exchange-Only and Hybrid Qubits Quantum Dot Fabrication Techniques Material Systems:...

Table of Contents Introduction What Are Photonic Qubits? Quantum Properties of Light Qubit Encodings in Photons Polarization Encoding Path Encoding Time-Bin and Frequency Encoding Advantages of Photonic Qubits Challenges in Photonic Quantum Computing Single-Photon...

Table of Contents Introduction What Are Trapped Ion Qubits? Historical Development Physical Principles Ion Trapping Mechanisms Paul Traps and RF Confinement Common Ion Species Used Qubit Encoding in Ion States Qubit Initialization Qubit Manipulation...