Related papers: On construction of projection operators
We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search…
Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number…
The quantum mechanics of an N=1 supersymmetric dynamical system constrained to a hypersurface embedded in the higher dimensional Euclidean space is investigated by using the projection-operator method (POM) of constrained systems. It is…
A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations,…
In these lectures we develop the projection operator method for quantum groups. Here the term "quantum groups" means q-deformed universal enveloping algebras of contragredient Lie (super)algebras of finite growth. Contains of the lectures…
By means of the technique of integration within an ordered product of operators and Dirac notation, we introduce a new kind of asymmetric integration projection operators in entangled state representations. These asymmetric projection…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if $p$ is a positive contraction in an operator system $V$ which satisfies certain…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…
Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible…
The Frobenius covariant is used to construct a projection operator onto the spin-S eigenspaces associated with the squares of the total and orbital angular momenta. The covariant admits two equivalent representations: as a polynomial in…
We construct a projection operator on an unbounded worm domain which maps subspaces of $W^s$ to themselves. The subspaces are determined by a Fourier decomposition of $W^s$ according to a rotational invariance of the worm domain.
The problem of immersing a simply connected surface with a prescribed shape operator is discussed. From classical and more recent work, it is known that, aside from some special degenerate cases, such as when the shape operator can be…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…