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At least 145 records · Page 8

Variational quantum algorithms

Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers, owing to the extremely high computational cost. Quantum computers promise a solution, although fault-tolerant quantum computers will probably not be available in the near future. Current quantum devices have serious constraints, including limited numbers of qubits and noise processes that limit circuit depth. Variational quantum algorithms (VQAs), which use a classical optimizer to train a parameterized quantum circuit, have emerged as a leading strategy to address these constraints. VQAs have now been proposed for essentially all applications that researchers have envisaged for quantum computers, and they appear to be the best hope for obtaining quantum advantage. Nevertheless, challenges remain, including the trainability, accuracy and efficiency of VQAs. Here we overview the field of VQAs, discuss strategies to overcome their challenges and finally, we highlight the exciting prospects for using them to obtain quantum advantage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mid-circuit correction of correlated phase errors using an array of spectator qubits

Scaling up invariably error-prone quantum processors is a formidable challenge. Although quantum error correction ultimately promises fault-tolerant operation, the required qubit overhead and error thresholds are daunting. In a complementary proposal, colocated, auxiliary “spectator” qubits act as in situ probes of noise and enable real-time, coherent corrections of data qubit errors. We used an array of cesium spectator qubits to correct correlated phase errors on an array of rubidium data qubits. By combining in-sequence readout, data processing, and feedforward operations, these correlated errors were suppressed within the execution of the quantum circuit. The protocol is broadly applicable to quantum information platforms and establishes key tools for scaling neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time processing and feedforward, and coherent mid-circuit reloading of atomic qubits.

Science & Technology - Other Topics↗

Majorana pair based qubits for fault tolerant quantum computing architecture using superconducting gold surface states

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Here we disclose a metal-based heterostructure platform to produce these Majorana zero modes which utilizes the surface states of certain metals in combination with a ferromagnetic insulator and a superconductor. This platform has the advantage of having a robust energy scale and the possibility of realizing complex circuit designs using lithographic methods. The Majorana zero modes are interrogated using planar tunnel junctions and electrostatic gates to selectively tunnel into designated pairs of Majorana zero modes. We give example of qubit designs and circuits that are particularly suitable for the metal-based heterostructures.

Moodera, Jagadeesh S.↗

Improved Charge Sensing on a SiMOS Double Quantum Dot using a Cryogenic Skipper Readout ASIC (Quandarum)

Major outstanding questions in high-energy physics such as the nature of dark matter and the existence of interactions beyond the standard model require new measurement techniques which are extremely sensitive to minute electromagnetic fields. An array of entangled spin qubits is a promising system for building novel detectors due to its combination of sensitivity and controllability. CMOS-based electron spin qubits, which have demonstrated the operational requirements for fault-tolerant quantum computing [1], offer a particular opportunity due to their compatibility with classical electronics, which allows the leveraging of decades of development of low-noise cryogenic detectors for physics. In this work, we combine a SiMOS double-quantum dot device architecture with a state-of-the-art cryoelectronic readout circuit [2-3] aimed to demonstrate improved charge readout using a single-electron transistor (SET). We identify the design characteristics for an SET that facilitate the use of on-chip classical electronics as a low-power, high-bandwidth first amplification stage and explore opportunities for sensor-readout co-design to minimize noise. This is the first of a series of steps to demonstrate high-fidelity readout of a large array of spin qubit with enough sensitivity to probe processes of interest for the investigation of beyond-standard-model physics.

Quinn, Adam [Fermilab]↗

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗

Quantum Zeno Monte Carlo for computing observables

The recent development of logical quantum processors marks a pivotal transition from the noisy intermediate-scale quantum (NISQ) era to the fault-tolerant quantum computing (FTQC) era. These devices have the potential to address classically challenging problems with polynomial computational time using quantum properties. However, they remain susceptible to noise, necessitating noise resilient algorithms. We introduce Quantum Zeno Monte Carlo (QZMC), a classical-quantum hybrid algorithm that demonstrates resilience to device noise and Trotter errors while showing polynomial computational cost for a gapped system. QZMC computes static and dynamic properties without requiring initial state overlap or variational parameters, offering reduced quantum circuit depth.

