1 Fundamental Problems for Universal Quantum Computers

Yu Shi

Jincheng Zhang

This paper proposes a novel computational architecture centered around the fundamental principles of quantum state superposition and quantum entanglement. The core claim is the design of a universally applicable quantum computing framework that, without relying on pre-defined algorithms, can tackle any solvable computational problem. The proposed mechanism leverages the creation of highly entangled quantum systems, exploiting superposition to enable parallel information processing and transformation. Unlike existing quantum computing approaches which are often tailored to specific problems, this architecture represents a shift towards a truly general-purpose quantum computer. The theoretical underpinnings of this architecture are explored, focusing on the necessary conditions for achieving universal computation and outlining potential challenges and future research directions. We introduce a framework that moves beyond algorithmic constraints, offering a pathway toward harnessing the full potential of quantum mechanics for computational tasks.

QNFO

The physical realization of any computational model is fundamentally bounded not by algorithmic complexity alone, but by the thermodynamic and quantum statistical limits of its substrate, a constraint that recasts computationally hard problems as problems of physical resource scaling and forces a distinction between abstract universality and practical realizability.

Willem L. Fouché, Johannes Heidema, Glyn Jones +1 more

Diederik Aerts, Sven Aerts, Marek Czachor +4 more

During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process). In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the fundamentals of quantum computation; and (2) a theoretical experimental part, which focuses on the theoretical aspects of applications that arise from new technology and novel research perspectives such as quantum optics and quantum cryptography. Particular attention is also paid to the measurement problem, the classical limit and alternative interpretations (such as the hidden measurement approach).

Emmanuel Jeandel