arXiv subjects

Xiufan Li

Publications and source records attributed to Xiufan Li.

6 recordsLinked to original sources

arXiv2026

Quantum Tilted Loss in Variational Optimization: Theory and Applications

Variational quantum algorithms (VQAs) are leading strategies for using near-term quantum devices, with a well-studied bottleneck being their trainability. Standard expectation-value objectives with expressive circuits frequently encounter barren plateaus in the optimization landscape during training. To address this challenge, we introduce the Quantum Tilted Loss (QTL), an operator-level generalization of classical exponential tilting designed to systematically reshape the optimization landscape. By tuning a single continuous parameter, QTL can amplify gradient signals in structured settings while preserving the problem's true global minima. We provide a theoretical foundation that unifies standard expectation minimization with popular tunable heuristics, such as Conditional Value-at-Risk (CVaR) and Gibbs formulations. Deploying this framework requires balancing the geometric benefits of a sharpened landscape against the statistical cost of estimating nonlinear gradients from finite quantum measurements. We formalize this trainability-estimability trade-off, demonstrating how aggressive tilting fundamentally shifts the optimization bottleneck from landscape flatness to sample complexity. Thus, the operational bottleneck shifts from vanishing gradients to measurement sampling variance. Finally, we exhibit through numerical simulations that ascending tilt schedules can outperform fixed-tilt training in finite-shot regimes.

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arXiv2026

Trainability Beyond Linearity in Variational Quantum Objectives

Barren-plateau results have established exponential gradient suppression as a widely cited obstacle to the scalability of variational quantum algorithms. When and whether these results extend to a given objective has been addressed through loss-specific arguments, but a general structural characterization has remained open. We show that the objective itself admits a fixed-observable representation if and only if the loss is affine in the measured statistics, thereby identifying the exact boundary of the standard concentration-based proof template. Existing transfer results for non-affine losses achieve this reduction under additional assumptions; our characterization implies that such a reduction is not structurally available for a class of non-affine objectives, placing them outside the automatic reach of the existing proof template. Beyond the affine regime, a chain-rule decomposition reveals three governing factors -- model responsivity, loss-side signal, and transmittance -- and induces a loss-class dichotomy: bounded-gradient losses inherit suppression, while amplification-capable losses can in principle counteract it. In the exponentially wide setting, both classes fail, but for different structural reasons. When the interface is instead designed at polynomial width -- exposing coarse-grained statistics rather than individual bitstring probabilities -- the exponential-dimensional obstruction is relaxed and the dichotomy plays a genuine role. In a numerical demonstration on a charge-conserving quantum system, the amplification-capable objective produces resolved gradients several orders of magnitude larger than affine and inheriting baselines at comparable shot budgets. Over the tested interval, its scaling trend is statistically distinguished from the exponential trend of both alternatives. The boundary is affine; what lies beyond it is a representation-design problem.

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arXiv2024

A Comprehensive Study of Quantum Arithmetic Circuits

In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as a prominent illustration. Quantum arithmetic circuits, which are the fundamental building blocks in numerous quantum algorithms, have attracted much attention. Despite extensive exploration of various designs in the existing literature, researchers remain keen on developing novel designs and improving existing ones. In this review article, we aim to provide a systematically organized and easily comprehensible overview of the current state-of-the-art in quantum arithmetic circuits. Specifically, this study covers fundamental operations such as addition, subtraction, multiplication, division and modular exponentiation. We delve into the detailed quantum implementations of these prominent designs and evaluate their efficiency considering various objectives. We also discuss potential applications of presented arithmetic circuits and suggest future research directions.

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arXiv2023

Classical combinations of quantum states for solving banded circulant linear systems

Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems appear in many physics-related differential equations. An interesting case is banded circulant linear systems whose non-zero terms are within distance K of the main diagonal. For these systems, we propose an approach based on the classical combination of quantum states (CQS) method relying on convex optimization against the available analytical solution. From decompositions into cyclic permutations, the solution can be approximately represented by a classical combination of a polynomial number of quantum states. We validate our methods using classical simulations as well as execution on an IBM quantum computer. While in the setting of this paper, efficient classical algorithms are available, our results demonstrate the potential applicability of the CQS method for solving physics problems such as heat transfer.

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arXiv2023

Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz (HVA) aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate the effectiveness, efficiency, and advantages of the two-dimensional Heisenberg model and the Fermi-Hubbard chain. Numerical experiments show that MBHVA is expected to reduce resource overhead compared to quantum circuits, especially in the presence of large multi-qubit rotation operations. Furthermore, when compared to Measurement-based Hardware Efficient Ansatz (MBHEA), MBHVA also demonstrates superior performance. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in terms of both resource efficiency and error mitigation, particularly for photonic platforms.

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arXiv2022

Quantum NETwork: from theory to practice

The quantum internet is envisioned as the ultimate stage of the quantum revolution, which surpasses its classical counterpart in various aspects, such as the efficiency of data transmission, the security of network services, and the capability of information processing. Given its disruptive impact on the national security and the digital economy, a global race to build scalable quantum networks has already begun. With the joint effort of national governments, industrial participants and research institutes, the development of quantum networks has advanced rapidly in recent years, bringing the first primitive quantum networks within reach. In this work, we aim to provide an up-to-date review of the field of quantum networks from both theoretical and experimental perspectives, contributing to a better understanding of the building blocks required for the establishment of a global quantum internet. We also introduce a newly developed quantum network toolkit to facilitate the exploration and evaluation of innovative ideas. Particularly, it provides dual quantum computing engines, supporting simulations in both the quantum circuit and measurement-based models. It also includes a compilation scheme for mapping quantum network protocols onto quantum circuits, enabling their emulations on real-world quantum hardware devices. We showcase the power of this toolkit with several featured demonstrations, including a simulation of the Micius quantum satellite experiment, a testing of a four-layer quantum network architecture with resource management, and a quantum emulation of the CHSH game. We hope this work can give a better understanding of the state-of-the-art development of quantum networks and provide the necessary tools to make further contributions along the way.

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