Han, Mancheon [Korea Institute for Advanced Study ↗

Acoustic Tomography of the Atmosphere: A Large-Eddy Simulation Sensitivity Study

Accurate measurement of atmospheric turbulent fluctuations is critical for understanding environmental dynamics and improving models in applications such as wind energy. Advanced remote sensing technologies are essential for capturing instantaneous velocity and temperature fluctuations. Acoustic tomography (AT) offers a promising approach that utilizes sound travel times between an array of transducers to reconstruct turbulence fields. This study presents a systematic evaluation of the time-dependent stochastic inversion (TDSI) algorithm for AT using synthetic travel-time measurements derived from large-eddy simulation (LES) fields under both neutral and convective atmospheric boundary-layer conditions. Unlike prior work that relied on field observations or idealized fields, the LES framework provides a ground-truth atmospheric state, enabling quantitative assessment of TDSI retrieval reliability, sensitivity to travel-time measurement noise, and dependence on covariance model parameters and temporal data integration. A detailed sensitivity analysis was conducted to determine the best-fit model parameters, identify the tolerance thresholds for parameter mismatch, and establish a maximum spatial resolution. The TDSI algorithm successfully reconstructed large-scale velocity and temperature fluctuations with root mean square errors ( RMSE s) below 0.35 m/s and 0.12 K, respectively. Spectral analysis established a maximum spatial resolution of approximately 1.4 m, and reconstructions remained robust for travel-time measurement uncertainties up to 0.002 s. These findings provide critical insights into the operational limits of TDSI and inform future applications of AT for atmospheric turbulence characterization and system design.

17 WIND ENERGY↗

Electronic control circuits: A compilation

A compilation of technical R and D information on circuits and modular subassemblies is presented as a part of a technology utilization program. Fundamental design principles and applications are given. Electronic control circuits discussed include: anti-noise circuit; ground protection device for bioinstrumentation; temperature compensation for operational amplifiers; hybrid gatling capacitor; automatic signal range control; integrated clock-switching control; and precision voltage tolerance detector.

Source record↗

The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter

The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.

Herren, Kenneth A.↗

Optimising the processing and storage of visibilities using lossy compression

The next-generation radio astronomy instruments are providing a massive increase in sensitivity and coverage, largely through increasing the number of stations in the array and the frequency span sampled. The two primary problems encountered when processing the resultant avalanche of data are the need for abundant storage and the constraints imposed by I/O, as I/O bandwidths drop significantly on cold storage. An example of this is the data deluge expected from the SKA Telescopes of more than 60 PB per day, all to be stored on the buffer filesystem. While compressing the data is an obvious solution, the impacts on the final data products are hard to predict. In this paper, we chose an error-controlled compressor – MGARD – and applied it to simulated SKA-Mid and real pathfinder visibility data, in noise-free and noise-dominated regimes. As the data have an implicit error level in the system temperature, using an error bound in compression provides a natural metric for compression. MGARD ensures the compression incurred errors adhere to the user-prescribed tolerance. To measure the degradation of images reconstructed using the lossy compressed data, we proposed a list of diagnostic measures, exploring the trade-off between these error bounds and the corresponding compression ratios, as well as the impact on science quality derived from the lossy compressed data products through a series of experiments. We studied the global and local impacts on the output images for continuum and spectral line examples. We found relative error bounds of as much as 10%, which provide compression ratios of about 20, have a limited impact on the continuum imaging as the increased noise is less than the image RMS, whereas a 1% error bound (compression ratio of 8) introduces an increase in noise of about an order of magnitude less than the image RMS. For extremely sensitive observations and for very precious data, we would recommend a 0.1% error bound with compression ratios of about 4. These have noise impacts two orders of magnitude less than the image RMS levels. At these levels, the limits are due to instabilities in the deconvolution methods. We compared the results to the alternative compression tool DYSCO, in both the impacts on the images and in the relative flexibility. MGARD provides better compression for similar error bounds and has a host of potentially powerful additional features.

