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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
NASA NTRS1992

A domain-specific design architecture for composite material design and aircraft part redesign

Advanced composites have been targeted as a 'leapfrog' technology that would provide a unique global competitive position for U.S. industry. Composites are unique in the requirements for an integrated approach to designing, manufacturing, and marketing of products developed utilizing the new materials of construction. Numerous studies extending across the entire economic spectrum of the United States from aerospace to military to durable goods have identified composites as a 'key' technology. In general there have been two approaches to composite construction: build models of a given composite materials, then determine characteristics of the material via numerical simulation and empirical testing; and experience-directed construction of fabrication plans for building composites with given properties. The first route sets a goal to capture basic understanding of a device (the composite) by use of a rigorous mathematical model; the second attempts to capture the expertise about the process of fabricating a composite (to date) at a surface level typically expressed in a rule based system. From an AI perspective, these two research lines are attacking distinctly different problems, and both tracks have current limitations. The mathematical modeling approach has yielded a wealth of data but a large number of simplifying assumptions are needed to make numerical simulation tractable. Likewise, although surface level expertise about how to build a particular composite may yield important results, recent trends in the KBS area are towards augmenting surface level problem solving with deeper level knowledge. Many of the relative advantages of composites, e.g., the strength:weight ratio, is most prominent when the entire component is designed as a unitary piece. The bottleneck in undertaking such unitary design lies in the difficulty of the re-design task. Designing the fabrication protocols for a complex-shaped, thick section composite are currently very difficult. It is in fact this difficulty that our research will address.

Punch, W. F., III↗
DOE OSTI2026

Diagonal state designs with reconfigurable real-time circuits

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state 3-design based on real-time evolutions under 2-local Hamiltonians. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of many random-phase states. Though the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms. Moreover, we show how to extend our construction to achieve diagonal state designs of arbitrarily high order.

Shen, Yizhi [LBL, Berkeley] (ORCID:000000024160548↗
DOE OSTI2026

Qudit Designs and Where to Find Them

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing exponential separations between classical and quantum query complexity. While unitary designs originating from a group structure, such as the Clifford group, have proven to be incredibly useful for qubit systems, unfortunately, this is no longer true for qudits. In fact, the classification of finite-group representations rules out the existence of unitary 2-designs for arbitrary qudit dimensions. This severely limits the applicability of standard quantum information primitives when it comes to qudit systems. We overcome these limitations with a three-fold contribution. First, we introduce a general technique to construct families of weighted state t-designs in arbitrary qudit dimensions. These weighted state-designs generalize classical shadow tomography protocol from qubits to qudits. Second, we introduce a Clifford character RB that allows us to benchmark the qudit Clifford group in any dimension, including non-prime-power dimensions. And third, we establish bounds on the quantum circuit complexity of generating approximate unitary-designs from native gates in existing quantum hardware such as high-spin and cavity-QED qudits. Our work further highlights the analogy between spin and optical coherent states by proving that spin-GKP codewords form a state 2-design while spin coherent states do not; in direct analogy with the optical case. This work is structured as a pedagogical and self-contained introduction to unitary designs and their applications to qudit systems.

Anand, Namit [NASA, Ames; Unlisted, US] (ORCID:000↗
NASA NTRS2004

Design for a Unitary Graphite Composite Instrument Boom

This paper describes development of a Unitary graphite composite instrument boom that incorporates carpenter-tape like hinges for stowage. While light and stiff, graphite composite is not ordinarily thought of as a flexible material. This design has taken advantage of the stiffness of the composite in tubular geometry, yet leveraged its thin- section behavior to place flexibility at the required locations. Key is the proprietary layup, which results in a tough yet flexible hinge capable of rotating over 90 degrees in each direction. When the boom deploys, there is enough torque to overcome parasitic resistance from harness, etc. It will snap to the fully extended, rigid shape. The design has addressed materials issues such as out-of-plane bending, edge cracking, and interlaminar ply separation.

