We present a recipe for simulating one-dimensional quantum systems for low and high energies with $L$ qubits within the framework of first quantisation. Assuming a minimum grid spacing $ΔL$ in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ ΔL \ll \hbar$. However, for finite $ΔL \neq 0$ , the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit $ΔL = 0$ . Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.We present a recipe for simulating one-dimensional quantum systems for low and high energies with $L$ qubits within the framework of first quantisation. Assuming a minimum grid spacing $ΔL$ in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ ΔL \ll \hbar$. However, for finite $ΔL \neq 0$, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit $ΔL = 0$. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.

quant-pharXiv:2607.19602Jul 23, 2026

Quantum Simulations of Classical Systems

Rolando D. Somma, Gerardo Ortíz, Cristian D. Batista +1 more

Bulletin of the American Physical SocietyMar 8, 20070 citations

Theoretical aspects of analogue quantum simulation

Andrew J. Daley

In these lectures, we discuss theoretical aspects of analogue quantum simulation, focussing on ultracold atoms in optical lattices as a specific example. We touch on the motivation for quantum simulation, before going into detail on the first-principles microscopic understanding of the system that allows us to use ultra-cold atoms as quantum simulators. This level of understanding and control crucially also exists for the dominant dissipative processes in experiments. We conclude by discussing the verification of quantum simulators, comparison with classical simulations, and the current role of many-body entanglement in this discussion.In these lectures, we discuss theoretical aspects of analogue quantum simulation, focussing on ultracold atoms in optical lattices as a specific example. We touch on the motivation for quantum simulation, before going into detail on the first-principles microscopic understanding of the system that allows us to use ultra-cold atoms as quantum simulators. This level of understanding and control crucially also exists for the dominant dissipative processes in experiments. We conclude by discussing the verification of quantum simulators, comparison with classical simulations, and the current role of many-body entanglement in this discussion.

IOS Press eBooksMay 15, 20180 citations

The Simulation of Quantum Systems

David M. Ceperley

Recent Progress in Many-Body TheoriesJan 1, 19953 citations

Toward Nuclear Physics from Lattice QCD on Quantum Computers

Arata Yamamoto, Takumi Doi

Abstract One of the ultimate missions of lattice quantum chromodynamics (QCD) is to simulate atomic nuclei from the first principles of the strong interaction. This is an extremely hard task for current computational technology, but might be reachable in the coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of nucleon number and thus will outperform classical simulation for large nuclei.Abstract One of the ultimate missions of lattice quantum chromodynamics (QCD) is to simulate atomic nuclei from the first principles of the strong interaction. This is an extremely hard task for current computational technology, but might be reachable in the coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of nucleon number and thus will outperform classical simulation for large nuclei.

arXiv:2211.14550Progress of Theoretical and Experimental PhysicsFeb 5, 20246 citations

We present a recipe for simulating one-dimensional quantum systems for low and high energies with

L

qubits within the framework of first quantisation. Assuming a minimum grid spacing

ΔL

in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ ΔL \ll \hbar$. However, for finite

ΔL \neq 0

, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit

ΔL = 0

. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.