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Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory

Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the first principle description of many-electron dynamics in chemical and materials systems. Practical rt-TDDFT calculations often avoid the direct simulation of the von Neumann equation, and solve instead a set of Schrödinger equations, of which the dynamics is equivalent to that of the von Neumann equation. However, the time step size employed by the Schrödinger dynamics is often much smaller. Here, in order to improve the time step size and the overall efficiency of the simulation, we generalize a recent work of the parallel transport (PT) dynamics for simulating pure states [An, Lin, Multiscale Model. Simul. 18, 612, 2020] to general quantum states. The PT dynamics provides the optimal gauge choice, and can employ a time step size comparable to that of the von Neumann dynamics. Going beyond the linear and near adiabatic regime in previous studies, we find that the error of the PT dynamics can be bounded by certain commutators between Hamiltonians, density matrices, and their derived quantities. Such a commutator structure is not present in the Schrödinger dynamics. We demonstrate that the parallel transport-implicit midpoint (PT-IM) method is a suitable method for simulating the PT dynamics, especially when the spectral radius of the Hamiltonian is large. The commutator structure of the error bound, and numerical results for model rt-TDDFT calculations in both linear and nonlinear regimes, confirm the advantage of the PT dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ferromagnetic MnBi 4 Te 7 obtained with low-concentration Sb doping: A promising platform for exploring topological quantum states

The tuning of the magnetic phase, chemical potential, and structure is crucial to observe diverse exotic topological quantum states in Mn Bi 2 Te 4 (Bi 2 Te 3 ) m (m = 0–3). Here we show a ferromagnetic (FM) phase with a chiral crystal structure in Mn (Bi 1–x Sb x ) 4 Te 7 , obtained via tuning the growth conditions and Sb concentration. Unlike previously reported Mn (Bi 1–x Sb x ) 4 Te 7 , which exhibits FM transitions only at high Sb doping levels, our samples show FM transitions (T C = 13.5 K) at 15%–27% doping levels. Furthermore, our single-crystal x-ray-diffraction structure refinements find Sb doping leads to a chiral structure with the space group of P3, contrasted with the centrosymmetric $P\bar{3}m1$ crystal structure of the parent compound MnBi 4 Te 7 . Through angle-resolved photoemission spectroscopy measurements, we also demonstrated that the nontrivial band topology is preserved in the Sb-doped FM samples. Given that the nontrivial band topology of this system remains robust for low Sb doping levels, our success in making FM Mn(Bi 1–x Sb x ) 4 Te 7 with x = 0.15, 0.175, 0.2, and 0.27 paves the way for realizing the predicted topological quantum states, such as the axion insulator and Weyl semimetals. Additionally, we also observed magnetic glassy behavior in both antiferromagnetic MnBi 4 Te 7 and FM Mn (Bi 1–x Sb x )4 Te 7 samples, which we believe originates from cluster spin-glass phases coexisting with long-range antiferromagnetic/FM orders. Further, we have also discussed how the antisite Mn ions impact the interlayer magnetic coupling and how FM interlayer coupling is stabilized in this system.

36 MATERIALS SCIENCE↗

Demonstration of machine-learning-enhanced Bayesian quantum state estimation

Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for defining custom prior distributions that are automatically tuned using ML for Bayesian quantum state estimation methods that generally better conform to the physical properties of the underlying system than standard fixed prior distributions. Previously, researchers have looked to Bayesian quantum state tomography for advantages like uncertainty quantification, the return of reliable estimates under any measurement condition, and minimal mean-squared error. However, practical challenges related to long computation times and conceptual issues concerning how to incorporate prior knowledge most suitably can overshadow these benefits. Using both simulated and experimental measurement results, we demonstrate that ML-defined prior distributions reduce net convergence times and provide a natural way to incorporate both implicit and explicit information directly into the prior distribution. These results constitute a promising path toward practical implementations of Bayesian quantum state tomography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Geometric quantum states beyond the AdS/CFT correspondence

