arXiv subjects

Xiaozhen Ge

Publications and source records attributed to Xiaozhen Ge.

7 recordsLinked to original sources

arXiv2026

Optimization landscapes of variational quantum algorithms

Optimization plays a central role in variational quantum algorithms, where the objective function typically takes the form $F(\boldsymbol{\theta})= \sum_{m=1}^{M} f_m \left(\mathrm{Tr}[U(\boldsymbol{\theta})\rho_m U^\dagger(\boldsymbol{\theta}) O_m]\right)$, with $U(\boldsymbol{\theta})$ being a parameterized quantum ansatz. Understanding the optimization landscape of such objective functions is crucial for assessing the trainability and performance of these algorithms. For the special case $M=1$, it is known that under certain assumptions, the landscape is free of false traps (FTs), i.e., local optima that are not global. In this work, we investigate optimization landscapes of the general case $M\geq1$ and show that the landscape becomes intrinsically more complex. First, we establish a complete framework for analyzing critical features of the optimization landscape, by deriving necessary and sufficient conditions to identify and classify all critical points under some assumptions, which is also of practical importance in designing efficient algorithms independent of whether these assumptions are satisfied. Then, we show that FTs can still emerge on landscapes for $M>1$, standing in stark contrast to the $M=1$ case and further revealing that parameter sufficiency alone is not enough to guarantee a trap-free landscape. Moreover, we uncover a close connection that the emergence of FTs is necessarily attributed to the loss of distinguishability among the states and/or operators, and fundamentally, to the loss of compatibility of the spectral ordering governed by different objective terms. Our results provide a deeper understanding of the optimization complexity and practical guidance for both algorithmic and problem-setting designs.

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arXiv2024

The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement

In a recent work [Ge {\it et al.}, arXiv: 2312. 17496 (2023)], we have derived the polygon relation of bipartite entanglement measures that is useful to reveal the entanglement properties of discrete, continuous, and even hybrid multipartite quantum systems. In this work, with the information-theoretical measures of Rényi and Tsallis entropies, we study the relationship between the polygon relation and the subadditivity of entropy. In particular, the entropy-polygon relations are derived for pure multi-qubit states and generalized to multi-mode Gaussian states, by utilizing the known results from the quantum marginal problem. Moreover, the equivalence between the polygon relation and subadditivity is established, in the sense that for all discrete or continuous multipartite states, the polygon relation holds if and only if the underlying entropy is subadditive. As byproduct, the subadditivity of Rényi and Tsallis entropies is proven for all bipartite Gaussian states. Finally, the difference between polygon relations and monogamy relations is clarified, and generalizations of our results are discussed. Our work provides a better understanding of the rich structure of multipartite states, and hence is expected to be helpful for the study of multipartite entanglement.

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arXiv2024

Faithful geometric measures for genuine tripartite entanglement

We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation $\mathcal{E}^α_{i|jk}\leq \mathcal{E}^α_{j|ik}+\mathcal{E}^α_{k|ij}$ holds for all subadditive bipartite entanglement measure $\mathcal{E}$, all permutations under parties $i, j, k$, all $α\in [0, 1]$, and all pure tripartite states. It provides a geometric interpretation that bipartition entanglement, measured by $\mathcal{E}^α$, corresponds to the side of a triangle, of which the area with $α\in (0, 1)$ is nonzero if and only if the underlying state is genuinely entangled. Then, we rigorously prove the non-obtuse triangle area with $0<α\leq 1/2$ is a measure for genuine tripartite entanglement. Useful lower and upper bounds for these measures are obtained, and generalizations of our results are also presented. Finally, it is significantly strengthened for qubits that, given a set of subadditive and non-additive measures, some state is always found to violate the triangle relation for any $α>1$, and the triangle area is not a measure for any $α>1/2$. Hence, our results are expected to aid significant progress in studying both discrete and continuous multipartite entanglement.

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arXiv2023

Tripartite entanglement measure under local operations and classical communication

Multipartite entanglement is an indispensable resource in quantum communication and computation, however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work, we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system in [S. Xie {\it et al.}, Phys. Rev. Lett. \textbf{127}. 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show the concurrence fill can be increased under local operation and classical communications (LOCCs) {\it on average}, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC-monotonicity of three-tangle and find that the bipartite concurrence and the squared can have distinct performances under the same LOCCs. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalised to the multipartite system. Our results shed light on studying genuine entanglement and also reveal the complex structure of multipartite systems.

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arXiv2022

The Optimization Landscape of Hybrid Quantum-Classical Algorithms: from Quantum Control to NISQ Applications

This review investigates the landscapes of prevalent hybrid quantum-classical optimization algorithms in many rapidly developing quantum technologies, where the objective function is either computed by a natural quantum system or a quantum ansatz that is engineered, but the optimizer is classical. In any particular case, the nature of the underlying control landscape is fundamentally important for systematic optimization of the objective. In early studies on the optimal control of few-body dynamics, the optimizer could take full control of the quantum systems to be manipulated whose Hilbert space dimension is relatively small. Stepping into the noisy intermediate-scale quantum (NISQ) era, the experimentally growing computational power of the ansatz expressed as quantum hardware may bring quantum advantage over classical computers, but the classical optimizer is often limited by the available control resources. Across these different scales, we will show that the landscape's geometry experiences morphological changes from favorable trap-free landscapes to easily trapping rugged landscapes, and eventually to barren-plateau landscapes on which the optimizer can hardly move. This unified view provides the basis for understanding classes of systems that may be readily controlled out to those with special consideration, including the difficulties and potential advantages of NISQ technologies, as well as seeking possible ways to escape traps or plateaus, in particular circumstances.

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arXiv2021

Risk-sensitive Optimization for Robust Quantum Controls

Highly accurate and robust control of quantum operations is vital for the realization of error-correctible quantum computation. In this paper, we show that the robustness of high-precision controls can be remarkably enhanced through sampling-based stochastic optimization of a risk-sensitive loss function. Following the stochastic gradient-descent direction of this loss function, the optimization is guided to penalize poor-performance uncertainty samples in a tunable manner. We propose two algorithms, which are termed as the risk-sensitive GRAPE and the adaptive risk-sensitive GRAPE. Their effectiveness is demonstrated by numerical simulations, which is shown to be able to achieve high control robustness while maintaining high fidelity.

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arXiv2019

Robust Quantum Control in Games: an Adversarial Learning Approach

High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. In this paper, we show that through a game played between the uncertainties (or noises) and the controls, adversarial uncertainty samples can be generated to find highly robust controls through the search for Nash equilibria (NE). We propose a broad family of adversarial learning algorithms, namely a-GRAPE algorithms, which include two effective learning schemes referred to as the best-response approach and the better-response approach within the game-theoretic terminology, providing options for rapidly learning robust controls. Numerical experiments demonstrate that the balance between fidelity and robustness depends on the details of the chosen adversarial learning algorithm, which can effectively lead to a significant enhancement of control robustness while attaining high fidelity.

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