相关论文: Sigma models on quantum computers
We define a model of quantum computation with local fermionic modes (LFMs) -- sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of $m$ LFMs and the Hilbert space of $m$ qubits,…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms…
Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common…
Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that uses the minimum amount of qubits are desirable. We present a practical scheme for digitizing $SU(3)$ gauge…
We consider the discretized version of the sigma-model with supersphere target space $OSp(N+2m|2m)/OSp(N+2m-1|2m)$ and present a preliminary numerical study of bosonic and fermionic two-point functions for the cases $OSp(3|2)$ and…
We argue that the model of a quantum computer with N qubits on a quantum space background, which is a fuzzy sphere with n=2^N elementary cells, can be viewed as the minimal model for Quantum Gravity. In fact, it is discrete, has no free…
Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources to realize this potential, we employ state-of-the-art…
In computational physics it is standard to approximate continuum systems with discretised representations. Here we consider a specific discretisation of the continuum complex Hilbert space of quantum mechanics - a discretisation where…
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…
We propose a numerical scheme to solve the time dependent linear Schr\"odinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a finite element discretization in space. Since the…
We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates…
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type…
A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The…
The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin…