Related papers: Complexity measures in QFT and constrained geometr…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
In a recent contribution we identified possible points of contact between the asymptotically safe and canonical approach to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of…
We propose and investigate bounds on quantum process fidelity of quantum filters, i.e. probabilistic quantum operations represented by a single Kraus operator K. These bounds generalize the Hofmann bounds on quantum process fidelity of…
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show under which conditions measurements, state preparations, and unitary implementations on the system can be performed by quantum…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
This is the second paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we begin with the simplest examples: Finite dimensional models with…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is an extensive debate over the question how the sensitivity scales with the resources (such as the average photon number) and…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
The quantum Fourier transform (QFT) is a crucial subroutine in many quantum algorithms. In this paper, we study the exact lower bound problem of CNOT gate complexity for fault-tolerant QFT. First, we consider approximating the ancilla-free…
In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our…
A recurring challenge in quantum science and technology is the precise control of their underlying dynamics that lead to the desired quantum operations, often described by a set of quantum gates. These gates can be subject to…