Related papers: Hamiltonian complexity
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. The ability of quantum computers to scale computations exponentially imply better…
In the half century since the 1950s computer simulation has transformed our understanding of physics. The rare, expensive, slow, and bulky mainframes of World War II have given way to today's millions of cheap, fast, desksized workstations…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians. During the past decade, most of…
With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the…
This paper presents the principal challenges and opportunities associated with computational biomechanics research. The underlying cognitive control involved in the process of human motion is inherently complex, dynamic, multidimensional,…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
The Hamiltonian operator describing a quantum particle on a path often extends holomorphically to a complex neighborhood of the path. When it does, it can be seen as the local expression of a complex projective structure, and its…
Computer-based modelling and simulation have become useful tools to facilitate humans to understand systems in different domains, such as physics, astrophysics, chemistry, biology, economics, engineering and social science. A complex system…