Noise Resilience Research Articles

Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well-known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a variational quantum eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on noisy intermediate-scale quantum devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.

A local-global shape characterization scheme using quadratic Bezier triangle aiding retrieval

Shape characterization plays a highly prominent role in retrieval and relies extremely upon descriptors inbuilt with lightweight operations and compaction qualities. However, realizing such a simple and robust shape descriptor capable of dealing with noise, variations in brightness, and deformations pose a significant challenge. In this regard, a simple and effective shape descriptor using the Quadratic Bezier Triangle (QBT) targeting shape matching and retrieval is presented in this work. The mechanism commences with triangular tessellation of each image followed by determining their side-wise intensity differences that are then mapped to QBT vertices to yield the order-wise control points. The maxima of the resulting points are transformed into the binary equivalent of the given shape that is compacted into octal values. Later, these localized values are globally transformed into shape histograms to yield the QBT-based Feature (QBTF) descriptor representing the given input. QBTFs performance is exhaustively analyzed in terms of Bulls Eye Retrieval (BER) score and classification accuracy using the public datasets namely Kimia-99, MPEG-7 CE-1 part B, PHOS, and Tari-1000. Relative BER investigations witnessed across diverse datasets reveal a consistent and improved score of 93% achieved by this scheme over its peers. Mathematical analysis of invariance, noise resilience, and the complexities involved in realizing QBTF, establish the robustness and suitability of this scheme for real-time shape description.

Long-time simulations for fixed input states on quantum hardware

Publicly accessible quantum computers open the exciting possibility of experimental dynamical quantum simulations. While rapidly improving, current devices have short coherence times, restricting the viable circuit depth. Despite these limitations, we demonstrate long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on Rigetti and IBM quantum computers, maintaining a fidelity over 0.9 for 150 times longer than is possible using the iterated Trotter method. Our simulations use an algorithm we call fixed state Variational Fast Forwarding (fsVFF). Recent work has shown an approximate diagonalization of a short time evolution unitary allows a fixed-depth simulation. fsVFF substantially reduces the required resources by only diagonalizing the energy subspace spanned by the initial state, rather than over the total Hilbert space. We further demonstrate the viability of fsVFF through large numerical simulations, and provide an analysis of the noise resilience and scaling of simulation errors.

Cardiac phase-resolved late gadolinium enhancement imaging.

Late gadolinium enhancement (LGE) with cardiac magnetic resonance (CMR) imaging is the clinical reference for assessment of myocardial scar and focal fibrosis. However, current LGE techniques are confined to imaging of a single cardiac phase, which hampers assessment of scar motility and does not allow cross-comparison between multiple phases. In this work, we investigate a three step approach to obtain cardiac phase-resolved LGE images: (1) Acquisition of cardiac phase-resolved imaging data with varying T1 weighting. (2) Generation of semi-quantitative maps for each cardiac phase. (3) Synthetization of LGE contrast to obtain functional LGE images. The proposed method is evaluated in phantom imaging, six healthy subjects at 3T and 20 patients at 1.5T. Phantom imaging at 3T demonstrates consistent contrast throughout the cardiac cycle with a coefficient of variation of 2.55 ± 0.42%. In-vivo results show reliable LGE contrast with thorough suppression of the myocardial tissue is healthy subjects. The contrast between blood and myocardium showed moderate variation throughout the cardiac cycle in healthy subjects (coefficient of variation 18.2 ± 3.51%). Images were acquired at 40–60 ms and 80 ms temporal resolution, at 3T and 1.5, respectively. Functional LGE images acquired in patients with myocardial scar visualized scar tissue throughout the cardiac cycle, albeit at noticeably lower imaging resolution and noise resilience than the reference technique. The proposed technique bears the promise of integrating the advantages of phase-resolved CMR with LGE imaging, but further improvements in the acquisition quality are warranted for clinical use.

Quantum and non-local effects offer over 40 dB noise resilience advantage towards quantum lidar.

Non-local effects have the potential to radically move forward quantum enhanced imaging to provide an advantage over classical imaging not only in laboratory environments but practical implementation. In this work, we demonstrate a 43dB higher signal-to-noise ratio (SNR) using a quantum enhanced LiDAR based on time-frequency entanglement compared with a classical phase-insensitive quantum imaging system. Our system can tolerate more than 3 orders of magnitude higher noise than classical single-photon counting quantum imaging systems before detector saturation with a detector dead time of 25ns. To achieve these advantages, we use non-local cancellation of dispersion to take advantage of the strong temporal correlations in photon pairs in spite of the orders of magnitude larger detector temporal uncertainty. We go on to incorporate this scheme with purpose-built scanning collection optics to image non-reflecting targets in an environment with noise.