We characterize the quantum states dual to entanglement wedges in arbitrary spacetimes, in settings where the matter entropy can be neglected compared to the geometric entropy. In AdS/CFT, such states obey special entropy inequalities known as the holographic entropy cone. In particular, the mutual information of CFT subregions is monogamous (MMI). We extend this result to arbitrary spacetimes, using a recent proposal for the generalized entanglement wedge e ( a ) of a gravitating region a . Given independent input regions a , b , and c , we prove MMI: Area [ e ( a ) ] + Area [ e ( b ) ] + Area [ e ( c ) ] − Area [ e ( a b ) ] − Area [ e ( b c ) ] − Area [ e ( c a ) ] + Area [ e ( a b c ) ] ≤ 0 . We expect that the full holographic entropy cone can be extended to arbitrary spacetimes using similar methods. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo–based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ion trap long-range XY model for quantum state transfer and optimal spatial search

Abstract Linear ion trap chains are a promising platform for quantum computation and simulation. The XY model with long-range interactions can be implemented with a single side-band Mølmer–Sørensen scheme, giving interactions that decay as 1 / r α , where α parameterises the interaction range. Lower α leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing α causes an increased generation of coherent phonons and appears to dephase the effective XY interaction model. We characterise and show how to correct for this effect completely, allowing lower α interactions to be coherently implemented. Ion trap chains are thus shown to be a viable platform for spatial quantum search in optimal O ( N ) time, for N ions. Finally, we introduce a O ( N ) quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Distilling the Essential Elements of Nuclear Binding via Neural-Network Quantum States

To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. Furthermore, we address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to 𝐴 = 20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

Binding energy & masses↗

Continuous-Variable Quantum State Designs: Theory and Applications

We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state t -designs from [Blume-Kohout , ], no state designs exist for t ≥ 2 . Similarly, we prove that no CV unitary t -designs exist for t ≥ 2 . We propose an alternative definition for CV state designs, which we call rigged t -designs, and provide explicit constructions for t = 2 . As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus 2-designs and complete sets of mutually unbiased bases. Published by the American Physical Society 2024

Physics↗

Quantum states of a skyrmion in a two-dimensional antiferromagnet

Quantum states of a skyrmion in a two-dimensional antiferromagnetic lattice are obtained by quantizing the scaling parameter of Belavin-Polyakov model. Skyrmion classical collapse due to violation of the translational invariance of the continuous spin-field model by the lattice is replaced in quantum mechanics by transitions between discrete energy levels of the skyrmion. Here, the rates of transitions due to emission of magnons are computed. Ways of detecting quantization of skyrmion states are discussed.

36 MATERIALS SCIENCE↗

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can leverage quantum computers. Moreover, as the available qubits increase, the computational complexity grows exponentially, posing additional challenges. Consequently, there is an urgent need to use qubits efficiently and mitigate both present limitations and future complexities. To address this, existing quantum applications attempt to integrate classical and quantum systems in a hybrid framework. In this study, we concentrate on quantum deep learning and introduce a collaborative classical-quantum architecture called co-TenQu. The classical component employs a tensor network for compression and feature extraction, enabling higher-dimensional data to be encoded onto logical quantum circuits with limited qubits. On the quantum side, we propose a quantum-state-fidelity-based evaluation function to iteratively train the network through a feedback loop between the two sides. co-TenQu has been implemented and evaluated with both simulators and the IBM-Q platform. Compared to state-of-the-art approaches, co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. Additionally, it outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.

42 ENGINEERING↗

Quantum state preparation and nonunitary evolution with diagonal operators

Realizing nonunitary transformations on unitary-gate-based quantum devices is critically important for simulating a variety of physical problems, including open quantum systems and subnormalized quantum states. Here, we present a dilation-based algorithm to simulate nonunitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal nonunitary operator, which we show can be implemented by a diagonal unitary operator in a one-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random subnormalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate nonunitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude-damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general nonunitary operations when the SVD can be readily computed, which is the case for most operators in the noisy intermediate-scale quantum computing era.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Neural-network quantum states for the nuclear many-body problem

A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.

