Related papers: Zeta-regularized vacuum expectation values from qu…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
Hawking's zeta function regularization procedure is shown to be rigorously and uniquely defined, thus putting and end to the spreading lore about different difficulties associated with it. Basic misconceptions, misunderstandings and errors…
We analyze renormalization and the high temperature expansion of the one-loop effective action of the space-time noncommutative \phi^4 theory by using the zeta function regularization in the imaginary time formalism (i.e., on S^1 x R^3).…
It is indicated that principal models of computation are indeed significantly related. The quantum field computation model contains the quantum computation model of Feynman. (The term "quantum field computer" was used by Freedman.) Quantum…
Reduction to physical degrees of freedom before quantization leads to predictions for one-loop amplitudes in quantum cosmology in the presence of boundaries which disagree with the results obtained from Faddeev-Popov theory and…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the…
The quantum or quantum field theory concept of a complex wave function is useful for understanding the information transport in classical statistical generalized Ising models. We relate complex conjugation to the discrete transformations…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many…
We study the connection between $\zeta $- and cutoff-regularized Casimir energies for scalar fields. We show that, in general, both regularization schemes lead to divergent contributions, and to finite parts which do not coincide. We…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum…
The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external…
Continuous gauge theories, because of their bosonic degrees of freedom, have an infinite-dimensional local Hilbert space. Encoding these degrees of freedom on qubit-based hardware demands some sort of ``qubitization'' scheme, where one…
We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…
The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta…