Advances in Computational Complexity and Quantum Computing

The field of computational complexity and quantum computing is rapidly advancing, with significant breakthroughs in recent years. One of the key areas of research is the development of new algorithms and techniques for solving complex problems efficiently. For example, researchers have made progress in improving the competitiveness of online algorithms, such as the List Update problem, and developing new approximation schemes for problems like the k-Subset Sum Ratio and Multiway Number Partitioning Ratio. Additionally, there have been significant advances in quantum computing, including the development of new quantum algorithms and the exploration of the computational implications of a superposition of spacetimes. Furthermore, researchers have made progress in understanding the hardness hierarchy for certain complexity classes, such as the O(n√log n) complexity class, and have developed new techniques for output-sensitive approximate counting. Notably, the work on quantum constraint generation frameworks and problem-structure-informed quantum approximate optimization algorithms has the potential to significantly improve the efficiency of solving large-scale unit commitment problems. Some particularly noteworthy papers include the development of a 3.3904-competitive online algorithm for List Update with uniform costs, an approximation scheme for k-Subset Sum Ratio running in O(n^{2k}/ε^{k-1}) time, and a quantum constraint generation framework for binary linear programs. Overall, these advances have significant implications for the field of computational complexity and quantum computing, and are expected to lead to further breakthroughs in the coming years.

Sources

A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs

Approximation Schemes for k-Subset Sum Ratio and Multiway Number Partitioning Ratio

Bernstein-Vazirani Algorithm with A CCNOT-Based Oracle

Upper and Lower Bounds for the Linear Ordering Principle

Long Arithmetic Progressions in Sumsets and Subset Sums: Constructive Proofs and Efficient Witnesses

Online Stochastic Matching with Unknown Arrival Order: Beating $0.5$ against the Online Optimum

Beyond Worst-Case Subset Sum: An Adaptive, Structure-Aware Solver with Sub-$2^{n/2}$ Enumeration

Problem-Structure-Informed Quantum Approximate Optimization Algorithm for Large-Scale Unit Commitment with Limited Qubits

On the Hardness Hierarchy for the $O(n \sqrt{\log n})$ Complexity in the Word RAM

A Quantum Constraint Generation Framework for Binary Linear Programs

Lattice Based Crypto breaks in a Superposition of Spacetimes

Time hierarchies for sublogarithmic-space quantum computation

Output-sensitive approximate counting via a measure-bounded hyperedge oracle, or: How asymmetry helps estimate $k$-clique counts faster

Average-Case Hardness of Parity Problems: Orthogonal Vectors, k-SUM and More

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