arXiv subjects

Xiao Yuan

Publications and source records attributed to Xiao Yuan.

At least 73 records · Page 4Linked to original sources

arXiv2024

Error Interference in Quantum Simulation

Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle inequality to provide an upper bound for the error. However, these often yield overly conservative and inaccurate estimates as they neglect error interference -- a phenomenon where errors in different segments can destructively interfere. Here, we introduce a novel method that directly estimates the long-time algorithmic errors with multiple segments, thereby establishing a comprehensive framework for characterizing algorithmic error interference. We identify the sufficient and necessary condition for strict error interference and introduce the concept of approximate error interference, which is more broadly applicable to scenarios such as power-law interaction models, the Fermi-Hubbard model, and higher-order Trotter formulas. Our work demonstrates significant improvements over prior ones and opens new avenues for error analysis in quantum simulation, offering potential advancements in both theoretical algorithm design and experimental implementation of Hamiltonian simulation.

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arXiv2024

Efficient Characterizations of Multiphoton States with an Ultra-thin Optical Device

Metasurface enables the generation and manipulation of multiphoton entanglement with flat optics, providing a more efficient platform for large-scale photonic quantum information processing. Here, we show that a single metasurface optical device would allow more efficient characterizations of multiphoton entangled states, such as shadow tomography, which generally requires fast and complicated control of optical setups to perform information-complete measurements, a demanding task using conventional optics. The compact and stable device here allows implementations of general positive observable value measures with a reduced sample complexity and significantly alleviates the experimental complexity to implement shadow tomography. Integrating self-learning and calibration algorithms, we observe notable advantages in the reconstruction of multiphoton entanglement, including using fewer measurements, having higher accuracy, and being robust against experimental imperfections. Our work unveils the feasibility of metasurface as a favorable integrated optical device for efficient characterization of multiphoton entanglement, and sheds light on scalable photonic quantum technologies with ultra-thin optical devices.

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arXiv2024

Quantification of Entanglement and Coherence with Purity Detection

Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing.

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arXiv2024

Experimental virtual distillation of entanglement and coherence

Noise is in general inevitable and detrimental to practical and useful quantum communication and computation. Under the resource theory framework, resource distillation serves as a generic tool to overcome the effect of noise. Yet, conventional resource distillation protocols generally require operations on multi-copies of resource states, and strong limitations exist that restrict their practical utilities. Recently, by relaxing the setting of resource distillation to only approximating the measurement statistics instead of the quantum state, a resource-frugal protocol, virtual resource distillation, is proposed, which allows more effective distillation of noisy resources. Here, we report its experimental implementation on a photonic quantum system for the distillation of quantum coherence (up to dimension 4) and bipartite entanglement. We show the virtual distillation of the maximal superposed state of dimension four from the state of dimension two, an impossible task in conventional coherence distillation. Furthermore, we demonstrate the virtual distillation of entanglement with operations acting only on a single copy of the noisy EPR pair and showcase the quantum teleportation task using the virtually distilled EPR pair with a significantly improved fidelity of the teleported state. These results illustrate the feasibility of the virtual resource distillation method and pave the way for accurate manipulation of quantum resources with noisy quantum hardware.

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arXiv2024

Experimental quantum computational chemistry with optimised unitary coupled cluster ansatz

Quantum computational chemistry has emerged as an important application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers (VQE), have been designed as promising solutions to quantum chemistry problems, yet challenges due to theoretical complexity and experimental imperfections hinder progress in achieving reliable and accurate results. Experimental works for solving electronic structures are consequently still restricted to nonscalable (hardware efficient) or classically simulable (Hartree-Fock) ansatz, or limited to a few qubits with large errors. The experimental realisation of scalable and high-precision quantum chemistry simulation remains elusive. Here, we address the critical challenges {associated with} solving molecular electronic structures using noisy quantum processors. Our protocol presents significant improvements in the circuit depth and running time, key metrics for chemistry simulation. Through systematic hardware enhancements and the integration of error mitigation techniques, we push forward the limit of experimental quantum computational chemistry and successfully scale up the implementation of VQE with an optimised unitary coupled-cluster ansatz to 12 qubits. We produce high-precision results of the ground-state energy for molecules with error suppression by around two orders of magnitude. We achieve chemical accuracy for H$_2$ at all bond distances and LiH at small bond distances in the experiment, even beyond the two recent concurrent works. Our work demonstrates a feasible path towards a scalable solution to electronic structure calculation, validating the key technological features and identifying future challenges for this goal.

