Tag: Quantum Complexity

Table of Contents Introduction What Is Approximation in Quantum Contexts? Exact vs Approximate Computation Complexity of Approximate Decision Problems Quantum Approximation Algorithms Variational Quantum Algorithms and Heuristics Approximating Ground State Energies The...

Table of Contents Introduction What Is Zero Knowledge? Classical Zero Knowledge: An Overview Quantum Zero Knowledge: Definition and Goals Models of Quantum Interactive Proofs Honest-Verifier vs General Zero Knowledge Types of...

Table of Contents Introduction What Is QIP? Interactive Proofs in Classical Computation Quantum Interactive Proofs Definition of the QIP Class QIP vs IP: A Natural Extension Communication in QIP Protocols Completeness and...

Table of Contents Introduction What Are Proof Systems? Classical Proof Systems Overview Quantum Proof Systems: Motivation and Need QMA: Quantum Merlin-Arthur QCMA: Quantum-Classical Merlin-Arthur QIP: Quantum Interactive Proofs QMA(k): Multiple Quantum Provers Quantum...

Table of Contents Introduction Classical Interactive Proofs Recap Quantum Interactive Proofs (QIP): Definition The QIP Complexity Class One-Round vs Multi-Round QIP QIP(3) = QIP: Compression of Interaction QIP and PSPACE: QIP...

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...