Related papers: Constraint Inequalities from Hilbert Space Geometr…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
One of the most difficult problems in quantum mechanics is the analysis of the measurement processes. In this paper, we point out that many of these difficulties originate from the different roles of measurement outcomes and observable…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
One of the methods proposed in the last years for studying non-perturbative gauge theory physics is quantum simulation, where lattice gauge theories are mapped onto quantum devices which can be built in the laboratory, or quantum computers.…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
To facilitate the design and optimization of nanomaterials for a given application it is necessary to understand the relationship between structure and physical properties. For large nanomaterials, there is imprecise structural information…
In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…
The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
As quantum computers of non-trivial size become available in the near future, it is imperative to develop tools to emulate small quantum computers. This allows for validation and debugging of algorithms as well as exploring…