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arXiv2024

Molecular docking via quantum approximate optimization algorithm

Molecular docking plays a pivotal role in drug discovery and precision medicine, enabling us to understand protein functions and advance novel therapeutics. Here, we introduce a potential alternative solution to this problem, the digitized-counterdiabatic quantum approximate optimization algorithm (DC-QAOA), which utilizes counterdiabatic driving and QAOA on a quantum computer. Our method was applied to analyze diverse biological systems, including the SARS-CoV-2 Mpro complex with PM-2-020B, the DPP-4 complex with piperidine fused imidazopyridine 34, and the HIV-1 gp120 complex with JP-III-048. The DC-QAOA exhibits superior performance, providing more accurate and biologically relevant docking results, especially for larger molecular docking problems. Moreover, QAOA-based algorithms demonstrate enhanced hardware compatibility in the noisy intermediate-scale quantum era, indicating their potential for efficient implementation under practical docking scenarios. Our findings underscore quantum computing's potential in drug discovery and offer valuable insights for optimizing protein-ligand docking processes.

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arXiv2024

Transition Role of Entangled Data in Quantum Machine Learning

Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

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arXiv2024

Circuit complexity of quantum access models for encoding classical data

Classical data encoding is usually treated as a black-box in the oracle-based quantum algorithms. On the other hand, their constructions are crucial for practical algorithm implementations. Here, we open the black-boxes of data encoding and study the Clifford$+T$ complexity of constructing some typical quantum access models. For general matrices, we show that both sparse-access input models and block-encoding require nearly linear circuit complexities relative to the matrix dimension, even if matrices are sparse. We also gives construction protocols achieving near-optimal gate complexities. On the other hand, the construction becomes efficient with respect to the data qubit when the matrix is the linear combination polynomial terms of efficient unitaries. As a typical example, we propose improved block encoding when these unitaries are Pauli strings. Our protocols are built upon improved quantum state preparation and a selective oracle for Pauli strings, which hold independent value. Our access model constructions offer considerable flexibility, allowing for tunable ancillary qubit number and offers corresponding space-time trade-offs.

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arXiv2024

Virtual quantum resource distillation

Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted 'free' operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call virtual resource distillation, provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.

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arXiv2024

Boson sampling enhanced quantum chemistry

In this work, we give a hybrid quantum-classical algorithm for solving electronic structure problems of molecules using only linear quantum optical systems. The variational ansatz we proposed is a hybrid of non-interacting Boson dynamics and classical computational chemistry methods, specifically, the Hartree-Fock method and the Configuration Interaction method. The Boson part is built by a linear optical interferometer which is easier to realize compared with the well-known Unitary Coupled Cluster (UCC) ansatz composed of quantum gates in conventional VQE and the classical part is merely classical processing acting on the Hamiltonian. We called such ansatzes Boson Sampling-Classic (BS-C). The appearance of permanents in the Boson part has its physical intuition to provide different kinds of resources from commonly used single-, double-, and higher-excitations in classical methods and the UCC ansatz to exploring chemical quantum states. Such resources can help enhance the accuracy of methods used in the classical parts. We give a scalable hybrid homodyne and photon number measurement procedure for evaluating the energy value which has intrinsic abilities to mitigate photon loss errors and discuss the extra measurement cost induced by the no Pauli exclusion principle for Bosons with its solutions. To demonstrate our proposal, we run numerical experiments on several molecules and obtain their potential energy curves reaching chemical accuracy.

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arXiv2024

Leakage Benchmarking for Universal Gate Sets

Errors are common issues in quantum computing platforms, among which leakage is one of the most challenging to address. This is because leakage, i.e., the loss of information stored in the computational subspace to undesired subspaces in a larger Hilbert space, is more difficult to detect and correct than errors that preserve the computational subspace. As a result, leakage presents a significant obstacle to the development of fault-tolerant quantum computation. In this paper, we propose an efficient and accurate benchmarking framework called leakage randomized benchmarking (LRB) for measuring leakage rates on multi-qubit quantum systems. Our approach is more insensitive to state preparation and measurement (SPAM) noise than existing leakage benchmarking protocols, requires fewer assumptions about the gate set itself, and can be used to benchmark multi-qubit leakages, which was not done previously. We also extend the LRB protocol to an interleaved variant called interleaved LRB (iLRB), which can benchmark the average leakage rate of generic $n$-site quantum gates with reasonable noise assumptions. We demonstrate the iLRB protocol on benchmarking generic two-qubit gates realized using flux tuning, and analyze the behavior of iLRB under corresponding leakage models. Our numerical experiments show good agreement with theoretical estimations, indicating the feasibility of both the LRB and iLRB protocols. Keywords: quantum computing; randomized benchmarking; leakage error; quantum gates

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arXiv2024

Low-depth Hamiltonian Simulation by Adaptive Product Formula

Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep quantum circuit that is beyond the capability of near-term noisy quantum devices. Here, focusing on the time evolution of a fixed input quantum state, we propose an adaptive approach to construct a low-depth time evolution circuit. By introducing a measurable quantifier that characterizes the simulation error, we use an adaptive strategy to learn the shallow quantum circuit that minimizes that error. We numerically test the adaptive method with electronic Hamiltonians of the $\mathrm{H_2O}$ and $\mathrm{H_4}$ molecules, and the transverse field Ising model with random coefficients. Compared to the first-order Suzuki-Trotter product formula, our method can significantly reduce the circuit depth (specifically the number of two-qubit gates) by around two orders while maintaining the simulation accuracy. We show applications of the method in simulating many-body dynamics and solving energy spectra with the quantum Krylov algorithm. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.