Techniques: interferometric↗

Wide-Field Optic for Autonomous Acquisition of Laser Link

An innovation reported in Two-Camera Acquisition and Tracking of a Flying Target, NASA Tech Briefs, Vol. 32, No. 8 (August 2008), p. 20, used a commercial fish-eye lens and an electronic imaging camera for initially locating objects with subsequent handover to an actuated narrow-field camera. But this operated against a dark-sky background. An improved solution involves an optical design based on custom optical components for the wide-field optical system that directly addresses the key limitations in acquiring a laser signal from a moving source such as an aircraft or a spacecraft. The first challenge was to increase the light collection entrance aperture diameter, which was approximately 1 mm in the first prototype. The new design presented here increases this entrance aperture diameter to 4.2 mm, which is equivalent to a more than 16 times larger collection area. One of the trades made in realizing this improvement was to restrict the field-of-view to +80 deg. elevation and 360 azimuth. This trade stems from practical considerations where laser beam propagation over the excessively high air mass, which is in the line of sight (LOS) at low elevation angles, results in vulnerability to severe atmospheric turbulence and attenuation. An additional benefit of the new design is that the large entrance aperture is maintained even at large off-axis angles when the optic is pointed at zenith. The second critical limitation for implementing spectral filtering in the design was tackled by collimating the light prior to focusing it onto the focal plane. This allows the placement of the narrow spectral filter in the collimated portion of the beam. For the narrow band spectral filter to function properly, it is necessary to adequately control the range of incident angles at which received light intercepts the filter. When this angle is restricted via collimation, narrower spectral filtering can be implemented. The collimated beam (and the filter) must be relatively large to reduce the incident angle down to only a few degrees. In the presented embodiment, the filter diameter is more than ten times larger than the entrance aperture. Specifically, the filter has a clear aperture of about 51 mm. The optical design is refractive, and is comprised of nine custom refractive elements and an interference filter. The restricted maximum angle through the narrow-band filter ensures the efficient use of a 2-nm noise equivalent bandwidth spectral width optical filter at low elevation angles (where the range is longest), at the expense of less efficiency for high elevations, which can be tolerated because the range at high elevation angles is shorter. The image circle is 12 mm in diameter, mapped to 80 x 360 of sky, centered on the zenith.

Page, Norman A.↗

Quantitative 14 N NMR with Monte Carlo Uncertainty Analysis of Nitrate/Nitrite in Alkaline Nuclear Waste

While monitoring of nitrate and nitrite concentrations is important for managing corrosion in nuclear waste systems, existing analytical methods are hindered by turbidity, spectral interference, and delays from sample handling. Here, we demonstrate quantitative 14 N nuclear magnetic resonance (qNMR) spectroscopy as a direct, matrix-tolerant approach for nitrate and nitrite detection at natural abundance. Monte Carlo resampling was integrated into the workflow to quantify random error, establish precision–time tradeoffs, and separate noise-limited uncertainty from systematic bias arising from shimming, transmitter offset, or excitation pulse conditions. Quantification of nitrate and nitrite were validated in controlled alkaline matrix challenges and in 18-component Hanford-type simulants. These results establish 14 N qNMR as a practical, uncertainty-bounded tool for monitoring redox-active nitrogen species in chemically complex environments and provide a generalizable framework for quantitative analysis of quadrupolar nuclei.

Graham, Trent R. [Pacific Northwest National Labor↗

A Computational Framework for Simulations of Dissipative Nonadiabatic Dynamics on Hybrid Oscillator-Qubit Quantum Devices

Here, we introduce a computational framework for simulating nonadiabatic vibronic dynamics on circuit quantum electrodynamics (cQED) platforms. Our approach leverages hybrid oscillator-qubit quantum hardware with midcircuit measurements and resets, enabling the incorporation of environmental effects such as dissipation and dephasing. To demonstrate its capabilities, we simulate energy transfer dynamics in a triad model of photosynthetic chromophores inspired by natural antenna systems. We specifically investigate the role of dissipation during the relaxation dynamics following photoexcitation, where electronic transitions are coupled to the evolution of quantum vibrational modes. Our results indicate that hybrid oscillator-qubit devices, operating with noise levels below the intrinsic dissipation rates of typical molecular antenna systems, can achieve the simulation fidelity required for practical computations on near-term and early fault-tolerant quantum computing platforms.

