Related papers: Path Integration on a Quantum Computer
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…
This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. A $L^2$ Riemannian metric $G_P$ is given on the space of piecewise geodesic paths $H_P(M)$ adapted to…
The use of mid-circuit measurement and qubit reset within quantum programs has been introduced recently and several applications demonstrated that perform conditional branching based on these measurements. In this work, we go a step further…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
Quantum measurement problem is still unconsensus since it has existed many years and inspired a large of literature in physics and philosophy. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by…
Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
Expectations of path integrals of killed stochastic processes play a central role in several applications across physics, chemistry, and finance. Simulation-based evaluation of these functionals is often biased and numerically expensive due…
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…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…