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 $\Delta L$ 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 $ \Delta L \ll \hbar$. However, for finite $\Delta L \neq 0$, 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 $\Delta L = 0$. 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.
Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $\phi^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $\phi^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.
Gaétan Bardy, M. Saubanère, A. Tanasa· 0 citations
The spherical-to-deformed quantum phase transition of the Interacting Boson Model (IBM) is investigated using the variational quantum eigensolver (VQE). The $U(5)$--$SU(3)$ transitional Hamiltonian is studied with $\chi=-\sqrt{7}/2$. We develop a symmetry-preserving, minimum-qubit VQE framework for collective nuclear models, achieving a substantial reduction in qubit requirements without compromising the finite-size quantum-phase-transition physics. The transition is characterized through the normalized $d$-boson occupation and ground-state energy derivatives. Finite-size results are found to approach the analytic critical point $\xi_c=8/17\simeq0.470588$, with an independent order-parameter extrapolation yielding $\xi_\infty=0.46986(61)$. The VQE reproduces ground-state energies and structural observables to numerical precision. These results demonstrate the potential of symmetry-reduced VQE for efficient quantum simulations of collective nuclear dynamics and quantum phase transitions.
The Equation of State (EoS) of Nuclear Matter at high densities, and particularly that of neutron stars, resists $\mathit{ab}$ $\mathit{initio}$ Quantum Chromodynamics (QCD) computations due to the notorious sign problem of Lattice Gauge Theory at finite chemical potential. A quantum computer deploying QCD in canonical quantization should be able to make substantial progress. We set some basic goals for a future quantum computer to predict the EoS, and thus the basic static observables of the star (mass, radius and Tidal deformability, for example). We then develop the basic theory to address the canonical Hamiltonian in Weyl (time-axial) gauge expressed in normal modes, together with the squared Gauss operator $\mathcal{G}^2$ necessary to execute energy minimization algorithms restricted to the physical Fock subspace. Finally, we deploy our particle-quantum register encoding of a generic field theory to demonstrate QCD at finite chemical potential for a few (three-four) particles with a modest number of momentum modes, by simulating the quantum computer on a classical cluster. This opens the possibility for effective quantum computers to constrain the microscopic physics of neutron stars simultaneously to the operation of third--generation gravitational wave detectors such as the Einstein Telescope, providing more detailed predictions than has been possible until now.
Adrián Castaño-García, Nahia J. Dios-Bilbao, J. J. G'alvez-Viruet et al.· 0 citations
The results provide a rigorous complexity-theoretic demonstration that non-Abelian Yang--Mills theories can be simulated efficiently on quantum computers, paving the way toward first-principles quantum simulations of non-perturbative QCD dynamics.
Tianyin Li, Ying-Ying Li, Xiao-Yang Wang et al.· 0 citations
Entanglement entropy (EE) is commonly studied using real-space bipartitions. We show that, in quantum impurity models, an energy-space bipartition, equivalent to the momentum-space bipartition of the bath, can display universal behavior. Motivated by poor man's scaling, we logarithmically discretize the bath and partition it into high- and low-energy sectors. For models with Fermi-liquid fixed points, including the Anderson model and fully screened or underscreened Kondo models, the low-energy EE flows to constants independent of model parameters. These constants are integer multiples of $\ln 2$ plus corrections that depend only on the logarithmic discretization parameter $\Lambda$. We show that scale invariance of the fixed-point wavefunction in energy space maps to effective translation invariance along a one-dimensional chain, allowing the fixed points to be classified by one-dimensional topological band theory. With low-energy chiral symmetry, each $\ln 2$ contribution originates from a topological edge mode. We also study transitions between distinct Fermi-liquid fixed points using the local-singlet--Kondo-singlet transition in a two-orbital Anderson model driven by an inter-orbital antiferromagnetic coupling. The local-singlet phase has an effectively decoupled impurity and nearly vanishing EE, whereas the Kondo-singlet phase has finite EE larger than $\ln 2$ per spin and orbital. When chiral symmetry holds at low energies, this distinction corresponds to a topological transition of the effective bath chain. At the non-Fermi-liquid critical point, the EE develops an unstable plateau. Its $\Lambda$ dependence resembles that of the overscreened two-channel Kondo model, supporting universality within the same non-Fermi-liquid universality class.
Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been extended beyond the measurement of conventional linear observables. This review summarizes recent progress in adapting QMC to many-body quantum-information, focusing on qubit or spin-$1/2$ systems as a concrete setting while keeping the discussion broadly applicable to qudit and bosonic systems. We present a unified perspective on the extraction of nonlinear diagnostics, including entanglement entropies and entanglement spectra, R\'enyi negativities for mixed-state entanglement, stabilizer entropies for quantum magic, and decoherence-driven phenomena such as the interplay between imaginary-time evolution and decoherence and strong-to-weak spontaneous symmetry breaking.
Yi-Ming Ding, Bin-Bin Mao, Zheng Yan· 0 citations
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