Damage localization and characterization using one-dimensional convolutional neural network and a sparse network of transducers

Early damage identification and continuous system monitoring save dramatically maintenance costs and increase the lifespan of priceless structures. Convolutional neural networks (CNNs) have attracted the attention of the structural health monitoring (SHM) community in recent years due to their great potential for identifying underlying data patterns. However, employing two-dimensional convolutional layers in a CNN necessitates the use of strong computing resources. Therefore, based on the present state-of-the-art technical solutions, a two-dimensional CNN is not suitable for real-time SHM applications with stand-alone processing units. One-dimensional convolutional networks (1D-CNN) have recently been employed in Ultrasonic Guided Wave-based (UGW-based) damage detection to address the aforementioned disadvantage. In this paper, a methodology for damage assessment at three levels – detection, localization, and characterization – based on 1D-CNN is put forward. Furthermore, the sequence length of the time-domain signals is significantly shortened by the application of a novel approach for processing them. Additionally, it is shown to what extend this method can improve the distinguishability between datapoints obtained from various damage scenarios. Consequently, by reducing the dimensionality of the problem, the proposed approach significantly reduces the memory usage of the classification algorithm. Experimental measurements as well as Numerical simulations, in which various damage scenarios such as corrosion, circular hole and cracks have been considered, are carried out to evaluate the efficacy of the proposed algorithm. It is shown that the suggested approach has benefits in terms of true classification rate of instances (above 93 percent for detection, localization, and characterization), computing time, in-situ monitoring, and noise resilience.

Numerical optimization of amplitude-modulated pulses in microwave-driven entanglement generation

Microwave control of trapped ions can provide an implementation of high-fidelity two-qubit gates free from errors induced by photon scattering. Furthermore, microwave conductors may be embedded into a scalable trap structure, providing the chip-level integration of control that is desirable for scaling. Recent developments have demonstrated how amplitude modulation of the gate drive can permit a two-qubit entangling operation to become robust against motional mode noise and other experimental imperfections. Here, we discuss a method for the numerical optimization of the microwave pulse envelope to produce gate pulses with noise resilience, considerably faster operation and high energy efficiency.

Robust nonadiabatic geometric quantum computation by dynamical correction

Besides the intrinsic noise resilience property, nonadiabatic geometric phases are of the fast evolution nature, and thus can naturally be used in constructing quantum gates with excellent performance, i.e., the so-called nonadiabatic geometric quantum computation (NGQC). However, previous single-loop NGQC schemes are sensitive to the operational control error, i.e., the $X$ error, due to the limitations of the implementation. Here, we propose a robust scheme for NGQC combining with the dynamical correction technique, which still uses only simplified pulses, and thus being experimental friendly. We numerically show that our scheme can greatly improve the gate robustness in previous protocols, retaining the intrinsic merit of geometric phases. Furthermore, to fight against the dephasing noise, due to the $Z$ error, we can incorporate the decoherence-free subspace encoding strategy. In this way, our scheme can be robust against both types of errors. Finally, we also propose how to implement the scheme with encoding on superconducting quantum circuits with experimentally demonstrated technology. Therefore, due to the intrinsic robustness, our scheme provides a promising alternation for the future scalable fault-tolerant quantum computation.

Implementation of Single-Qubit Gates via Parametric Modulation in the Majorana Transmon

Analysis shows that controlling Majorana transmon qubit via a gate-based parametric modulation can lead to fidelities close to 99.99%, qubit coherence in the millisecond timescale, and remarkable noise resilience.

A Perspective on Passive Human Sensing with Bluetooth.

Passive human sensing approaches based on the analysis of the radio signals emitted by the most common wireless communication technologies have been steadily gaining momentum during the last decade. In this context, the Bluetooth technology, despite its widespread adoption in mobile and IoT applications, so far has not received all the attention it deserves. However, the introduction of the Bluetooth direction finding feature and the application of Artificial Intelligence techniques to the processing and analysis of the wireless signal for passive human sensing pave the way for novel Bluetooth-based passive human sensing applications, which will leverage Bluetooth Low Energy features, such as low power consumption, noise resilience, wide diffusion, and relatively low deployment cost. This paper provides a reasoned analysis of the data preprocessing and classification techniques proposed in the literature on Bluetooth-based remote passive human sensing, which is supported by a comparison of the reported accuracy results. Building on such results, the paper also identifies and discusses the multiple factors and operating conditions that explain the different accuracy values achieved by the considered techniques, and it draws the main research directions for the near future.

