Related papers: Feynman's clock, a new variational principle, and …
Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks---generalised time evolution with…
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
We present a diagrammatic approach to quantum dynamics based on the categorical algebraic structure of strongly complementary observables. We provide physical semantics to our approach in terms of quantum clocks and quantisation of time. We…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
Feynman's circuit-to-Hamiltonian construction enables the mapping of a quantum circuit to a time-independent Hamiltonian. This model introduces a Hilbert space made from an ancillary clock register tracking the progress of the computation.…
The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is…
We summarize our investigation of the extent to which the choice of internal clock influences the dynamics in quantum models of gravity. Firstly, at the classical level, we define an extension to the Hamilton-Jacobi theory of contact…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we…
We consider a periodic quantum clock based on cooperative resonance fluorescence at zero temperature. In the quantum case, this system has an exact steady state and the limit cycle appears in conditional quantum dynamics under homodyne…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…
We consider possible extensions to quantum mechanics proposed by Steven Weinberg, and re-analyze his prediction of a new test based upon three atomic clocks in the same atom. We propose realistic experimental systems where this hypothesis…
We study the quantum fermions+gravity system, that is, the gravitational counterpart of QED. We start from the standard Einstein-Weyl theory, reformulated in terms of Ashtekar variables; and we construct its non- perturbative quantum theory…
Motivated by recent progress of quantum technologies, we study a discretized quantum adiabatic process for a one-dimensional free fermion system described by a variational wave function, i.e., a parametrized quantum circuit. The wave…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…