Tag: Quantum Complexity

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...

Table of Contents Introduction What Are Relativized Worlds? Classical Context: P vs NP with Oracles Motivation for Studying Relativization Quantum Oracle Machines BQP with Oracles (BQP^O) Relativized Separations: BQP vs BPP BQP...

Table of Contents Introduction Classical PCP Theorem: A Quick Recap Motivation for Quantum PCPs What Are Probabilistically Checkable Quantum Proofs? Quantum PCP Conjecture Quantum Locally Checkable Proofs Complexity Classes: QMA and...

Table of Contents Introduction Classical Hardness vs Randomness: A Brief Overview Quantum Analogs of Pseudorandomness Derandomization and Quantum Algorithms Quantum Pseudorandom Generators (QPRGs) BQP vs BPP and Randomness Elimination Hardness Assumptions...

Table of Contents Introduction What Are Black-Box Models? Motivation for Black-Box Separations Classical Black-Box Separation Examples Quantum Black-Box Access Oracle Constructions in Quantum Complexity Quantum vs Classical Separation Techniques Separating BQP from...

Table of Contents Introduction What Are Reductions in Complexity Theory? Classical vs Quantum Reductions Types of Quantum Reductions Turing Reductions in Quantum Settings Many-One Quantum Reductions Oracle Reductions and Relativized Worlds Reductions...

Table of Contents Introduction Classical Computability: A Brief Review What Is Quantum Computability? Quantum Turing Machines (QTMs) Relationship to Church-Turing Thesis Quantum Extensions of Recursive Functions Quantum Decidability and Semidecidability Halting Problem...