We theoretically investigate the single-particle excitation spectra of a one-dimensional Hubbard model at half filling using an infinite matrix-product state and elucidate the discretized energy spectra emerging under the influence of a dc electric field. In a weak electric-field regime, we observe two kinds of spectral structures in the density of states. With increasing the electric-field strength, the discretized spectra, the period of which is proportional to the strength, become dominant, and the density of states exhibits the Wannier-Stark ladder in their spectra. In addition, we also simulate time- and angle-resolved photoemission spectroscopy using an ultrashort terahertz pump pulse that approximates a dc electric field. Our results represent a significant step forward in understanding the states in strongly correlated electron systems driven by a static electric field.

Constrained combinatorial optimization problems (CCOPs) are challenging to solve due to the exponential growth of the solution space. When tackled with Ising machines, constraints are typically enforced by the penalty function method, whose coefficients must be carefully tuned to balance feasibility and objective quality. Variable-reduction techniques such as sample persistence variable reduction (SPVAR) can mitigate hardware limitations of Ising machines, yet their behavior on CCOPs remains insufficiently understood. Building on our prior proposal, we extend and comprehensively evaluate multi-penalty SPVAR (MP-SPVAR), which fixes variables using solution persistence aggregated across multiple penalty coefficients. Experiments on benchmark problems, including the quadratic assignment problem and the quadratic knapsack problem, demonstrate that MP-SPVAR attains higher feasible-solution ratios while matching or improving approximation ratios relative to the conventional SPVAR algorithm. An examination of low-energy states under small penalties clarifies when feasibility degrades and how encoding choices affect the trade-off between solution quality and feasibility. These results position MP-SPVAR as a practical variable-reduction strategy for CCOPs and lay a foundation for systematic penalty tuning, broader problem classes, and integration with quantum-inspired optimization hardware as well as quantum algorithms.

Density matrix exponentiation (DME) is a general procedure that converts an unknown quantum state into the Hamiltonian evolution. This enables state-dependent operations and can reveal nontrivial properties of the state, among other applications, without full tomography. However, it has been proven that for any physical process, the DME requires $\Theta(1/\varepsilon)$ state copies in error $\varepsilon$. In this work, we go beyond the lower bound and propose a procedure called the virtual DME that achieves $\mathcal{O}(\log(1/\varepsilon))$ or $\mathcal{O}(1)$ state copies, by using non-physical processes. Using the virtual DME in place of its conventional counterpart realizes a general-purpose quantum algorithm for property estimation, that achieves exponential circuit-depth reductions over existing protocols across tasks including quantum principal component analysis, quantum emulator, calculation of nonlinear functions such as entropy, and linear system solver with quantum precomputation. In such quantum algorithms, the non-physical process for virtual DME can be effectively simulated via simple classical post-processing while retaining a near-unity measurement overhead. We numerically verify this small constant overhead together with the exponential reduction of copy count in the quantum principal component analysis task. The number of state copies used in our algorithm essentially saturates the theoretical lower bound we proved.

Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement, mitigating the bond-dimension bottleneck in TN simulations. In this work, we develop a variational TN framework based on Grassmann tensor networks, which natively encode fermionic statistics while preserving locality. By incorporating locally defined Clifford circuits within the fermionic formalism, we simulate benchmark models including the tight-binding and $t$-$V$ models. Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates. Interestingly, imposing the natural Grassmann-evenness constraint on the Clifford circuits significantly reduces the number of disentangling gates, from 720 to just 32, yielding a far more efficient implementation. These findings highlight the potential of Clifford-augmented Grassmann TNs as a scalable and accurate tool for studying strongly correlated fermionic systems, particularly in higher dimensions.

Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically suffers from small subgroup-wise sample sizes, which makes the estimation results highly instable. To solve this issue, we introduce hierarchical RDD (HRDD), a hierarchical Bayes approach for pursuing treatment effect heterogeneity in RDD. A key feature of HRDD is to employ a pseudo-model based on a loss function to estimate subgroup-level parameters of treatment effects under RDD, and assign a hierarchical prior distribution to ''borrow strength'' from other subgroups. The posterior computation can be easily done by a simple Gibbs sampling, and the optimal bandwidth can be automatically selected by the Hyv\"{a}rinen scores for unnormalized models. We demonstrate the proposed HRDD through simulation and real data analysis, and show that HRDD provides much more stable point and interval estimation than separately applying the standard RDD method to each subgroup.

