Related papers: Histories quantisation of parameterised systems: I…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic…
The Dirac method of canonical quantization of theories with second class constraints has to be modified if the constraints depend on time explicitly. A solution of the problem was given by Gitman and Tyutin. In the present work we propose…
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
One-time programs, computer programs which self-destruct after being run only once, are a powerful building block in cryptography and would allow for new forms of secure software distribution. However, ideal one-time programs have been…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
We consider distributed iterative algorithms for the averaging problem over time-varying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of…
Recently, the makespan-minimization problem of compiling a general class of quantum algorithms into near-term quantum processors has been introduced to the AI community. The research demonstrated that temporal planning is a strong approach…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
Working within the HPO (History Projection Operator) Consistent Histories formalism, we follow the work of Savvidou on (scalar) field theory and that of Savvidou and Anastopolous on (first-class) constrained systems to write a histories…