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Free, publicly-accessible full text available October 1, 2025
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Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings.
Published by the American Physical Society 2024 Free, publicly-accessible full text available July 1, 2025 -
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order.
Published by the American Physical Society 2024 Free, publicly-accessible full text available May 1, 2025 -
We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.
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Abstract Vanadium (V) pollution potentially threatens human health. Here, it is found that
nsp1 andnsp2 ,Rhizobium symbiosis defective mutants ofMedicago truncatula , are sensitive to V. Concentrations of phosphorus (P), iron (Fe), and sulfur (S) with V are negatively correlated in the shoots of wild‐type R108, but not in mutantnsp1 andnsp2 shoots. Mutations in the P transporterPHT1 ,PHO1 , andVPT families, Fe transporterIRT1 , and S transporterSULTR1/3/4 family confer varying degrees of V tolerance on plants. Among these gene families,MtPT1 ,MtZIP6 ,MtZIP9 , andMtSULTR1; 1 in R108 roots are significantly inhibited by V stress, whileMtPHO1; 2 ,MtVPT2 , andMtVPT3 are significantly induced. Overexpression ofArabidopsis thaliana VPT1 orM. truncatula MtVPT3 increases plant V tolerance. However, the response of these genes to V is weakened innsp1 ornsp2 and influenced by soil microorganisms. Mutations inNSPs reduce rhizobacterial diversity under V stress and simplify the V‐responsive operational taxonomic unit modules in co‐occurrence networks. Furthermore, R108 recruits more beneficial rhizobacteria related to V, P, Fe, and S than doesnsp1 ornsp2 . Thus, NSPs can modulate the accumulation and tolerance of legumes to V through P, Fe, and S transporters, ion homeostasis, and rhizobacterial community responses.Free, publicly-accessible full text available March 1, 2025 -
Alber, Mark (Ed.)Multi-view data can be generated from diverse sources, by different technologies, and in multiple modalities. In various fields, integrating information from multi-view data has pushed the frontier of discovery. In this paper, we develop a new approach for multi-view clustering, which overcomes the limitations of existing methods such as the need of pooling data across views, restrictions on the clustering algorithms allowed within each view, and the disregard for complementary information between views. Our new method, called CPS-merge analysis , merges clusters formed by the Cartesian product of single-view cluster labels, guided by the principle of maximizing clustering stability as evaluated by CPS analysis. In addition, we introduce measures to quantify the contribution of each view to the formation of any cluster. CPS-merge analysis can be easily incorporated into an existing clustering pipeline because it only requires single-view cluster labels instead of the original data. We can thus readily apply advanced single-view clustering algorithms. Importantly, our approach accounts for both consensus and complementary effects between different views, whereas existing ensemble methods focus on finding a consensus for multiple clustering results, implying that results from different views are variations of one clustering structure. Through experiments on single-cell datasets, we demonstrate that our approach frequently outperforms other state-of-the-art methods.more » « less