Fidelity Estimation Research Articles

Error mitigated metasurface-based randomized measurement schemes

Estimating properties of quantum states via randomized measurements has become a significant part of quantum information science. In this paper, we design an innovative approach leveraging metasurfaces to perform randomized measurements on photonic qubits, together with error mitigation techniques that suppress realistic metasurface measurement noise. Through fidelity and purity estimation, we confirm the capability of metasurfaces to implement randomized measurements and the unbiased nature of our error-mitigated estimator. Our findings show the potential of metasurface-based randomized measurement schemes in achieving robust and resource-efficient estimation of quantum state properties. Published by the American Physical Society 2024

Efficient fidelity estimation: alternative derivation and related applications

In [Phys. Rev. A 107 012427 (2023)], Baldwin and Jones prove that Uhlmann–Jozsa’s fidelity between two quantum states ρ and σ, i.e., F(ρ,σ)≔Trρσρ2 , can be written in a simplified form as F(ρ,σ)=Trρσ2 . In this article, we give an alternative proof of this result, using a function power series expansion and the properties of the trace function. Our approach not only reinforces the validity of the simplified expression but also facilitates the exploration of novel dissimilarity functions for quantum states and more complex trace functions of density operators.

Theory of versatile fidelity estimation with confidence

Theory of versatile fidelity estimation with confidence

Versatile Fidelity Estimation with Confidence.

As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge is quantifying how close an experimentally prepared quantum state is to the desired one. Here we present a method to construct an estimator for the quantum state fidelity that is compatible with any measurement protocol. Our method provides a confidence interval on this estimator that is guaranteed to be nearly minimax optimal for the specified measurement protocol. For a well-chosen measurement scheme, our method is competitive in the number of measurement outcomes required for estimation. We demonstrate our method using simulations and experimental data from a trapped-ion quantum computer and compare the results to state-of-the-art techniques. Our method can be easily extended to estimate the expectation value of any observable, such as entanglement witnesses.

STAFFormer: Spatio-temporal adaptive fusion transformer for efficient 3D human pose estimation

Existing two-stage methods for 3D Human Pose Estimation often use 2D poses as input, which are then lifted to obtain 3D representations. This typically involves frame-by-frame estimation, whether in 2D or 3D, resulting in high computational demands unsuitable for edge devices. Due to the continuity of human movement, the differences between adjacent frames can be minimal, a question arises: is frame-by-frame estimation necessary? Previous works demonstrated the feasibility of using Transformer-based models to estimate poses with sparse frames, focusing on either temporal or spatial dependencies but neglecting holistic spatio-temporal correlations. To address this, we introduce the Spatio-Temporal Adaptive Fusion Transformer (STAFFormer). First, STAFFormer recovers dense temporal frames from sparsely sampled ones obtained from a 2D pose estimator through the Temporal Dense Frame Recovery (TDFR) module. This significantly reduces the computational complexity. Second, STAFFormer employs an adaptive fusion attention mechanism, enhancing accuracy by attentively navigating both spatial and temporal dimensions through the Spatio-Temporal Adaptive Fusion (STAF) module. Furthermore, We introduce a kinematic coherence loss to adapt to subtle joint movements, improving pose estimation fidelity. Finally, we explore the possibility of integrating different pre-training strategies using extensive marker-based datasets. Experimental results on challenging datasets show our network achieves state-of-the-art performance with low computational complexity.

Hybrid State Estimation: Integrating Physics-Informed Neural Networks with Adaptive UKF for Dynamic Systems

In this paper, we present a novel approach to state estimation in dynamic systems by combining Physics-Informed Neural Networks (PINNs) with an adaptive Unscented Kalman Filter (UKF). Recognizing the limitations of traditional state estimation methods, we refine the PINN architecture with hybrid loss functions and Monte Carlo Dropout for enhanced uncertainty estimation. The Unscented Kalman Filter is augmented with an adaptive noise covariance mechanism and incorporates model parameters into the state vector to improve adaptability. We further validate this hybrid framework by integrating the enhanced PINN with the UKF for a seamless state prediction pipeline, demonstrating significant improvements in accuracy and robustness. Our experimental results show a marked enhancement in state estimation fidelity for both position and velocity tracking, supported by uncertainty quantification via Bayesian inference and Monte Carlo Dropout. We further extend the simulation and present evaluations on a double pendulum system and state estimation on a quadcopter drone. This comprehensive solution is poised to advance the state-of-the-art in dynamic system estimation, providing unparalleled performance across control theory, machine learning, and numerical optimization domains.

Experimental Direct Quantum Fidelity Learning via a Data-Driven Approach.

