Related papers: Notes on Geometric-Algebra Quantum-Like Algorithms
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
Exponential parallelism, a defining principle of advanced computational systems, holds promise for transformative impacts across several scientific and industrial domains. This feature paper provides a comparative overview of Quantum…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the…
In the rapidly growing area of quantum information, the Deutsch algorithm is ubiquitous and, in most cases, the first one to be introduced to any student of this relatively new field of research. The reason for this historical relevance…
ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of…
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…
Quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era presents significant challenges in differentiating quantum software bugs from hardware noise. Traditional debugging techniques from classical software engineering cannot…
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…