Related papers: Quantum Computing: Theoretical versus Practical Po…

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory…

Quantum computers are expected to be able to solve mathematical problems that cannot be solved using conventional computers. Many of these problems are of practical importance, especially in the areas of cryptography and secure…

There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we…

General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or…

We investigate if physical laws can impose limit on computational time and speed of a quantum computer built from elementary particles. We show that the product of the speed and the running time of a quantum computer is limited by the type…

According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are…

Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as…

Quantum computing is an emerging paradigm that opens a new era for exponential computational speedup. Still, quantum computers have yet to be ready for commercial use. However, it is essential to train and qualify today the workforce that…

The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have…

In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…

A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…

Quantum computing (QC) has experienced rapid growth in recent years with the advent of robust programming environments, readily accessible software simulators and cloud-based QC hardware platforms, and growing interest in learning how to…

The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…

Since the introduction of quantum mechanics, it has been taught mostly as a theoretical subject. It is also viewed as a theory that provides a best understanding of the nature, but which does not have much practical applications in our day…

Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…

Quantum computation is an emerging technology that promises a wide range of possible use cases. This promise is primarily based on algorithms that are unlikely to be viable over the coming decade. For near-term applications, quantum…

The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and…

We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation…

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…

We use the benefits and components of classical computers every day. However, there are many types of problems which, as they grow in size, their computational complexity grows larger than classical computers will ever be able to solve.…