The Limits of Quantum Computers

Michael P. Frank

Many of the fundamental limits on information processing, from thermodynamics, relativity, and quantum mechanics, are only a few decades away. Novel physically motivated computing paradigms, such as reversible computing and quantum computing, may help in certain ways, but even they remain subject to some basic limits. One can arrive at several firm conclusions regarding upper bounds on the limits of computing. In this article, the author only reviews the fundamental technology-independent limits.

Scott Aaronson

Liam Graham

Computation and simulation are key parts of the scientific project and are also central to understanding emergence. After a general discussion of the role of simulations in science, the chapter turns to the theory of computation, Turing machines and the Church-Turing principle. Limits to the scope of simulation would imply limits to science. Absolute limits would arise if some things are non-computable. Thinking about practical limits leads us to quantum computers, quantum simulations and an estimation of the computational capacity of the universe. The physical version of the Church-Turing principle states that if we can build a universal quantum computer we can simulate every physical system.

Osama M. Raisuddin, Suvranu De

Mingji Xia, Zhengfeng Ji

The powerful idea of computation has accompanied the development of human civilization, has deeply changed the way we live and work, and has accelerated the advancement of many areas of sciences. In this article, we explore the power and limits of computation from several different perspectives. We will discuss topics from the models of computation and Church-Turing thesis, to the impact of the P versus NP problem and quantum computing on our understanding of the limits of computation. More concretely, we will explore the computability and the halting problem, the efficiency problem of computation, the P versus NP problem. We then move on to the discussion of quantum computation, quantum algorithm for factoring and its implications, quantum simulation and the relation between quantum and classical computations.