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Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
This report is concerned with the efficiency of numerical methods for simulating quantum spin systems, with the aim to implement an improved method for simulation of a time-dependent Hamiltonian that displays chirped pulses at a high…
This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We develop a finite-temperature perturbation theory for quasi-one-dimensional quantum spin systems, in the manner suggested by H.J. Schulz (1996) and use this formalism to study their dynamical response. The corrections to the random-phase…
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of…
The semiclassical Euclidean path integral method is applied to compute the low temperature quantum decay rate for a particle placed in the metastable minimum of a cubic potential in a {\it finite} time theory. The classical path, which…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and have been used in path integral Monte Carlo (PIMC) to accurately simulate warm dense matter with up to 1000 electrons (T.…
Simulating vibrational dynamics is essential for understanding molecular structure, unlocking useful applications such as vibrational spectroscopy for high-fidelity chemical detection. Quantum algorithms for vibrational dynamics are…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the…
Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum…
We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain, with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular…
Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum…
In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most…
We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…
We report recent progress in computer simulations of quantum systems described in the path-integral formulation. For the example of the $\phi^4$ quantum chain we show that the accuracy of the simulation may greatly be enhanced by a…