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arXiv2024

Virtual quantum resource distillation: General framework and applications

We develop the general framework of virtual resource distillation -- an alternative distillation strategy proposed in [Phys. Rev. Lett. 132, 050203 (2024)], which extends conventional quantum resource distillation by integrating the power of classical postprocessing. The framework presented here is applicable not only to quantum states, but also dynamical quantum objects such as quantum channels and higher-order processes. We provide a general characterization and benchmarks for the performance of virtual resource distillation in the form of computable semidefinite programs as well as several operationally motivated quantities. We apply our general framework to various concrete settings of interest, including standard resource theories such as entanglement, coherence, and magic, as well as settings involving dynamical resources such as quantum memory, quantum communication, and non-Markovian dynamics. The framework of probabilistic distillation is also discussed.

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arXiv2023

Coreset selection can accelerate quantum machine learning models with provable generalization

Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning challenges. Nonetheless, the training efficiency challenge poses a limitation on both QNNs and quantum kernels, curbing their efficacy when applied to extensive datasets. To confront this concern, we present a unified approach: coreset selection, aimed at expediting the training of QNNs and quantum kernels by distilling a judicious subset from the original training dataset. Furthermore, we analyze the generalization error bounds of QNNs and quantum kernels when trained on such coresets, unveiling the comparable performance with those training on the complete original dataset. Through systematic numerical simulations, we illuminate the potential of coreset selection in expediting tasks encompassing synthetic data classification, identification of quantum correlations, and quantum compiling. Our work offers a useful way to improve diverse quantum machine learning models with a theoretical guarantee while reducing the training cost.

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arXiv2023

Tensor-network-assisted variational quantum algorithm

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a classical tensor-network operator with a quantum circuit to effectively increase the circuit's expressivity without requiring a physically deeper circuit. We present a framework for tensor-network-assisted variational quantum algorithms that can solve quantum many-body problems using shallower quantum circuits. We demonstrate the efficiency of this approach by considering two examples of unitary matrix-product operators and unitary tree tensor networks, showing that they can both be implemented efficiently. Through numerical simulations, we show that the expressivity of these circuits is greatly enhanced with the assistance of tensor networks. We apply our method to two-dimensional Ising models and one-dimensional time-crystal Hamiltonian models with up to 16 qubits and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits.

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arXiv2023

Efficient measurement schemes for bosonic systems

Boson is one of the most basic types of particles and preserves the commutation relation. An efficient way to measure a bosonic system is important not only for simulating complex physics phenomena of bosons (such as nuclei) on a qubit based quantum computer, but for extracting classical information from a quantum simulator/computer that itself is built with bosons (such as a continuous variable quantum computer). Extending the recently proposed measurement schemes for qubits, such as shadow tomography and other local measurement schemes, here we study efficient measurement approaches for bosonic systems. We consider truncated qudit and continuous variable systems, corresponding to simulated bosons on a discrete quantum computer and an inherent boson system, respectively, and propose different measurement schemes with theoretical analyses of the variances for these two cases. We numerically test the schemes for measuring nuclei vibrations simulated using a discrete quantum computer and a continuous variable Gaussian state, and the simulation results show great improvement of the performance of the proposed method compared to conventional ones.

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arXiv2023

Schrödinger-Heisenberg Variational Quantum Algorithms

Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics. However, the extremely high accuracy needed to surpass classical computers poses a critical demand to the circuit depth, which is severely limited by the non-negligible gate infidelity, currently around 0.1-1%. Here, by incorporating a virtual Heisenberg circuit, which acts effectively on the measurement observables, to a real shallow Schrödinger circuit, which is implemented realistically on the quantum hardware, we propose a paradigm of Schrödinger-Heisenberg variational quantum algorithms to resolve this problem. We choose a Clifford virtual circuit, whose effect on the Hamiltonian can be efficiently and classically implemented according to the Gottesman-Knill theorem. Yet, it greatly enlarges the state expressivity, realizing much larger unitary t-designs. Our method enables accurate quantum simulation and computation that otherwise is only achievable with much deeper and more accurate circuits conventionally. This has been verified in our numerical experiments for a better approximation of random states and a higher-fidelity solution to the ground state energy of the XXZ model. Together with effective quantum error mitigation, our work paves the way for realizing accurate quantum computing algorithms with near-term quantum devices.

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arXiv2023

Robust and Efficient Hamiltonian Learning

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.

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