Ryui Kaneko

Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) wave functions of Abrikosov fermions are widely used to describe quantum many-body states. Taking the one-dimensional transverse-field Ising model as an example, we exactly embed any even-parity spinless fermionic Gaussian state representable as a paired exponential in the chosen particle basis into a projected BCS state of spinful Abrikosov fermions. The construction provides controlled initial states for variational Monte Carlo studies of nonintegrable models.

Triple-layer cuprate superconductor HgBa 2 Ca 2 Cu 3 O 8 (Hg1223) keeps the record of the highest superconducting (SC) critical temperature T c ∼ 134 K among all the existing materials at ambient pressure. T c further increases under pressure up to T c ∼ 160 K , thereby holding the key to the realistic and comprehensive understanding of the cuprate superconductors, which is one of the grand challenges in physics. However, the microscopic mechanism of high T c of Hg1223 remains to be elucidated. Here, we perform first-principles calculations of Hg1223 both at ambient and applied pressures by solving Hamiltonians with an accurate variational solver supplemented by a neural network. The pressure dependence of the calculated d -wave SC order parameter and estimated T c shows a structure supporting a T c peak around 30 GPa in quantitative agreement with the reported experimental indications. The origin of the strong SC amplitude of Hg1223 at ambient pressure compared to other cuprates is identified as strong local Coulomb repulsion U attributed to poorer screening of the Coulomb interaction in multilayer compounds. The origin of the further increase in T c under pressure is ascribed to a unique interplay of three elements, namely, increased electron hopping t , decreased U , and more importantly, strongly reduced nonlocal Coulomb repulsion V with increasing pressure. The origin of Cooper pairing is identified as the emergent local attraction counterintuitively arising from the strong bare local repulsion U for Hg1223. It explains why Hg1223 shows the highest T c among other cuprates, while the pairing mechanism is common in other cuprates as well. The emergent attraction is interpreted from “attraction from reduced repulsion,” originating from the release of the fluctuating doubly occupied sites characterized from the “false vacuum” in the Mott insulator to the double-occupation-free d -wave SC states caused by the carrier doping. This instantaneous and local attraction is in marked contrast with the case of the conventional BCS SC mediated by bosonic glues. The local attraction is consistent with the electron fractionalization supported in experimental analyses. The coexistence of SC and antiferromagnetic orders is also demonstrated as a characteristic feature of the multilayer system with self-doping in the underdoped region. The quantitative and microscopic understanding of the high T c in Hg1223 provides a new perspective on the origin of the cuprate superconductivity and offers a new route explicitly using this channel of the emergent attraction for future superconductivity research aiming at designing and optimizing SC materials.

Machine learning on quantum computers has attracted attention for its potential to deliver computational speedups in different tasks. However, deep variational quantum circuits require a large number of trainable parameters that grows with both qubit count and circuit depth, often rendering training infeasible. In this study, we introduce the Adaptive Interpolating Quantum Transform (AIQT), a quantum-native framework for flexible and efficient learning. AIQT defines a trainable unitary that interpolates between quantum transforms, such as the Hadamard and quantum Fourier transforms. This approach enables expressive quantum state manipulation while controlling parameter overhead. It also allows AIQT to inherit any quantum advantages present in its constituent transforms. Our results show that AIQT achieves high performance with minimal parameter count, offering a scalable and interpretable alternative to deep variational circuits.

Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a method that utilizes reliable short-time data of physical quantities to accurately forecast long-time behavior of the strongly entangled systems. We straightforwardly employ the simple dynamic mode decomposition (DMD), which is commonly used in fluid dynamics. Despite the simplicity of the method, the effectiveness and applicability of the DMD in quantum many-body systems such as the Ising model in the transverse field at the critical point are demonstrated, even when the time evolution at long time exhibits complicated features such as a volume-law entanglement entropy and consequential power-law decays of correlations characteristic of systems with long-ranged quantum entanglements unlike fluid dynamics. The present method, though simple, enables accurate forecasts amazingly at time as long as nearly an order of magnitude longer than that of the short-time training data. Effects of noise on the accuracy of the forecast are also investigated, because they are important especially when dealing with the experimental data. We find that a few percentages of noise do not affect the prediction accuracy destructively.