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1. Nonlinear speed-ups in ultracold quantum gases

   https://doi.org/10.1209/0295-5075/ac9fed  

   Deffner, Sebastian (November 2022, Europhysics Letters)

   Abstract Quantum mechanics is an inherently linear theory. However, collective effects in many body quantum systems can give rise to effectively nonlinear dynamics. In the present work, we analyze whether and to what extent such nonlinear effects can be exploited to enhance the rate of quantum evolution. To this end, we compute a suitable version of the quantum speed limit for numerical and analytical examples. We find that the quantum speed limit grows with the strength of the nonlinearity, yet it does not trivially scale with the “degree” of nonlinearity. This is numerically demonstrated for the parametric harmonic oscillator obeying Gross-Pitaevskii and Kolomeisky dynamics, and analytically for expanding boxes under Gross-Pitaevskii dynamics. 

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2. Integrating quantum computing into building-to-grid control framework: Application of benders decomposition in mixed-integer nonlinear programming

   https://doi.org/10.1007/s12273-025-1248-4  

   Deng, Zhipeng; Wang, Xuezheng; Dong, Bing (February 2025, Building Simulation)

   Abstract Buildings use a large amount of energy in the United States. It is important to optimally manage and coordinate the resources across building and power distribution networks to improve overall efficiency. Optimizing the power grid with discrete variables was very challenging for traditional computers and algorithms, as it is an NP-hard problem. In this study, we developed a new optimization solution based on quantum computing for BTG integration. We first used MPC for building loads connected with a commercial distribution grid for cost reduction. Then we used discretization and Benders Decomposition methods to reformulate the problem and decompose the continuous and discrete variables, respectively. We used D-Wave quantum computer to solve dual problems and used conventional algorithm for primal problems. We applied the proposed method to an IEEE 9-bus network with 3 commercial buildings and over 300 residential buildings to evaluate the feasibility and effectiveness. Compared with traditional optimization methods, we obtained similar solutions with some fluctuations and improved computational speed from hours to seconds. The time of quantum computing was greatly reduced to less than 1% of traditional optimization algorithm and software such as MATLAB. Quantum computing has proved the potential to solve large-scale discrete optimization problems for urban energy systems. 

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3. Interacting topological quantum chemistry in 2D with many-body real space invariants

   https://doi.org/10.1038/s41467-024-45395-9  

   Herzog-Arbeitman, Jonah; Bernevig, B Andrei; Song, Zhi-Da (December 2024, Nature Communications)

   Abstract The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using theU(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase. 

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4. Demonstrating two-qubit entangling gates at the quantum speed limit using superconducting qubits

   Joel Howard; Alexander Lidiak; Casey Jameson; Bora Basyildiz; Kyle Clark; Tongyu Zhao; Mustafa Bal; Junling Long; David P. Pappas; Meenakshi Singh; et al (June 2022, ArXivorg)

   The speed of elementary quantum gates, particularly two-qubit entangling gates, ultimately sets the limit on the speed at which quantum circuits can operate. In this work, we demonstrate experimentally two-qubit entangling gates at nearly the fastest possible speed allowed by the physical interaction strength between two superconducting transmon qubits. We achieve this quantum speed limit by implementing experimental gates designed using a machine learning inspired optimal control method. Importantly, our method only requires the single-qubit drive strength to be moderately larger than the interaction strength to achieve an arbitrary entangling gate close to its analytical speed limit with high fidelity. Thus, the method is applicable to a variety of platforms including those with comparable single-qubit and two-qubit gate speeds, or those with always-on interactions. 

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5. State preparation in a Jaynes-Cummings lattice with quantum optimal control

   https://doi.org/10.1038/s41598-023-47002-1  

   Parajuli, Prabin; Govindarajan, Anuvetha; Tian, Lin (December 2023, Scientific Reports)

   \High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation. 

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