Related papers: Perfect simulation for the Feynman-Kac law on the …
We present an algorithm that exploits quantum parallelism to simulate randomness in a quantum system. In our scheme, all possible realizations of the random parameters are encoded quantum mechanically in a superposition state of an…
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
In this article, given $y :[0,\eta)\rightarrow H$ a continuous map into a Hilbert space $H$ we study the equation \[\hat y(t) = e^{\int_0^tc(s,\hat y)}y(t)\] where $c(s,\cdot)$ is a given `potential' on $C([0,\eta),H)$. Applying the…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
We propose new approach to numerical study of quantum spin systems. Our method is based on a fact that one can use any set of states for the path integral as long as it is complete. We apply our method to one-dimensional quantum spin system…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
Adapting ideas of Daubechies and Klauder we derive a continuum path-integral formula for the time evolution generated by a spin Hamiltonian. For this purpose we identify the finite-dimensional spin Hilbert space with the ground-state…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications, phase space forms, master equation and liouville equation…
We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of…
We show how the Hamiltonian lattice loop representation can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. We also…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
The vacuum-adapted formulation of quantum stochastic calculus is employed to perturb expectation semigroups via a Feynman-Kac formula. This gives an alternative perspective on the perturbation theory for quantum stochastic flows that has…
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.…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
We propose a new solvable class of multidimensional quantum harmonic oscillators for a linear diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force. Under natural and easily checked…