Resilient Biomedical Systems Design Under Noise Using Logic-Based Machine Learning

Increased reliance on electronic health records and plethora of new sensor technologies has enabled the use of machine learning (ML) in medical diagnosis. This has opened up promising opportunities for faster and automated decision making, particularly in early and repetitive diagnostic routines. Nevertheless, there are also increased possibilities of data aberrance arising from environmentally induced noise. It is vital to create ML models that are resilient in the presence of data noise to minimize erroneous classifications that could be crucial. This study uses a recently proposed ML algorithm called the Tsetlin machine (TM) to study the robustness against noise-injected medical data. We test two different feature extraction methods, in conjunction with the TM, to explore how feature engineering can mitigate the impact of noise corruption. Our results show the TM is capable of effective classification even with a signal-to-noise ratio (SNR) of −15dB as its training parameters remain resilient to noise injection. We show that high testing data sensitivity can still be possible at very low SNRs through a balance of feature distribution–based discretization and a rule mining algorithm used as a noise filtering encoding method. Through this method we show how a smaller number of core features can be extracted from a noisy problem space resulting in reduced ML model complexity and memory footprint—in some cases up to 6x fewer training parameters while retaining equal or better performance. In addition, we investigate the cost of noise resilience in terms of energy when compared with recently proposed binarized neural networks.

Direct data-driven forecast of local turbulent heat flux in Rayleigh–Bénard convection

A combined convolutional autoencoder–recurrent neural network machine learning model is presented to directly analyze and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh–Bénard convection flow at Prandtl number Pr=7 and Rayleigh number Ra=107. Two recurrent neural networks are applied for the temporal advancement of turbulent heat transfer data in the reduced latent data space, an echo state network, and a recurrent gated unit. Thereby, our work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework. This suggests that the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to coarse grids of larger-scale computational models, such as global circulation models for atmosphere and ocean.

Applications of fractional calculus in computer vision: A survey

Fractional calculus is an abstract idea exploring interpretations of differentiation having non-integer order. For a very long time, it was considered as a topic of mere theoretical interest. However, the introduction of several useful definitions of fractional derivatives has extended its domain to applications. Supported by computational power and algorithmic representations, fractional calculus has emerged as a multifarious domain. It has been found that the fractional derivatives are capable of incorporating memory into the system and thus suitable to improve the performance of locality-aware tasks such as image processing and computer vision in general. This article presents an extensive survey of fractional-order derivative-based techniques that are used in computer vision. It briefly introduces the basics and presents applications of the fractional calculus in six different domains viz. edge detection, optical flow, image segmentation, image de-noising, image recognition, and object detection. The fractional derivatives ensure noise resilience and can preserve both high and low-frequency components of an image. The relative similarity of neighboring pixels can get affected by an error, noise, or non–homogeneous illumination in an image. In that case, the fractional differentiation can model special similarities and help compensate for the issue suitably. The fractional derivatives can be evaluated for discontinuous functions, which help estimate discontinuous optical flow. The order of the differentiation also provides an additional degree of freedom in the optimization process. This study shows the successful implementations of fractional calculus in computer vision and contributes to bringing out challenges and future scopes.

Remotely Establishing Polarization Entanglement Over Noisy Polarization Channels

The faithful distribution of entanglement over noisy channels is a vital prerequisite for many quantum technological applications. Quantum information can be encoded in different degrees of freedom (DOF) of photons, where each encoding comes with its own advantages and disadvantages with respect to noise resilience and practicality in manipulation. In this work, we experimentally implement a deterministic entanglement purification protocol that allows us to faithfully distribute entanglement in one DOF over a noisy channel and then remotely transfer it to another DOF for manipulation. In particular, we distribute robust energy-time entanglement and transfer it to polarization entanglement at the communicating parties. The remotely obtained polarization state is independent of the polarization noise during distribution and reaches fidelities to a Bell state of up to 97.6%. Our scheme enables robust and efficient polarization entanglement distribution in the presence of arbitrary polarization noise, which is relevant for future large-scale quantum networks.

