Continuous quantum computation: Difference between revisions

Revision as of 20:49, 9 February 2007

Revision as of 21:00, 9 February 2007

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* In their standard monograph Nielsen and Chuang state "Of particular interest is a decisive answer to the problem whether quantum computers are more powerful than classical computers." To answer this question one must know the classical and quantum computationsl complexities

In the section An Example: Path Integration solving a continuous problem on a quantum computer will be discussed. Here the second motivation will be amplified. By computational complexity (complexity for brevity) is meant the '''minimal''' computationslcomputational resources needed to solve a problem. Two of the most important resources for quantum computing are qubits and queries. Classical complexity has been extensively studied in [[Information-Based Complexity| informations-based complexity]]. The classical complexity of many continuous problems is known. Therefore, when the quantum complexity of these problems is obtained, the question as to whether quantum computers are more powerful than classical can be answered. Furthermore, it can be established how much more powerful. In contrast, the complexity of discrete problems is typically unknown; one has to settle for the complexity hierarchy. For example, the classical complexity of integrer factorization is unknown.

==An Example: Path Integration==