Hamiltonians↗

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O(2^{nQ})$ entangling gates on a quantum computer with $n_Q$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires $n_Q – 1$ entangling gates, the minimal number necessary to create an entangled state of all $n_Q$ qubits. This is compared with the $2^{nQ – 1} + n_Q – 3 + δ_{nQ, 1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site $(n_Q = 4)$, two-site $(n_Q = 3)$, and three-site ( n Q = 3 ) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with $n_Q = 3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. Further, in performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum $(|\textbf{0}\gg^{\bigotimes nQ})$ and in medium ($n_Q –1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Importance of Contrast-to-Noise Ratio Sensitivity Function in Nondestructive Evaluation

A reliable nondestructive evaluation (NDE) technique provides minimum 90% probability of detection (POD) with 95% confidence for detection of cracklike flaws of a specific size. This requirement comes from fracture control. Fracture control is a risk assessment and control approach for preventing structural failure of fracture critical hardware during its service life. One of the approaches of fracture control is damage tolerance safe life analysis, which assumes that NDE reliably detectable size flaw may exist in the hardware post nondestructive evaluation. Analysis and/or testing are performed to verify that the hardware will not fail during its service life despite existence of such a flaw. NDE methods are conventionally qualified by probability of detection (POD) demonstration testing to ensure reliable flaw detection. Here, a novel and alternative to POD flaw detection reliability approach that uses contrast-to-noise ratio (CNR) is given. The approach uses CNR sensitivity function (SF) and CNR. CNR SF is the minimum CNR needed for reliable flaw detection as a function of certain flaw indication characteristics. Primary difference between POD approaches and CNR flaw detection reliability approach is resolution of flaw detection system. POD approach does not account for the resolution of the system, while CNR approach accounts for the flaw detection resolution. Resolution is determined from the modulation transfer function (MTF) of the flaw detection system. CNR flaw detection reliability approach emphasizes quantitative assessment of “how well each flaw indication is detected”. Therefore, CNR approach is helpful in reducing number of flaws in the sample used in NDE procedure qualification, resulting in cost and time savings. CNR approach is also a case of multi-hit flaw detection analysis which has better flaw detectability size than conventional single-hit flaw detectability. Thus, CNR approach, where applicable, may be superior to conventional POD approach. The paper is an overview of development of CNR modeling, CNR SF modeling and measurement by the author. The paper gives key references to currently used NDE procedure POD qualification approaches including those specific to CNR and CNR SF development in multi-hit flaw detection in NDE. The paper covers core topics in nondestructive evaluation engineering.

Contrast-to-noise ratio↗

Benchmarking quantum logic operations relative to thresholds for fault tolerance

Contemporary methods for benchmarking noisy quantum processors typically measure average error rates or process infidelities. However, thresholds for fault-tolerant quantum error correction are given in terms of worst-case error rates—defined via the diamond norm—which can differ from average error rates by orders of magnitude. One method for resolving this discrepancy is to randomize the physical implementation of quantum gates, using techniques like randomized compiling (RC). In this work, we use gate set tomography to perform precision characterization of a set of two-qubit logic gates to study RC on a superconducting quantum processor. We find that, under RC, gate errors are accurately described by a stochastic Pauli noise model without coherent errors, and that spatially correlated coherent errors and non-Markovian errors are strongly suppressed. We further show that the average and worst-case error rates are equal for randomly compiled gates, and measure a maximum worst-case error of 0.0197(3) for our gate set. Our results show that randomized benchmarks are a viable route to both verifying that a quantum processor’s error rates are below a fault-tolerance threshold, and to bounding the failure rates of near-term algorithms, if—and only if—gates are implemented via randomization methods which tailor noise.

97 MATHEMATICS AND COMPUTING↗

The impact of emerging technologies on an advanced supersonic transport

The effects of advances in propulsion systems, structure and materials, aerodynamics, and systems on the design and development of supersonic transport aircraft are analyzed. Efficient propulsion systems with variable-cycle engines provide the basis for improved propulsion systems; the propulsion efficienies of supersonic and subsonic engines are compared. Material advances consist of long-life damage-tolerant structures, advanced material development, aeroelastic tailoring, and low-cost fabrication. Improvements in the areas of aerodynamics and systems are examined. The environmental problems caused by engine emissions, airport noise, and sonic boom are studied. The characteristics of the aircraft designed to include these technical advances are described.

Driver, C.↗

Design of LQG controllers with reduced parameter sensitivity

A method is presented for improving the tolerance of LQG controllers to parameter errors. The improvement is achieved by introducing terms reflecting the structure of the errors into the LQR cost function and the process and measurement noise models. Adjusting the sizes of these additional terms permits a tradeoff between robustness and nominal performance.

Lin, J. Y.↗