Fidelity estimation is an important technique for evaluating prepared quantum states in noisy quantum devices. A recent theoretical work proposed a frugal approach called neural quantum fidelity estimation (NQFE) [X. Zhang et al., Phys. Rev. Lett. 127, 130503 (2021).PRLTAO0031-900710.1103/PhysRevLett.127.130503]. While this requires a much smaller number of measurement operators than full quantum state tomography, it uses a weight-based floating measurement strategy that predetermines the top global Pauli operators that contribute the most to the fidelity and uses discrete fidelity intervals as predictions. In this Letter, we develop a measurement-fixed NQFE based on a transformer model which requires less measurement cost and can output continuous estimates of fidelity. Here we further experimentally apply the NQFE in a realistic situation using a nuclear spin quantum processor. We prepare the ground states of local Hamiltonians and arbitrary states and investigate how to estimate their fidelity with reference states, and we compare the fidelity estimation strategy with our and the original NQFE to conventional tomography. It is shown that NQFE can estimate the fidelity with comparable accuracy to the tomography approach. In the future, NQFE will become an important tool for benchmarking quantum states ahead of the advent of well-trusted fault-tolerant quantum computers.

Efficient adversarial training with multi-fidelity optimization for robust neural network

Adversarial examples (AEs) pose a significant threat to the security and reliability of deep neural networks. Adversarial training (AT) is one of the effective defense methods, involving the integration of a number of generated AEs into the training process to enhance model robustness. However, the computational cost associated with AE generation is unbearable, particularly for large-scale tasks. In pursuit of fast AT, many algorithms generate AEs by adopting a simple attack strategy, but they often sacrifice the quality of AEs and suffer from catastrophic overfitting, resulting in suboptimal model robustness. To address these issues, our approach incorporates multi-fidelity optimization, which employs a dynamic attack strategy to generate AEs with varying fidelity within a suitable range. Furthermore, we introduce a surrogate-assisted fidelity estimation module at the beginning of our proposed algorithm, allowing for the adaptive determination of the fidelity range tailored to specific tasks. Comparative experiments with seven state-of-the-art algorithms on three networks and three datasets demonstrate that the proposed algorithm obtains a competitive robust accuracy but spends only 50% of the training time of the projected gradient descent algorithm.

LTI/LQE: A Physics-Based Approach for Online Estimation of Dynamic Loads in the Rotating Frame

Accurate and online load monitoring of vital components located in the rotor system is important for not only inferring usage and estimating fatigue in those components but also for developing load alleviation/limiting control schemes. In the literature, on-board models for online (i.e., real-time) estimation of rotor component loads using available in-flight aircraft fixed-frame measurements are developed using neural networks, a statistical-based approach, or a combination of both. These models are aircraft-specific, do not capture the higher harmonic dynamics of the rotor system vibratory loads, and their synthesis requires obtaining a lot of data. To remedy these issues, this paper introduces a purely physics-based approach to online estimation of rotor system loads. The proposed approach can be applied to any rotary-wing vehicle, does not rely on a large amount of data, and captures the higher harmonic dynamics of the rotor system vibratory loads. The developed model entitled LTI/LQE is synthesized using a linear time invariant (LTI) model of helicopter-coupled body-rotor-inflow dynamics and a linear quadratic estimator (LQE), that is designed to correct the LTI model state response using fixed system measurements. The estimation fidelity of the LTI/LQE model is evaluated in simulation using a high-fidelity nonlinear model of a generic helicopter for online prediction of rotor blade pitch link loads arising from vehicle maneuvers. Results obtained using the LTI/LQE model revealed an interesting finding. It was found that the N/rev (where N is the number of blades) fixed system load measurements have information that can be leveraged to make an inference about the N/rev dynamic loads in the rotating system.

Hidden Follower Detection: How Is the Gaze-Spacing Pattern Embodied in Frequency Domain?

Spatiotemporal social behavior analysis is a technique that studies the social behavior patterns of objects and estimates their risks based on their trajectories. In social public scenarios such as train stations, hidden following behavior has become one of the most challenging issues due to its probability of evolving into violent events, which is more than 25%. In recent years, research on hidden following detection (HFD) has focused on differences in time series between hidden followers and normal pedestrians under two temporal characteristics: gaze and spatial distance. However, the time-domain representation for time series is irreversible and usually causes the loss of critical information. In this paper, we deeply study the expression efficiency of time/frequency domain features of time series, by exploring the recovery mechanism of features to source time series, we establish a fidelity estimation method for feature expression and a selection model for frequency-domain features based on the signal-to-distortion ratio (SDR). Experimental results demonstrate the feature fidelity of time series and HFD performance are positively correlated, and the fidelity of frequency-domain features and HFD performance are significantly better than the time-domain features. On both real and simulated datasets, the accuracy of the proposed method is increased by 3%, and the gaze-only module is improved by 10%. Related research has explored new methods for optimal feature selection based on fidelity, new patterns for efficient feature expression of hidden following behavior, and the mechanism of multimodal collaborative identification.

