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1. Nearly tight Trotterization of interacting electrons

   https://doi.org/10.22331/q-2021-07-05-495  

   Su, Yuan; Huang, Hsin-Yuan; Campbell, Earl T. (July 2021, Quantum)

   null (Ed.)

   We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the η -electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use ( n 5 / 3 η 2 / 3 + n 4 / 3 η 2 / 3 ) n o ( 1 ) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and η electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when n = η 2 − o ( 1 ) . We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons. 

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2. Coexistence of superconductivity with partially filled stripes in the Hubbard model

   https://doi.org/10.1126/science.adh7691  

   Xu, Hao; Chung, Chia-Min; Qin, Mingpu; Schollwöck, Ulrich; White, Steven R; Zhang, Shiwei (May 2024, Science)

   The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature (T_c) superconductivity. 

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3. Quantum critical dynamics in a spinor Hubbard model quantum simulator

   https://doi.org/10.1038/s42005-021-00562-y  

   Austin, Jared O.; Chen, Zihe; Shaw, Zachary N.; Mahmud, Khan W.; Liu, Yingmei (March 2021, Communications Physics)

   Abstract Three-dimensional (3D) strongly correlated many-body systems, especially their dynamics across quantum phase transitions, are prohibitively difficult to be numerically simulated. We experimentally demonstrate that such complex many-body dynamics can be efficiently studied in a 3D spinor Bose–Hubbard model quantum simulator, consisting of antiferromagnetic spinor Bose–Einstein condensates confined in cubic optical lattices. We find dynamics and scaling effects beyond the scope of existing theories at superfluid–insulator quantum phase transitions, and highlight spin populations as a good observable to probe the quantum critical dynamics. Our data indicate that the scaling exponents are independent of the nature of the quantum phase transitions. We also conduct numerical simulations in lower dimensions using time-dependent Gutzwiller approximations, which qualitatively describe our observations. 

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4. Robust preparation of many-body ground states in Jaynes–Cummings lattices

   https://doi.org/10.1038/s41534-021-00433-y  

   Cai, Kang; Parajuli, Prabin; Long, Guilu; Wong, Chee Wei; Tian, Lin (December 2021, npj Quantum Information)

   Abstract Strongly correlated polaritons in Jaynes–Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and superfluid phases at integer fillings. The prerequisite to observe such phase transitions is to pump polariton excitations into a JC lattice and prepare them into appropriate ground states. Despite previous efforts, it is still challenging to generate many-body states with high accuracy. Here, we present an approach for the robust preparation of many-body ground states of polaritons in finite-sized JC lattices by optimized nonlinear ramping. We apply a Landau–Zener type of estimation to this finite-sized system and derive the optimal ramping index for selected ramping trajectories, which can greatly improve the fidelity of the prepared states. With numerical simulation, we show that by choosing an appropriate ramping trajectory, the fidelity in this approach can remain close to unity in almost the entire parameter space. This approach can shed light on high-fidelity state preparation in quantum simulators and advance the implementation of quantum simulation with practical devices. 

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5. Strong pairing in mixed-dimensional bilayer antiferromagnetic Mott insulators

   https://doi.org/10.1038/s41567-022-01561-8  

   Bohrdt, Annabelle; Homeier, Lukas; Bloch, Immanuel; Demler, Eugene; Grusdt, Fabian (June 2022, Nature Physics)

   Abstract Interacting many-body systems in reduced-dimensional settings, such as ladders and few-layer systems, are characterized by enhanced quantum fluctuations. Recently, two-dimensional bilayer systems have sparked considerable interest because they can host unusual phases, including unconventional superconductivity. Here we present a theoretical proposal for realizing high-temperature pairing of fermions in a class of bilayer Hubbard models. We introduce a general and highly efficient pairing mechanism for mobile charge carriers in doped antiferromagnetic Mott insulators. The pairing is caused by the energy that one charge gains when it follows the path created by another charge. We show that this mechanism leads to the formation of highly mobile but tightly bound pairs in the case of mixed-dimensional Fermi–Hubbard bilayer systems. This setting is closely related to the Fermi–Hubbard model believed to capture the physics of copper oxides, and can be realized in currently available ultracold atom experiments. 

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