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Optical vortex beam with orbital angular momentum (OAM) has great potential to increase the capacity of optical communication and information processing in classical and quantum regimes. Nevertheless, important challenges that influence the optical data transmission in free space is the existence of diffusers along the optical path, which causes inevitable information loss during the wave propagation. Numerous algorithms have been proposed successively for identifying the modes of vortex beams propagating through scattering media. However, these methods all require completion on a computer, which is energyintensive and energy consuming. Here, we propose an all-optical regime for identifying the modes of vortex light fields propagating through scattering media. After training by deep learning, our model can recognize the mode of vortex beam through unknown phase diffusers, demonstrating generalization to new random diffusers that have never been encountered before. Once physically deployed, the entire setup will rapidly identify the modes of vortex light propagating through scattering media at the speed of light, and the entire inference process will consume zero energy except for illumination source. Our research represents a significant step towards highly accurate recognition of vortex light modes propagating through complex scattering media, providing significant guidance for the application of optical communication in complex environments.

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., Comment: 15 pages, 5 figures

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., Comment: 22 pages, 5 figures. Published version. Companion paper to arXiv:2303.00955, where the framework is introduced and some results on virtual resource distillation of quantum states are presented. Some of the content of this submission was originally a part of arXiv:2303.00955v1

The eigenvalue problem, a cornerstone in linear algebra, provides profound insights into studying matrix properties. Quantum algorithms addressing this problem have hitherto been constrained to special normal matrices assuming spectral decomposition, leaving the extension to general matrices an open challenge. In this work, we present a novel family of quantum algorithms tailored for solving the eigenvalue problem for general matrices, encompassing scenarios with complex eigenvalues or even defective matrices. Our approach begins by tackling the task of searching for an eigenvalue without additional constraints. For diagonalizable matrices, our algorithm has $\tilde O(\varepsilon^{-1})$ complexity with an error $\varepsilon$, achieving the nearly Heisenberg scaling. Subsequently, we study the identification of eigenvalues closest to a specified point or line, extending the results for ground energy and energy gap problems in Hermitian matrices. We achieve an accuracy scaling of $\tilde O(\varepsilon^{-2})$ for general diagonalizable matrices, further refining to $\tilde O(\varepsilon^{-1})$ under the condition of real eigenvalues or constant distance from the reference point. The algorithm's foundation lies in the synergy of three techniques: the relationship between eigenvalues of matrix $A$ and the minimum singular value of $A-\mu I$, quantum singular value threshold subroutine extended from quantum singular-value estimation, and problem-specific searching algorithms. Our algorithms find applications in diverse domains, including estimating the relaxation time of Markov chains, solving Liouvillian gaps in open quantum systems, and verifying PT-symmetry broken/unbroken phases. These applications underscore the significance of our quantum eigensolvers for problems across various disciplines., Comment: 6+10 pages, 1+1 figures

Sparse recovery is ubiquitous in machine learning and signal processing. Due to the NP-hard nature of sparse recovery, existing methods are known to suffer either from restrictive (or even unknown) applicability conditions, or high computational cost. Recently, iterative regularization methods have emerged as a promising fast approach because they can achieve sparse recovery in one pass through early stopping, rather than the tedious grid-search used in the traditional methods. However, most of those iterative methods are based on the $\ell_1$ norm which requires restrictive applicability conditions and could fail in many cases. Therefore, achieving sparse recovery with iterative regularization methods under a wider range of conditions has yet to be further explored. To address this issue, we propose a novel iterative regularization algorithm, IRKSN, based on the $k$-support norm regularizer rather than the $\ell_1$ norm. We provide conditions for sparse recovery with IRKSN, and compare them with traditional conditions for recovery with $\ell_1$ norm regularizers. Additionally, we give an early stopping bound on the model error of IRKSN with explicit constants, achieving the standard linear rate for sparse recovery. Finally, we illustrate the applicability of our algorithm on several experiments, including a support recovery experiment with a correlated design matrix., Comment: Accepted at AAAI 2024. Code at https://github.com/wdevazelhes/IRKSN_AAAI2024

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., Comment: 21 pages, 1 figure

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., Comment: 15 pages, 8 figures

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., Comment: 25 pages, 7 figures