Co-estimation of state-of-charge and state-of-temperature for large-format lithium-ion batteries based on a novel electrothermal model

The safe and efficient operation of the electric vehicle significantly depends on the accurate state-of-charge (SOC) and state-of-temperature (SOT) of Lithium-ion (Li-ion) batteries. Given the influence of cross-interference between the two states indicated above, this study establishs a co-estimation framework of battery SOC and SOT. This framwork is based on an innovative electrothermal model and adaptive estimation algorithms. The first-order RC electric model and an innovative thermal model are components of the electrothermal model. Specifically, the thermal model includes two lumped-mass thermal submodels for two tabs and a two-dimensional (2-D) thermal resistance network (TRN) submodel for the main battery body, capable of capturing the detailed thermodynamics of large-format Li-ion batteries. Moreover, the proposed thermal model strikes an acceptable compromise between the estimation fidelity and computational complexity by representing the heat transfer processes by the thermal resistances. Besides, the adaptive estimation algorithms are composed of an adaptive unscented Kalman filter (AUKF) and an adaptive Kalman filter (AKF), which adaptively update the state and noise covariances. Regarding the estimation results, the mean absolute errors (MAEs) of SOC and SOT estimation are controlled within 1% and 0.4 ​°C at two temperatures, indicating that the co-estimation method yields superior prediction performance in a wide temperature range of 5–35 ​°C.

On Exploring the Potential of Quantum Auto-Encoder for Learning Quantum Systems.

The frequent interactions between quantum computing and machine learning revolutionize both fields. One prototypical achievement is the quantum auto-encoder (QAE), as the leading strategy to relieve the curse of dimensionality ubiquitous in the quantum world. Despite its attractive capabilities, practical applications of QAE have yet largely unexplored. To narrow this knowledge gap, here, we devise three effective QAE-based learning protocols to address three classically computational hard learning problems when learning quantum systems, which are low-rank state fidelity estimation, quantum Fisher information (QFI) estimation, and Gibbs state preparation. Attributed to the versatility of QAE, our proposals can be readily executed on near-term quantum machines. Besides, we analyze the error bounds of the trained protocols and showcase the necessary conditions to provide practical utility from the perspective of complexity theory. We conduct numerical simulations to confirm the effectiveness of the proposed three protocols. This work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.

Benchmarking Quantum Simulators Using Ergodic Quantum Dynamics.

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced spatiotemporal control. Our protocol relies on universal fluctuations emerging from generic Hamiltonian dynamics, which we discover in the present work. It does not require fine-tuned control over state preparation, quantum evolution, or readout capability, while achieving near optimal sample complexity: a percent-level precision is obtained with ∼10^{3} measurements, independent of system size. Furthermore, the accuracy of our fidelity estimation improves exponentially with increasing system size. We numerically demonstrate our protocol in a variety of quantum simulator platforms, including quantum gas microscopes, trapped ions, and Rydberg atom arrays. We discuss applications of our method for tasks such as multiparameter estimation of quantum states and processes.

Simultaneous single-qubit driving of semiconductor spin qubits at the fault-tolerant threshold

Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

Scalable and Flexible Classical Shadow Tomography with Tensor Networks

Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of a quantum state with few measurements. Two classical shadow protocols have been extensively studied in the literature: the single-qubit (local) Pauli measurement, which is well suited for predicting local operators but inefficient for large operators; and the global Clifford measurement, which is efficient for low-rank operators but infeasible on near-term quantum devices due to the extensive gate overhead. In this work, we demonstrate a scalable classical shadow tomography approach for generic randomized measurements implemented with finite-depth local Clifford random unitary circuits, which interpolates between the limits of Pauli and Clifford measurements. The method combines the recently proposed locally-scrambled classical shadow tomography framework with tensor network techniques to achieve scalability for computing the classical shadow reconstruction map and evaluating various physical properties. The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead and is friendly to noisy intermediate-scale quantum (NISQ) devices. We show that the shallow-circuit measurement protocol provides immediate, exponential advantages over the Pauli measurement protocol for predicting quasi-local operators. It also enables a more efficient fidelity estimation compared to the Pauli measurement.

