Related papers: Efficient Quantum Simulation Algorithms in the Pat…
Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path…
Quantum chemistry and materials science are among the most promising areas for demonstrating algorithmic quantum advantage and quantum utility due to their inherent quantum mechanical nature. Still, large-scale simulations of quantum…
We {\em derive} the exact configuration space path integral, together with the way how to evaluate it, from the Hamiltonian approach for any quantum mechanical system in flat spacetime whose Hamiltonian has at most two momentum operators.…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
We present a way for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger--Dyson equations. The method agrees with the usual way of deriving the measure, however it may be applied to all theories, even…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
Common time-explicit numerical methods for kinetic simulations of plasmas in the low-collisions limit fall into two classes of algorithms: momentum conserving and energy conserving. Each has certain drawbacks. The PIC algorithm does not…
A method for nonperturbative path integral calculation is proposed. Quantum mechanics as a simplest example of a quantum field theory is considered. All modes are decomposed into hard (with frequencies $\omega^2 >\omega^2_0$) and soft (with…
We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
A path integral method, combined with atomistic spin dynamics simulations, has been developed to calculate thermal quantum expectation values using a classical approach. In this study, we show how to treat Hamiltonians with non-linear…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…
Major players in the global aerospace industry are shifting their focus toward achieving net carbon-neutral operations by 2050. A considerable portion of the overall carbon emission reduction is expected to come from new aircraft…