Protocol for generation of high-dimensional entanglement from an array of non-interacting photon emitters

Encoding high-dimensional quantum information into single photons can provide a variety of benefits for quantum technologies, such as improved noise resilience. However, the efficient generation of on-demand, high-dimensional entanglement was thought to be out of reach for current and near-future photonic quantum technologies. We present a protocol for the near-deterministic generation of N-photon, d-dimensional photonic Greenberger–Horne–Zeilinger (GHZ) states using an array of d non-interacting single-photon emitters. We analyse the impact on performance of common sources of error for quantum emitters, such as photon spectral distinguishability and temporal mismatch, and find they are readily correctable with time-resolved detection to yield high fidelity GHZ states of multiple qudits. When applied to a quantum key distribution scenario, our protocol exhibits improved loss tolerance and key rates when increasing the dimensionality beyond binary encodings.

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems.

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Geometric entanglement of a photon and spin qubits in diamond

Geometric nature, which appears in photon polarization, also appears in spin polarization under a zero magnetic field. These two polarized quanta, one travelling in vacuum and the other staying in matter, behave the same as geometric quantum bits or qubits, which are promising for noise resilience compared to the commonly used dynamic qubits. Here we show that geometric photon and spin qubits are entangled upon spontaneous emission with the help of the spin − orbit entanglement inherent in a nitrogen-vacancy center in diamond. The geometric spin qubit is defined in a degenerate subsystem of spin triplet electrons and manipulated with a polarized microwave. An experiment shows an entanglement state fidelity of 86.8%. The demonstrated entangled emission, combined with previously demonstrated entangled absorption, generates purely geometric entanglement between remote matters in a process that is insensitive of time, frequency, and space mode matching, which paves the way for building a noise-resilient quantum repeater network or a quantum internet.

Engineering high-coherence superconducting qubits

Advances in materials science and engineering have played a central role in the development of classical computers and will undoubtedly be critical in propelling the maturation of quantum information technologies. In approaches to quantum computation based on superconducting circuits, as one goes from bulk materials to functional devices, amorphous films and non-equilibrium excitations — electronic and phononic — are introduced, leading to dissipation and fluctuations that limit the computational power of state-of-the-art qubits and processors. In this Review, the major sources of decoherence in superconducting qubits are identified through an exploration of seminal qubit and resonator experiments. The proposed microscopic mechanisms associated with these imperfections are summarized, and directions for future research are discussed. The trade-offs between simple qubit primitives based on a single Josephson tunnel junction and more complex designs that use additional circuit elements, or new junction modalities, to reduce sensitivity to local noise sources are discussed, particularly in the context of materials optimization strategies for each architecture. Superconducting qubits hold great promise for quantum computing, and recently there have been dramatic improvements in both coherence times and the power of quantum processors. This Review explores how the path forward involves balancing circuit complexity and materials perfection, eliminating defects while designing qubits with engineered noise resilience.

Evaluating the noise resilience of variational quantum algorithms

We simulate the effects of different types of noise in state preparation circuits of variational quantum algorithms. We first use a variational quantum eigensolver to find the ground state of a Hamiltonian in presence of noise, and adopt two quality measures in addition to the energy, namely fidelity and concurrence. We then extend the task to the one of constructing, with a layered quantum circuit ansatz, a set of general random target states. We determine the optimal circuit depth for different types and levels of noise, and observe that the variational algorithms mitigate the effects of noise by adapting the optimised parameters. We find that the inclusion of redundant parameterised gates makes the quantum circuits more resilient to noise. For such overparameterised circuits different sets of parameters can result in the same final state in the noiseless case, which we denote as parameter degeneracy. Numerically, we show that this degeneracy can be lifted in the presence of noise, with some states being significantly more resilient to noise than others. We also show that the average deviation from the target state is linear in the noise level, as long as this is small compared to a circuit-dependent threshold. In this region the deviation is well described by a stochastic model. Above the threshold, the optimisation can converge to states with largely different physical properties from the true target state, so that for practical applications it is critical to ensure that noise levels are below this threshold.

An Improved Background Normalization Algorithm for Noise Resilience in Low Frequency

Background normalization algorithms attempt to suppress the ambient and self-noise during the measurements of sonar, which enhance the detection performance and the display effect of weak signals. Conventional background normalization methods are usually sensitive to the accuracy of prior set filtering interval and threshold, while significant noise is still detected in low frequency. In this paper, an improved background normalization algorithm is proposed by thresholding the processing interval between several local peak values and local valley values. Compared to the existing scenarios, the proposed approach automatically calculates the filtering interval and threshold, with substantial resilience to the noise level in low frequency. Experimental results illustrate the effectiveness of our algorithm.