Lovato, Alessandro [Argonne; TIFPA-INFN, Trento; V↗

Nuclear Responses with Neural-Network Quantum States

We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. Here, we demonstrate that a relatively simple nuclear Hamiltonian—based on a leading-order pionless EFT expansion and known to accurately reproduce ground-state energies of nuclei with 𝐴 ≤ 40—also provides a reliable description of the photoabsorption cross section.

Ab initio calculations↗

Nuclear responses with neural-network quantum states

We introduce a variational Monte Carlo framework that combines neural-network quantum states with the Lorentz integral transform technique to compute the dynamical properties of self-bound quantum many-body systems in continuous Hilbert spaces. While broadly applicable to various quantum systems, including atoms and molecules, in this initial application we focus on the photoabsorption cross section of light nuclei, where benchmarks against numerically exact techniques are available. Our accurate theoretical predictions are complemented by robust uncertainty quantification, enabling meaningful comparisons with experiments. We demonstrate that a simple nuclear Hamiltonian, based on a leading-order pionless effective field theory expansion and known to accurately reproduce the ground-state energies of nuclei with $A\leq 20$ nucleons also provides a reliable description of the photoabsorption cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Variational quantum and neural quantum states algorithms for the linear complementarity problem

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.

neural quantum states↗

Bayesian quantum state reconstruction with a learning-based tuned prior

We demonstrate machine-learning-enhanced Bayesian quantum state tomography on near-term intermediate-scale quantum hardware. Our approach to selecting prior distributions leverages pre-trained neural networks incorporating measurement data and enables improved inference times over standard prior distributions.

Regmi, Sangita↗

Optical-Gating of Spin-based Quantum States (Final Report)

This project developed a generalizable strategy for optical control of spin-based quantum states through the Photoisomerization-Induced Spin–Charge Excited State (PISCES) process, in which a photochromic spirooxazine ligand bound to an electronically bistable metal complex enables reversible, room-temperature optical switching of spin states in both dilute matrices and the solid state. A multidisciplinary team integrated synthesis, spectroscopy, theory, and surface science to establish design principles for opto-spintronic quantum materials. Systematic structure–property studies across four spirooxazine series revealed that donor–π–acceptor interactions govern thermal isomerization, which proceeds via a rotational pathway. Pulsed EPR measurements demonstrated millisecond-scale coherence times in cobalt-dioxolene-spirooxazine complexes, establishing their promise as optically addressable molecular qubits; the approach was extended to Cu(II), Ni(II), and lanthanide complexes, including optical modulation of zero-field splittings and clock transitions. Two-dimensional IR spectroscopy resolved picosecond ground-state population exchange dynamics, while ab initio calculations elucidated photoisomerization mechanisms and parametrized Hamiltonians for spin relaxation and decoherence. Toward device integration, the team fabricated 2D polymer scaffolds for covalent qubit organization, developed tip-enhanced Raman imaging of molecular monolayers, and demonstrated optical gating of gate voltage in spirooxazine-graphene field-effect transistors. The project produced numerous publications, dissertations, and presentations, and trained over 30 researchers.

2D polymers↗

Spatio-spectral quantum state estimation of photon pairs from optical fiber using stimulated emission

Developing a quantum light source that carries more than one bit per photon is pivotal for expanding quantum information applications. Characterizing a high-dimensional multiple-degree-of-freedom source at the single-photon level is challenging due to the large parameter space as well as limited emission rates and detection efficiencies. Here, we characterize photon pairs generated in optical fiber in the transverse-mode and frequency degrees of freedom by applying stimulated emission in both degrees of freedom while detecting in one of them at a time. This method may be useful in the quantum state estimation and optimization of various photon-pair source platforms in which complicated correlations across multiple degrees of freedom may be present.

Kim, Dong Beom (ORCID:0000000346887375)↗