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Abstract The variational quantum eigensolver (VQE) is a hybrid quantum–classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE—as well as any other heuristic algorithm for finding ground states of Hamiltonians—is to know how close the algorithm’s output solution is to the true ground state, when we do not know what the true ground state or ground-state energy is. This is especially important in iterative algorithms such as VQE, where we need to decide when to stop iterating. Stopping when the current solution energy no longer changes rapidly from one iteration to the next is a common choice but in many situations can lead to stopping too early and outputting an incorrect result. Recent developments in Hamiltonian reconstruction—the inference of a Hamiltonian given an eigenstate—give a tool that can be used to assess the quality of a variational solution to a Hamiltonian-eigensolving problem: a metric quantifying the distance between the problem Hamiltonian and the reconstructed Hamiltonian can give an indication of whether the variational solution is an eigenstate, which can (as a special case) indicate if the variational solution is not the ground state. Crucially, computing the Hamiltonian-reconstruction (HR) distance does not rely on knowing the true ground state or ground-state energy. We propose and study using the HR distance as a metric for assessing the success of VQE eigensolving. In numerical simulations and in demonstrations on a cloud-based trapped-ion quantum computer, we show that for examples of both one-dimensional transverse-field-Ising (11 qubits) and two-dimensionalJ₁–J₂transverse-field-Ising (6 qubits) spin problems, the HR distance gives a helpful indication of whether VQE has yet found the ground state or not. Our demonstrations included cases where the energy plateaus as a function of the VQE iteration, which could have resulted in erroneous early stopping of the VQE algorithm, but where the HR distance correctly suggests to continue iterating. We find that HR distance has a useful correlation with the fidelity (i.e. state overlap) between the VQE solution and the true ground state, and with the energy difference between VQE solution’s energy and the true ground-state energy. Our work suggests that HR distance may be a useful tool for assessing success in VQE, including on noisy quantum processors in practice. 

Recent experiments on twisted van der Waals materials, inspired our study of a simplified triangular trimer model, which captures electron behavior at one-third filling in twisted bilayer graphene. Though simple, the model shows rich physics, including fractional excitations and fracton-like particles with restricted motion. Using Monte Carlo simulations and effective field theory, we uncover two notable phases: 1. A polar fluid phase with directional order. 2. A critical trimer liquid phase, where excitations carry fractional charge and display power-law correlations. These fractionalized excitations are bionic—they carry pairs of emergent gauge charges, revealed by algebraic correlations with two distinct exponents. Our field theory supports the numerical findings and critical exponents. The triangular trimer model emerges as a key platform to study fractionalization and fractons, where bionic monomers can evolve into fractons in nearby phases. This motivates experimental work in twisted van der Waals systems and materials with intermediate-range interactions. 

Frustrated magnetic systems arising in geometrically constrained lattices represent rich platforms for exploring unconventional phases of matter, including fractional magnetization plateaus, incommensurate orders and complex domain dynamics. However, determining the microscopic spin configurations that stabilize such phases is a key challenge, especially when in-plane and out-of-plane spin components coexist and compete. Here, we combine neutron scattering and magnetic susceptibility experiments with simulations to investigate the emergence of field-induced fractional plateaus and the related criticality in a frustrated magnet holmium tetraboride (HoB4) that represents the family of rare earth tetraborides that crystalize in a Shastry–Sutherland lattice in the ab plane. We focus on the interplay between classical and quantum criticality near phase boundaries, as well as the role of material defects in the stabilization of the ordered phases. We find that simulations using classical annealing can explain certain observed features in the experimental Laue diffraction and the origin of multiple magnetization plateaus. Our results show that defects and out-of-plane interactions play an important role and can guide the route towards resolving microscopic spin textures in highly frustrated magnets. 

Abstract With rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining sampled projective snapshots with interpretable classical machine learning can unveil signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice under external magnetic field presents an ideal system to test QuCl, where simulations have found an intermediate gapless phase (IGP) sandwiched between known phases, launching a debate over its elusive nature. We use the correlator convolutional neural network, trained on labeled projective snapshots, in conjunction with regularization path analysis to identify signatures of phases. We show that QuCl reproduces known features of established phases. Significantly, we also identify a signature of the IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for spin liquids. 

Differentiable 3D-Gaussian splatting (GS) is emerging as a prominent technique in computer vision and graphics for reconstructing 3D scenes. GS represents a scene as a set of 3D Gaussians with varying opacities and employs a computationally efficient splatting operation along with analytical derivatives to compute the 3D Gaussian parameters given scene images captured from various viewpoints. Unfortunately, capturing surround view (360° viewpoint) images is impossible or impractical in many real-world imaging scenarios, including underwater imaging, rooms inside a building, and autonomous navigation. In these restricted baseline imaging scenarios, the GS algorithm suffers from a well-known ‘missing cone’ problem, which results in poor reconstruction along the depth axis. In this paper, we demonstrate that using transient data (from sonars) allows us to address the missing cone problem by sampling high-frequency data along the depth axis. We extend the Gaussian splatting algorithms for two commonly used sonars and propose fusion algorithms that simultaneously utilize RGB camera data and sonar data. Through simulations, emulations, and hardware experiments across various imaging scenarios, we show that the proposed fusion algorithms lead to significantly better novel view synthesis (5 dB improvement in PSNR) and 3D geometry reconstruction (60% lower Chamfer distance). 

Ciliates are powerful unicellular model organisms that have been used to elucidate fundamental biological processes. However, the high motility of ciliates presents a major challenge in studies using live-cell microscopy and microsurgery. While various immobilization methods have been developed, they are physiologically disruptive to the cell and incompatible with microscopy and/or microsurgery. Here, we describe a Simple Microfluidic Operating Room for the Examination and Surgery of Stentor coeruleus (SMORES). SMORES uses Quake valve-based microfluidics to trap, compress, and perform surgery on Stentor as our model ciliate. Compared with previous methods, immobilization by physical compression in SMORES is more effective and uniform. The mean velocity of compressed cells is 24 times less than that of uncompressed cells. The compression is minimally disruptive to the cell and is easily applied or removed using a 3D-printed pressure rig. We demonstrate cell immobilization for up to 2 h without sacrificing cell viability. SMORES is compatible with confocal microscopy and is capable of media exchange for pharmacokinetic studies. Finally, the modular design of SMORES allows laser ablation or mechanical dissection of a cell into many cell fragments at once. These capabilities are expected to enable biological studies previously impossible in ciliates and other motile species. 

Underwater perception and 3D surface reconstruction are challenging problems with broad applications in construction, security, marine archaeology, and environmental monitoring. Treacherous operating conditions, fragile surroundings, and limited navigation control often dictate that submersibles restrict their range of motion and, thus, the baseline over which they can capture measurements. In the context of 3D scene reconstruction, it is well-known that smaller baselines make reconstruction more challenging. Our work develops a physics-based multimodal acoustic-optical neural surface reconstruction framework (AONeuS) capable of effectively integrating high-resolution RGB measurements with low-resolution depth-resolved imaging sonar measurements. By fusing these complementary modalities, our framework can reconstruct accurate high-resolution 3D surfaces from measurements captured over heavily-restricted baselines. Through extensive simulations and in-lab experiments, we demonstrate that AONeuS dramatically outperforms recent RGB-only and sonar-only inverse-differentiable-rendering--based surface reconstruction methods.