Fundamental Limits to Computing

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.

Arturo A. L. Sangalli

Materov

Since Turing, it's been generally accepted that computing systems have two types of limitations: algorithmic (some problems are fundamentally unsolvable) and engineering (the hardware is imperfect, noisy, and breaks). Quantum computing has added a third type— complexity : some problems are solvable, but require resources that grow faster than any polynomial. This supplement introduces a fourth type of restriction, previously not described in the literature: The fundamental limit of quantum computing (FQC) is a limit on the precision of any quantum computing device, which arises not from imperfections in the implementation, but from the discrete structure of spacetime at the Planck scale. This limit cannot be overcome by any technological advancement. It is not a consequence of decoherence , thermal noise, or imperfect gates. It is built into the geometry of reality—just as the speed of light is built into the structure of spacetime and cannot be overcome by any acceleration.Unlike collapse-model-based limits on quantum hardware, the Fundamental Limit of Quantum Computation is proposed as an ontological bound arising from the discrete structure of spacetime itself.

Ashley M. Aitken

Vishal Kumar Jaiswal, Sam Goundar, Gurram Sunitha +3 more

Quantum computing is an emerging technology around the world. Even though it is limited to theory in most cases, it can break today’s encryption in seconds, unlike classical computers, which could take some years; however, quantum computers’ limited qubits stop them from being widely used in real-world situations, where they can demonstrate their superior efficiency. A lot of complex real-world problems have been solved using the fundamental concepts. So, unlike other books on quantum computing and quantum mechanics, this chapter aims to combine quantum mechanics and quantum computing to make sense of quantum computing efficiently. In this chapter, we will discuss the fundamental concepts of quantum computing, like qubits, as well as practical applications and error corrections. Along with this, it will provide insights into the latest evolution of quantum computing by major companies working on quantum computing. Finally, this chapter will not discuss pure theory but mostly focus on the fundamentals and their applications and their limitations. At the end, there are some open questions to encourage future research opportunities in quantum computing.