Related papers: Fermionic quantum operations: a computational fram…
By considering the fermionic realization of $G/H$ coset models, we show that the partition function for the $U(1)/U(1)$ model defines a Topological Quantum Field Theory and coincides with that for a 2-dimensional Abelian BF system. In the…
We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can…
Two complementary approaches of N = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra W(k) (that comprizes the affine quantum algebra…
A variational framework is developed here to quantize fermionic fields based on the extended stationary action principle. From the first principle, we successfully derive the well-known Floreanini-Jackiw representation of the…
We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…
We introduce the fermionic ZW calculus, a string-diagrammatic language for fermionic quantum computing (FQC). After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and…
We show that most of the applications of SU_q(2) fermions to statistical mechanics and quantum field theory, previously discussed in literature, are based on a wrong statement about the connection between deformed and undeformed fermion…
The spinor representation of the quantum group $U_q(su(N))$ is given in terms of a set of fermion creation and annihilation operators. It is shown that the $q$-fermion operators introduced earlier can be identifi ed with the conventional…
Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that…
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. $\textit{Higher-order quantum operations}\unicode{x2014}$quantum operations that transform quantum…
In this article, we find a $q$-analogue for Fomin's formulas. The original Fomin's formulas relate determinants of random walk excursion kernels to loop-erased random walk partition functions, and our formulas analogously relate conformal…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
In this paper, we first construct generalized $q^2$-cosine, $q^2$-sine and $q^2$-exponential functions. We then use $q^2$-exponential function in order to define and investigate a $q^2$-Fourier transform. We establish $q$-analogues of…
The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons, using a label $q$ that parametrizes a smooth interpolation between bosons ($q = 1$) and fermions ($q = -1$). Understanding the relation of quons on the…
We discuss the scaling behaviour of different fermion actions in dynamical simulations of the 2-dimensional massive Schwinger model. We have chosen Wilson, hypercube, twisted mass and overlap fermion actions. As physical observables, the…
Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…
Fermionic Gaussian operators are foundational tools in quantum many-body theory, numerical simulation of fermionic dynamics, and fermionic linear optics. While their structure is fully determined by two-point correlations, evaluating their…