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This viewpoint uncovers three key insights. First, we show that the ITE dynamics trace the shortest path between the initial and the solution states in complex projective space. Second, we prove that the geodesic length of ITE determines the query complexity of Grover's algorithm. This complexity notably aligns with the known optimal scaling for unstructured search. Lastly, utilizing the geodesic structure of ITE, we construct a quantum signal processing formulation for ITE without post-selection, and derive a new set of angles for the fixed-point search. These results collectively establish a deeper understanding of Grover's algorithm and suggest a potential role for thermodynamics and geometry in quantum algorithm design.

Domain wall (DW) networks may have formed in the early universe following the spontaneous breaking of a discrete symmetry. Notably, several particle physics models predict the existence of current-carrying DWs, which can capture and store particles as zero modes on it. In this study, we demonstrate that gravitational waves (GWs) generated by current-carrying DWs with fermionic zeromodes exhibit a novel feature: an additional peak in the GW spectrum resembling mountains, arising from metastable topological remnants, which we term ``spherons.'' This distinct signature could be detectable in upcoming GW observatories such as LISA and ET. The results suggest that DW networks in beyond Standard Model scenarios could emit GW signals that are significantly stronger and with greater detectability than previously expected.

Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a potential and promising approach to achieve this purpose. Actually, there are several oracle-based Hamiltonian simulations with potential quantum speedup, but their detailed implementations and accordingly the detailed computational complexities are all unclear. This paper presents a method that enables us to explicitly implement the quantum circuit for Hamiltonian simulation; the key technique is the explicit gate construction of differential operators contained in the target partial differential equation discretized by the finite difference method. Moreover, we show that the space and time complexities of the constructed circuit are exponentially smaller than those of conventional classical algorithms. We also provide numerical experiments and an experiment on a real device for the wave equation to demonstrate the validity of our proposed method.

Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to ground-state preparation that aim to replicate cooling processes via imaginary-time evolution. However, synthesizing quantum circuits that efficiently implement imaginary-time evolution is itself difficult, with prior proposals generally adopting heuristic variational approaches or using deep block encodings. Here, we use the insight that quantum imaginary-time evolution is a solution of Brockett's double-bracket flow and synthesize circuits that implement double-bracket flows coherently on the quantum computer. We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution. Concretely, each step is guaranteed to i) decrease the energy of an initial approximate ground-state by an amount proportion to the energy fluctuations of the initial state and ii) increase the fidelity with the ground-state. We provide gate counts for DB-QITE through numerical simulations in Qrisp which demonstrate scenarios where DB-QITE outperforms quantum phase estimation. Thus DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.

Gliomas are the most common primary brain malignancies, with different degrees of aggressiveness, variable prognosis and various heterogeneous histologic sub-regions, i.e., peritumoral edematous/invaded tissue, necrotic core, active and non-enhancing core. This intrinsic heterogeneity is also portrayed in their radio-phenotype, as their sub-regions are depicted by varying intensity profiles disseminated across multi-parametric magnetic resonance imaging (mpMRI) scans, reflecting varying biological properties. Their heterogeneous shape, extent, and location are some of the factors that make these tumors difficult to resect, and in some cases inoperable. The amount of resected tumor is a factor also considered in longitudinal scans, when evaluating the apparent tumor for potential diagnosis of progression. Furthermore, there is mounting evidence that accurate segmentation of the various tumor sub-regions can offer the basis for quantitative image analysis towards prediction of patient overall survival. This study assesses the state-of-the-art machine learning (ML) methods used for brain tumor image analysis in mpMRI scans, during the last seven instances of the International Brain Tumor Segmentation (BraTS) challenge, i.e., 2012-2018. Specifically, we focus on i) evaluating segmentations of the various glioma sub-regions in pre-operative mpMRI scans, ii) assessing potential tumor progression by virtue of longitudinal growth of tumor sub-regions, beyond use of the RECIST/RANO criteria, and iii) predicting the overall survival from pre-operative mpMRI scans of patients that underwent gross total resection. Finally, we investigate the challenge of identifying the best ML algorithms for each of these tasks, considering that apart from being diverse on each instance of the challenge, the multi-institutional mpMRI BraTS dataset has also been a continuously evolving/growing dataset.