The process of identifying and characterizing B-cell epitopes, which are the portions of antigens recognized by antibodies, is important for our understanding of the immune system, and for many applications including vaccine development, therapeutics, and diagnostics. Computational epitope prediction is challenging yet rewarding as it significantly reduces the time and cost of laboratory work. Most of the existing tools do not have satisfactory performance and only discriminate epitopes from non-epitopes. This paper presents a new deep learning-based multi-task framework for linear B-cell epitope prediction as well as antibody type-specific epitope classification. Specifically, a sequenced-based neural network model using recurrent layers and Transformer blocks is developed. We propose an amino acid encoding method based on eigen decomposition to help the model learn the representations of epitopes. We introduce modifications to standard cross-entropy loss functions by extending a logit adjustment technique to cope with the class imbalance. Experimental results on data curated from the largest public epitope database demonstrate the validity of the proposed methods and the superior performance compared to competing ones., Comment: 18 pages, 3 figures, accepted at ECML PKDD 2023

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., Comment: 17 pages, 8 figures. arXiv admin note: text overlap with arXiv:1707.09928

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., Comment: 24 pages, 12 figures

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., Comment: 23 pages, 17 figures, All comments are welcome

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., Comment: Accept to Nature Communications 15, 3716 (2024)

Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap between two eigenstates. Hence, how to efficiently solve the energy gap becomes an important motive for researching new quantum algorithms. In this work, we propose a hybrid non-variational quantum algorithm that uses the Monte Carlo method and real-time Hamiltonian simulation to evaluate the energy gap of a general quantum many-body system. Compared to conventional approaches, our algorithm does not require controlled real-time evolution, thus making its implementation much more experimental-friendly. Since our algorithm is non-variational, it is also free from the "barren plateaus" problem. To verify the efficiency of our algorithm, we conduct numerical simulations for the Heisenberg model and molecule systems on a classical emulator., Comment: 8 pages, 4 figures

Trapped-ion has shown great advantages in building quantum computers. While high fidelity entangling-gate has been realized for few ions, how to maintain the high fidelity for large scale trapped-ions still remains an open problem.Here, we present an analysis on arbitrary scale ion chain and focus on motional-related errors, reported as one of the leading error sources in state-of-the-art experiments. We theoretically analyze two-qubit entangling-gate infidelity in a large ion crystal. To verify our result, we develop an efficient numerical simulation algorithm that avoids exponential increases of the Hilbert space dimension. For the motional heating error, We derive a much tighter bound of gate infidelity than previously estimated $O(N\Gamma\tau)$, and we give an intuitive understanding from the trajectories in the phase space of motional modes. Our discoveries may inspire the scheme of pulse design against incoherent errors and shed light on the way toward constructing scalable quantum computers with large ion crystals., Comment: 17 pages, 7 figures

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, Comment: 27 pages, 5 figures

Quantum computers capable of fault-tolerant operation are expected to provide provable advantages over classical computational models. However, the question of whether quantum advantages exist in the noisy intermediate-scale quantum era remains a fundamental and challenging problem. The root of this challenge lies in the difficulty of exploring and quantifying the power of noisy quantum states. In this work, we focus on the complexity of weakly noisy states, which we define as the size of the shortest quantum circuit required to prepare the noisy state. To analyze this complexity, we first establish a general relationship between circuit depth, noise model, and purity. Based on this necessary condition, we propose a quantum machine learning (QML) algorithm that exploits the intrinsic-connection property of structured quantum neural networks. The proposed QML algorithm enables efficiently predicting the complexity of weakly noisy states from measurement results, representing a paradigm shift in our ability to characterize the power of noisy quantum computation., Comment: Revise the statement in Main Results

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., Comment: 6 pages, 2 figures; See also the companion paper arXiv:2404.13048 for the broader framework and complete technical proofs

In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial scale but by pushing the envelope as far as possible through optimal choices of algorithms and hardware the value of the simulator tool is maximized. This work reviews the state-of-the-art numerical simulation methods i.e. the classical algorithms that emulate quantum computer evolution under specific operations. We focus on the mainstream state-vector and tensor-network paradigms while briefly mentioning alternative methods. Moreover we review the diverse applications of simulation across different facets of quantum computer development such as understanding the fundamental difference between quantum and classical computations exploring algorithm design spaces for quantum advantage predicting quantum processor performance at the design stage and characterizing fabricated devices efficiently for fast iterations. This review complements recent surveys on today's tools and implementations here we seek to acquaint the reader with an essential understanding of the theoretical basis of classical simulations detailed discussions on the advantages and limitations of different methods and the demands and challenges arising from practical use cases., Comment: 14 pages

