A Method For Solving Np-complete Problems By Use Of Graph Embodiment On A Quantum Computation Paradigm Using A Relational Database Query

Shadrack Mwanik, Andrew Mwaura Kahonge, Evans Kirimi Miriti

The relationship between the complexity class P and NP is one of the most fascinating and unresolved question in theoretical Computer Science. The classical computational paradigm, hedged on Turing thesis may be by itself the limiting factor. To investigate this relationship, a method for solving a query problem on a relational database on the classical and the quantum computational paradigm has been developed. The method solves queries or database problems through the use of graphs. The results indicate that the solution to the P vs NP cannot be resolved under the current computation paradigms and may requires a new computation paradigm to resolve it.

Dhananjay P. Mehendale

Valter Uotila, Cong Yu, Bo Zhao

Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be optimized and adapted for target hardware through quantum circuit compilation. We introduce ZX-DB, a data-driven system that performs quantum circuit simplification and rewriting inside a graph database using ZX-calculus, a complete graphical formalism for quantum mechanics. ZX-DB encodes ZX-calculus rewrite rules as standard openCypher queries and executes them on an example graph database engine, Memgraph, enabling efficient, database-native transformations of large-scale quantum circuits. ZX-DB integrates correctness validation via tensor and graph equivalence checks and is evaluated against the state-of-the-art PyZX framework. Experimental results show that ZX-DB achieves up to an order-of-magnitude speedup for independent rewrites, while exposing pattern-matching bottlenecks in current graph database engines. By uniting quantum compilation and graph data management, ZX-DB opens a new systems direction toward scalable, database-supported quantum computing pipelines.

Scott Aaronson

This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable axiom called "indifference to the identity," we could solve the Graph Isomorphism and Approximate Shortest Vector problems in polynomial time, as well as an oracle problem that is known to require quantum exponential time. We could also search an N-item database using O(N^{1/3}) queries, as opposed to O(N^{1/2}) queries with Grover's search algorithm. On the other hand, the N^{1/3} bound is optimal, meaning that we could probably not solve NP-complete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.

Martin Fürer

Colin P. Williams