Related papers: Quantum circuit dynamics via path integrals: Is th…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
A discrete path integral formalism is used to obtain the transition amplitude between 'sources' (slits and detector) in the twin-slit experiment of quantum mechanics. This method explicates the normally tacit construct of dynamic entities…
By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which…
Interacting many-body systems with explicitly accessible spatio-temporal correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems and termed them…
Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it…
Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a…
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…
To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
We give a path integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hbar$. The largest power…
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
By the Gottesman-Knill Theorem, the outcome probabilities of Clifford circuits can be computed efficiently. We present an alternative proof of this result for quopit Clifford circuits (i.e., Clifford circuits on collections of $p$-level…