arXiv subjects

Xiaodie Lin

Publications and source records attributed to Xiaodie Lin.

11 recordsLinked to original sources

arXiv2026

Complementing Quantum Error Correction in Quantum Metrology via Swap Test

The precision and sensitivity achievable in quantum metrology are often compromised by the presence of noise. While quantum error correction has emerged as a promising strategy, it is ineffective in addressing noise that is indistinguishable from the signal. To address this challenge, virtual state purification was introduced as a complementary approach to quantum error correction. However, significant noise accumulation can impede its performance. To overcome this limitation, we propose a swap test-based method specifically designed to address indistinguishable noise, even under high noise levels. A systematic error-scaling analysis demonstrates that this method enables quantum-enhanced precision in certain scenarios. Furthermore, numerical simulations demonstrate that our method surpasses virtual state purification in both single- and multi-parameter estimation tasks. The significant improvements in precision across diverse settings underscore the robustness and practicality of our method for real-world applications.

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arXiv2025

Scalable Quantum Error Mitigation with Neighbor-Informed Learning

Noise in quantum hardware is the primary obstacle to realizing the transformative potential of quantum computing. Quantum error mitigation (QEM) offers a promising pathway to enhance computational accuracy on near-term devices, yet existing methods face a difficult trade-off between performance, resource overhead, and theoretical guarantees. In this work, we introduce neighbor-informed learning (NIL), a versatile and scalable QEM framework that unifies and strengthens existing methods such as zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC), while offering improved flexibility, accuracy, efficiency, and robustness. NIL learns to predict the ideal output of a target quantum circuit from the noisy outputs of its structurally related ``neighbor'' circuits. A key innovation is our 2-design training method, which generates training data for our machine learning model. In contrast to conventional learning-based QEM protocols that create training circuits by replacing non-Clifford gates with uniformly random Clifford gates, our approach achieves higher accuracy and efficiency, as demonstrated by both theoretical analysis and numerical simulation. Furthermore, we prove that the required size of the training set scales only \emph{logarithmically} with the total number of neighbor circuits, enabling NIL to be applied to problems involving large-scale quantum circuits. Our work establishes a theoretically grounded and practically efficient framework for QEM, paving a viable path toward achieving quantum advantage on noisy hardware.

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arXiv2025

Error-mitigated quantum metrology via enhanced virtual purification

Quantum metrology stands as a leading application of quantum science and technology, yet noise often constrains its precision and sensitivity. In near-term quantum metrology, existing protocols largely depend on virtual state purification, but significant noise accumulation and additional noise from the implementations of these protocols can impede their effectiveness. We propose enhanced virtual channel purification to address these problems, yielding enhanced virtual state purification as a by-product. Within sequential quantum metrology schemes, our error analysis reveals substantial bias reduction and quantum advantages in sampling cost when the number of encoding channels is ${\mathcal{O}}(p^{-1})$, where $p$ represents the error rate of encoding channels. In this range, our methods demonstrate significant improvements in parameter estimation precision and robustness against practical noise, as evidenced by numerical simulations for both single- and multi-parameter tasks. Particularly, these methods can naturally extend beyond quantum metrology, indicating their broad applicability in quantum information and quantum computation.

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arXiv2024

Variational Optimization for Quantum Problems using Deep Generative Networks

Optimization drives advances in quantum science and machine learning, yet most generative models aim to mimic data rather than to discover optimal answers to challenging problems. Here we present a variational generative optimization network that learns to map simple random inputs into high quality solutions across a variety of quantum tasks. We demonstrate that the network rapidly identifies entangled states exhibiting an optimal advantage in entanglement detection when allowing classical communication, attains the ground state energy of an eighteen spin model without encountering the barren plateau phenomenon that hampers standard hybrid algorithms, and-after a single training run-outputs multiple orthogonal ground states of degenerate quantum models. Because the method is model agnostic, parallelizable and runs on current classical hardware, it can accelerate future variational optimization problems in quantum information, quantum computing and beyond.

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arXiv2023

Certifying bipartite pure quantum states efficiently using untrusted devices

It has been known that all bipartite pure quantum states can be certified by quantum self-testing, i.e., any such states can be pinned down completely based on the statistics produced by local quantum measurements. A notable feature of quantum self-testing is that the conclusions remain reliable even when the quantum measurements involved are untrusted, where quantum nonlocality is crucial. This necessitates that each party conducts at least two different quantum measurements to produce the desired correlation. Here, we prove that when the underlying Hilbert space dimension is known beforehand, which is very common in quantum experiments, an arbitrary $d\times d$ bipartite pure state can be certified completely (up to local unitaries) by a certain correlation generated with a single measurement setting on each party, where each measurement yields only $2d$ or even $d+1$ outcomes. We also prove the robustness of our protocols to quantum noises and experimental imperfections. Compared with quantum self-testing, our protocols do not hinge on quantum nonlocality and are much more efficient, yet they maintain the essential feature of not requiring additional assumptions about the quantum devices involved. This advancement could offer significant convenience when certifying bipartite quantum states using untrusted quantum devices in future quantum industries.