A Survey of Quantum Entanglement Routing Protocols—Challenges for Wide‐Area Networks

AbstractIn this paper, the key challenges (loss due to distance, entanglement routing, multi‐commodities) for the coming quantum internet, relying on entanglement of quantum bits (for short, qubits) on top of an existing network, are analyzed. A unifying framework enabling to compare the various entanglement distribution, purification, and routing protocols published so far is presented. With regard to entanglement routing, the introduction of different time windows will be essential in order to cope efficiently with the main challenges like complex route calculation and fidelity estimation on the one hand, actual entanglement route selection and entangled photon generation on the other hand. For a roll‐out on top of existing transmission networks, all the research publications for the last 20 years start to cover pretty well the global scheme. Nevertheless, open questions remain, like the actual advantage of some task execution prior to the online quantum path selection, or the design of algorithms approximating the multi‐commodities flow optimization problem, or the issue of dealing with a processing time not much longer than the qubit life time.

Nonstabilizerness determining the hardness of direct fidelity estimation

In this work, we show how the resource theory of nonstabilizerness quantifies the hardness of direct fidelity estimation protocols. In particular, the resources needed for a direct fidelity estimation conducted on generic states, such as Pauli fidelity estimation and shadow fidelity estimation protocols, grow exponentially with the stabilizer R\'enyi entropy. Remarkably, these protocols are shown to be feasible only for those states that are useless to attain any quantum speedup or advantage. This result suggests the impossibility of estimating efficiently fidelity for generic states and, at the same time, leaves the window open to those protocols specialized at directly estimating the fidelity of particular states. We then extend our results to quantum evolutions, showing that the resources needed to certify the quality of the implementation of a given unitary $U$ are governed by the nonstabilizerness in the Choi state associated with $U$, which is shown to possess a profound connection with out-of-time order correlators.

Nondestructive verification of entangled states via fidelity witnessing

Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation can be employed to characterize states. Here we propose several methods to directly distinguish between two different sets of states, e.g. if their fidelity is above or below a certain threshold value. This turns out to be significantly more efficient, and importantly keeps the verified states intact. We make use of auxiliary entanglement or an ensemble of larger size, where we operate on the whole ensemble, but measure only a small fraction where information has been concentrated. For certain state families, we demonstrate that such an approach can even outperform optimal methods that collectively measure directly a fixed fraction of the ensemble.

Preparing random states and benchmarking with many-body quantum chaos.

Producing quantum states at random has become increasingly important in modern quantum science, with applications being both theoretical and practical. In particular, ensembles of such randomly distributed, but pure, quantum states underlie our understanding of complexity in quantum circuits1 and black holes2, and have been used for benchmarking quantum devices3,4 in tests of quantum advantage5,6. However, creating random ensembles has necessitated a high degree of spatio-temporal control7-12 placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization13. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 104 experimental samples. This method has broad applicability, as we demonstrate for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analogue and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics14 and enables applications of this concept in a much wider context4,5,9,10,15-20.

On the learnability of quantum state fidelity

Current quantum processing technology is generally noisy with a limited number of qubits, stressing the importance of quantum state fidelity estimation. The complexity of this problem is mainly due to not only accounting for single gates and readout errors but also for interactions among which. Existing methods generally rely on either reconstructing the given circuit state, ideal state, and computing the distance of which; or forcing the system to be on a specific state. Both rely on conducting circuit measurements, in which computational efficiency is traded off with obtained fidelity details, requiring an exponential number of experiments for full information. This paper poses the question: Is the mapping between a given quantum circuit and its state fidelity learnable? If learnable, this would be a step towards an alternative approach that relies on machine learning, providing much more efficient computation. To answer this question, we propose three deep learning models for 1-, 3-, and 5-qubit circuits and experiment on the following real-quantum processors: ibmq_armonk (1-qubit), ibmq_lima (5-qubit) and ibmq_quito (5-qubit) backends, respectively. Our models achieved a mean correlation factor of 0.74, 0.67 and 0.66 for 1-, 3-, and 5-qubit random circuits, respectively, with the exponential state tomography method. Additionally, our 5-qubit model outperforms simple baseline state fidelity estimation method on three quantum benchmarks. Our method, trained on random circuits only, achieved a mean correlation factor of 0.968 while the baseline method achieved 0.738. Furthermore, we investigate the effect of dynamic noise on state fidelity estimation. The correlation factor substantially improved to 0.82 and 0.74 for the 3- and 5-qubit models, respectively. The results show that machine learning is promising for predicting state fidelity from circuit representation and this work may be considered a step towards efficient end-to-end learning.