A new local watermarking method based on histogram shifting has been proposed in this paper to deal with various signal processing attacks (e.g. median filtering, JPEG compression and Gaussian noise addition) and geometric attacks (e.g. rotation, scaling and cropping). A feature detector is used to select local areas for embedding. Then stationary wavelet transform (SWT) is applied on each local area for denoising by setting the corresponding diagonal coefficients to zero. With the implementation of histogram shifting, the watermark is embedded into denoised local areas. Meanwhile, a secret key is used in the embedding process which ensures the security that the watermark cannot be easily hacked. After the embedding process, the SWT diagonal coefficients are used to reconstruct the watermarked image. With the proposed watermarking method, we can achieve higher image quality and less bit error rate (BER) in the decoding process even after some attacks. Compared with global watermarking methods, the proposed watermarking scheme based on local histogram shifting has the advantages of higher security and larger capacity. The experimental results show the better image quality as well as lower BER compared with the state-of-art watermarking methods.

The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to no cost of computational overhead added. In this article, we study a minibatch variant of SPP, namely M-SPP, for solving convex composite risk minimization problems. The core contribution is a set of novel excess risk bounds of M-SPP derived through the lens of algorithmic stability theory. Particularly under smoothness and quadratic growth conditions, we show that M-SPP with minibatch-size $n$ and iteration count $T$ enjoys an in-expectation fast rate of convergence consisting of an $\mathcal{O}\left(\frac{1}{T^2}\right)$ bias decaying term and an $\mathcal{O}\left(\frac{1}{nT}\right)$ variance decaying term. In the small-$n$-large-$T$ setting, this result substantially improves the best known results of SPP-type approaches by revealing the impact of noise level of model on convergence rate. In the complementary small-$T$-large-$n$ regime, we provide a two-phase extension of M-SPP to achieve comparable convergence rates. Moreover, we derive a near-tight high probability (over the randomness of data) bound on the parameter estimation error of a sampling-without-replacement variant of M-SPP. Numerical evidences are provided to support our theoretical predictions when substantialized to Lasso and logistic regression models.

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 parameterized 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 2D Ising models and 1D time crystal Hamiltonian models with up to 16 qubits, and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits., Comment: 9 pages, 4 figures, 41 references

Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(\Lambda^2)$ with a constant sampling overhead, where $\Lambda$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS., Comment: 13 pages, 2 figures

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., Comment: 11 pages, 4 figures in the main text, and 29 pages supplementary materials with 17 figures

Fermi acceleration by collisionless shocks is believed to be the primary mechanism to produce high energy charged particles in the Universe,where charged particles gain energy successively from multiple reflections off the shock front.Here,we present the first direct experimental evidence of ion energization from reflection off a supercritical quasi perpendicular collisionless shock,an essential component of Fermi acceleration in a laser produced magnetized plasma. We observed a quasi monoenergetic ion beam with 2,4 times the shock velocity in the upstream flow using time of flight method. Our related kinetic simulations reproduced the energy gain and showed that these ions were first reflected and then accelerated mainly by the motional electric field associated with the shock. This mechanism can also explain the quasi monoenergetic fast ion component observed in the Earth's bow shock.

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.

In the noisy-intermediate-scale-quantum era, Variational Quantum Eigensolver (VQE) is a promising method to study ground state properties in quantum chemistry, materials science, and condensed physics. However, general quantum eigensolvers are lack of systematical improvability, and achieve rigorous convergence is generally hard in practice, especially in solving strong-correlated systems. Here, we propose an Orbital Expansion VQE~(OE-VQE) framework to construct an efficient convergence path. The path starts from a highly correlated compact active space and rapidly expands and converges to the ground state, enabling simulating ground states with much shallower quantum circuits. We benchmark the OE-VQE on a series of typical molecules including H$_{6}$-chain, H$_{10}$-ring and N$_2$, and the simulation results show that proposed convergence paths dramatically enhance the performance of general quantum eigensolvers., Comment: Wu et al 2023 Quantum Sci. Technol