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arXiv2023

The Generations of Classical Correlations via Quantum Schemes

Suppose two separated parties, Alice and Bob, share a bipartite quantum state or a classical correlation called a \emph{seed}, and they try to generate a target classical correlation by performing local quantum or classical operations on the seed, i.e., any communications are not allowed. We consider the following fundamental problem about this setting: whether Alice and Bob can use a given seed to generate a target classical correlation. We show that this problem has rich mathematical structures. Firstly, we prove that even if the seed is a pure bipartite state, the above decision problem is already NP-hard and a similar conclusion can also be drawn when the seed is also a classical correlation, implying that this problem is hard to solve generally. Furthermore, we prove that when the seed is a pure quantum state, solving the problem is equivalent to finding out whether the target classical correlation has some diagonal form of positive semi-definite factorizations that matches the seed pure state, revealing an interesting connection between the current problem and optimization theory. Based on this observation and other insights, we give several necessary conditions where the seed pure state has to satisfy to generate the target classical correlation, and it turns out that these conditions can also be generalized to the case that the seed is a mixed quantum state. Lastly, since diagonal forms of positive semi-definite factorizations play a crucial role in solving the problem, we develop an algorithm that can compute them for an arbitrary classical correlation, which has decent performance on the cases we test.

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arXiv2022

Certifying Unknown Genuine Multipartite Entanglement by Neural Networks

Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already NP-Hard to determine whether it is entangled or not. Therefore, it is hard to efficiently solve the above problem generally. However, since genuine multipartite entanglement is such a fundamental concept that plays a crucial role in many-body physics and quantum information processing tasks, finding realistic approaches to certify genuine multipartite entanglement is undoubtedly necessary. In this work, we show that neural networks can provide a nice solution to this problem, where measurement statistics data produced by measuring involved quantum states with local measurement devices serve as input features of neural networks. By testing our models on many specific multipartite quantum states, we show that they can certify genuine multipartite entanglement very accurately, which even include some new results unknown before. We also exhibit a possible way to improve the efficiency of our models by reducing the size of features. Lastly, we show that our models enjoy remarkable robustness against flaws in measurement devices, implying that they are very experiment-friendly.

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arXiv2022

Quantifying Unknown Quantum Entanglement via a Hybrid Quantum-Classical Machine Learning Framework

Quantifying unknown quantum entanglement experimentally is a difficult task, but also becomes more and more necessary because of the fast development of quantum engineering. Machine learning provides practical solutions to this fundamental problem, where one has to train a proper machine learning model to predict entanglement measures of unknown quantum states based on experimentally measurable data, say moments or correlation data produced by local measurements. In this paper, we compare the performance of these two different machine learning approaches systematically. Particularly, we first show that the approach based on moments enjoys a remarkable advantage over that based on correlation data, though the cost of measuring moments is much higher. Next, since correlation data is much easier to obtain experimentally, we try to better its performance by proposing a hybrid quantum-classical machine learning framework for this problem, where the key is to train optimal local measurements to generate more informative correlation data. Our numerical simulations show that the new framework brings us comparable performance with the approach based on moments to quantify unknown entanglement. Our work implies that it is already practical to fulfill such tasks on near-term quantum devices.

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arXiv2021

Quantifying Unknown Entanglement by Neural Networks

Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by any observables directly. In this paper, we train neural networks to quantify unknown entanglement, where the input features of neural networks are the outcome statistics data produced by locally measuring target quantum states, and the training labels are well-chosen quantities. For bipartite quantum states, this quantity is coherent information, which is a lower bound for the entanglement of formation and the entanglement of distillation. For multipartite quantum states, we choose this quantity as the geometric measure of entanglement. It turns out that the neural networks we train have very good performance in quantifying unknown quantum states, and can beat previous approaches like semi-device-independent protocols for this problem easily in both precision and application range. We also observe a surprising phenomenon that on quantum states with stronger quantum nonlocality, the neural networks tend to have better performance, though we do not provide them any knowledge on quantum nonlocality.

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arXiv2020

Experimental Entanglement Quantification for Unknown Quantum States in a Semi-Device-Independent Manner

Using the concept of non-degenerate Bell inequality, we show that quantum entanglement, the critical resource for various quantum information processing tasks, can be quantified for any unknown quantum states in a semi-device-independent manner, where the quantification is based on the experimentally obtained probability distribution and beforehand knowledge on quantum dimension only. Specifically, as an application of our approach on multi-level systems, we experimentally quantify the entanglement of formation and the entanglement of distillation for qutrit-qutrit quantum systems. In addition, to demonstrate our approach for multi-partite systems, we further quantify the geometry measure of entanglement of three-qubit quantum systems. Our results supply a general way to reliably quantify entanglement in multi-level and multi-partite systems, thus paving the way to characterize many-body quantum systems by quantifying involved entanglement.

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arXiv2020

Quantum and Classical Hybrid Generations for Classical Correlations

We consider two-stage hybrid protocols that combine quantum resource and classical resource to generate classical correlations shared by two separated players. Our motivation is twofold. First, in the near future the scale of quantum information processing is quite limited, and when quantum resource available is not sufficient for certain tasks, a possible way to strengthen the capability of quantum schemes is introducing extra classical resource. We analyze the mathematical structures of these hybrid protocols, and characterize the relation between the amount of quantum resource and classical resource needed. Second, a fundamental open problem in communication complexity theory is to describe the advantages of sharing prior quantum entanglement over sharing prior randomness, which is still widely open. It turns out that our quantum and classical hybrid protocols provide new insight into this important problem.

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