Related papers: Quantum Statistical Calculations and Symplectic Co…
The Heisenberg evolution of a given unitary operator corresponds classically to a fixed canonical transformation that is viewed through a moving coordinate system. The operators that form the bases of the Weyl representation and its Fourier…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
We continue to derive spacetime quantities and spin 1/2 propagators from rotations. Rotation-invariant projection operators are found for each element of a four element basis, i.e. a basis for four component quantities with specific…
We propose and develop a general method of numerical calculation of the wave function time evolution in a quantum system which is described by Hamiltonian of an arbitrary dimensionality and with arbitrary interactions. For this, we obtain a…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
The formulae for correlators K2 and K3 of a given particle observable (e.g. energy or transverse momentum) accounting for the track reconstruction efficiency are presented. Similar to the case of an ideal detector, the correlators can be…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from…
The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data. Accurate solutions can be systematically derived by decomposing the exponential in a product form. For…
The multiple-quantum operator algebra formalism has been exploited to construct generally an unsorted quantum search algorithm. The exponential propagator and its corresponding effective Hamiltonian are constructed explicitly that describe…
Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution.…
We present a simple method to expedite simulation of quantum wave-packet dynamics by more than a factor of $2$ with the Strang split-operator propagation. Dynamics of quantum wave-packets are often evaluated using the the \emph{Strang}…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most…
We reformulate the Lanczos algorithm for quantum wave function propagation in terms of variational principle. By including some basis states of previous time steps into the variational subspace, the resultant accuracy increases by several…
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…
A quantum algorithm for simulating multidimensional scalar transport problems using a time-marching strategy is presented. A direct unitary block encoding of the explicit time-marching operator is constructed, resulting in the intrinsic…