$\ell_0$ constrained optimization is prevalent in machine learning, particularly for high-dimensional problems, because it is a fundamental approach to achieve sparse learning. Hard-thresholding gradient descent is a dominant technique to solve this problem. However, first-order gradients of the objective function may be either unavailable or expensive to calculate in a lot of real-world problems, where zeroth-order (ZO) gradients could be a good surrogate. Unfortunately, whether ZO gradients can work with the hard-thresholding operator is still an unsolved problem. To solve this puzzle, in this paper, we focus on the $\ell_0$ constrained black-box stochastic optimization problems, and propose a new stochastic zeroth-order gradient hard-thresholding (SZOHT) algorithm with a general ZO gradient estimator powered by a novel random support sampling. We provide the convergence analysis of SZOHT under standard assumptions. Importantly, we reveal a conflict between the deviation of ZO estimators and the expansivity of the hard-thresholding operator, and provide a theoretical minimal value of the number of random directions in ZO gradients. In addition, we find that the query complexity of SZOHT is independent or weakly dependent on the dimensionality under different settings. Finally, we illustrate the utility of our method on a portfolio optimization problem as well as black-box adversarial attacks., Comment: Accepted for publication at NeurIPS 2022

Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules, ab initio simulation of solid-state materials on quantum computers is still in its early stage, mostly owing to the fact that the system size quickly becomes prohibitively large when approaching the thermodynamic limit. In this work, we introduce an orbital-based multi-fragment approach on top of the periodic density matrix embedding theory, resulting in a significantly smaller problem size for the current near-term quantum computer. We demonstrate the accuracy and efficiency of our method compared with the conventional methodologies and experiments on solid-state systems with complex electronic structures. These include spin polarized states of a hydrogen chain (1D-H), the equation of states of a boron nitride layer (h-BN) as well as the magnetic ordering in nickel oxide (NiO), a prototypical strongly correlated solid. Our results suggest that quantum embedding combined with a chemically intuitive fragmentation can greatly advance quantum simulation of realistic materials, thereby paving the way for solving important yet classically hard industrial problems on near-term quantum devices., Comment: 23 pages, 7 figures, and 3 tables

We propose to use quantum computers to simulate infection spreading in networks. We first show the analogy between the infection distribution and spin-lattice configurations with Ising-type interactions. Then, since the spreading process can be modeled as a classical Markovian process, we show that the spreading process can be simulated using the evolution of a quantum thermal dynamic model with a parameterized Hamiltonian. In particular, we analytically and numerically analyze the evolution behavior of the Hamiltonian, and prove that the evolution simulates a classical Markovian process, which describes the well-known epidemiological stochastic susceptible and infectious (SI) model. A practical method to determine the parameters of the thermal dynamic Hamiltonian from epidemiological inputs is exhibited. As an example, we simulate the infection spreading process of the SARS-Cov-2 variant Omicron in a small-world network., Comment: 13 pages, 10 figures, one supplementary material

Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, which measure the sign problem, the most notable limitation of QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N$_2$ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.

The FedProx algorithm is a simple yet powerful distributed proximal point optimization method widely used for federated learning (FL) over heterogeneous data. Despite its popularity and remarkable success witnessed in practice, the theoretical understanding of FedProx is largely underinvestigated: the appealing convergence behavior of FedProx is so far characterized under certain non-standard and unrealistic dissimilarity assumptions of local functions, and the results are limited to smooth optimization problems. In order to remedy these deficiencies, we develop a novel local dissimilarity invariant convergence theory for FedProx and its minibatch stochastic extension through the lens of algorithmic stability. As a result, we contribute to derive several new and deeper insights into FedProx for non-convex federated optimization including: 1) convergence guarantees independent on local dissimilarity type conditions; 2) convergence guarantees for non-smooth FL problems; and 3) linear speedup with respect to size of minibatch and number of sampled devices. Our theory for the first time reveals that local dissimilarity and smoothness are not must-have for FedProx to get favorable complexity bounds. Preliminary experimental results on a series of benchmark FL datasets are reported to demonstrate the benefit of minibatching for improving the sample efficiency of FedProx.

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating distribution. Under the weaker and distribution dependent notions of stability such as hypothesis stability and $L_2$-stability, the literature suggests that only polynomial generalization bounds are possible in general cases. The present paper addresses this long standing tension between these two regimes of results and makes progress towards relaxing it inside a classic framework of confidence-boosting. To this end, we first establish an in-expectation first moment generalization error bound for potentially randomized learning algorithms with $L_2$-stability, based on which we then show that a properly designed subbagging process leads to near-tight exponential generalization bounds over the randomness of both data and algorithm. We further substantialize these generic results to stochastic gradient descent (SGD) to derive improved high-probability generalization bounds for convex or non-convex optimization problems with natural time decaying learning rates, which have not been possible to prove with the existing hypothesis stability or uniform stability based results.