Alexander, Wes↗
DOE OSTI2024

Approximate 𝑡-Designs in Generic Circuit Architectures

Unitary 𝑡-designs are distributions on the unitary group whose first 𝑡 moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate 𝑡-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of one-dimensional brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is bounded, the circuit forms an approximate 𝑡-design in at most linear depth. We give numerical evidence for a stronger bound that depends only on the number of connected blocks into which the architecture can be divided. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures.

information scrambling↗
DOE OSTI2024

Designs from Local Random Quantum Circuits with SU ( d ) Symmetry

The generation of k -designs (pseudorandom distributions that emulate the Haar measure up to k moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations in which symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. Here, we construct explicit local unitary ensembles that can achieve high-order unitary k -designs under transversal continuous symmetry, in the particularly important SU ( d ) case. Specifically, we define the convolutional quantum alternating (CQA) group generated by 4-local SU ( d ) -symmetric Hamiltonians as well as associated 4-local SU ( d ) -symmetric random unitary circuit ensembles and prove that they form and converge to SU ( d ) -symmetric k -designs, respectively, for all k < n ( n − 3 ) / 2 , with n being the number of qudits. A key technique that we employ to obtain the results is the Okounkov-Vershik approach to S n representation theory. To study the convergence time of the CQA ensemble, we develop a numerical method using the Young orthogonal form and the S n branching rule. We provide strong evidence for a subconstant spectral gap and certain convergence time scales of various important circuit architectures, which contrast with the symmetry-free case. We also provide comprehensive explanations of the difficulties and limitations in rigorously analyzing the convergence time using methods that have been effective for cases without symmetries, including Knabe’s local gap threshold and Nachtergaele’s martingale methods. This suggests that a novel approach is likely necessary for understanding the convergence time of SU ( d ) -symmetric local random circuits. Published by the American Physical Society 2024

Li, Zimu (ORCID:0000000314736492)↗
NASA NTRS2004

Non-unitary probabilistic quantum computing

We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.

quantum gate↗
NASA NTRS1992

Study of optical techniques for the Ames unitary wind tunnels. Part 1: Schlieren

Alignment procedures and conceptual designs for the rapid alignment of the Ames Unitary Wind Tunnel schlieren systems were devised. The schlieren systems can be aligned by translating the light source, the mirrors, and the knife edge equal distances. One design for rapid alignment consists of a manual pin locking scheme. The other is a motorized electronic position scheme. A study of two optical concepts which can be used with the schlieren system was made. These are the 'point diffraction interferometers' and the 'focus schlieren'. Effects of vibrations were studied.

Lee, George↗
DOE OSTI2025

Solving reaction dynamics with quantum computing algorithms

The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. However, the time evolution of quantum states is a natural application for quantum computers that are designed to efficiently perform unitary transformations. Here, in this paper, we study quantum algorithms for response functions, relevant for describing different reactions governed by linear response. We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations. For the case of a contact interaction, we develop an algorithm for time evolution based on the Trotter approximation that scales logarithmically with the lattice size and is combined with quantum phase estimation. We eventually focus on the nuclear two-body system and a typical response function relevant for electron scattering as an example. We also investigate ground-state preparation and examine the total circuit depth required for a realistic calculation and the hardware noise level required to interpret the signal.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1979

Advanced vehicle separation apparatus

A method of obtaining test data from two independent models or bodies in a conventional wind tunnel is described. The system makes efficient use of wind tunnel test time with computer control performing complex coordinate transformations necessary for model positioning. The apparatus is designed to be used in any of the three Unitary Wind Tunnels at NASA-Ames Research Center. Mechanical design details and a brief description of the control system for the separation apparatus are presented.

Ospring, M. J.↗
DOE OSTI2025

Toward a Balanced Description of Ground and Excited States with Transcorrelated F12 Methods

By correlating only the 1-particle states occupied in the reference determinant, the conventional design for the single-reference R12/F12 explicitly correlated methods biases them toward the ground-state description, thereby making the treatment of response properties of the ground state, and energies and other properties of excited states less robust. While the use of multireference methods and/or extensions of the standard SP-projected geminals can achieve a more balanced description of ground and excited states, here we show that the same goals can be achieved by extending the action of F12 correlators to the occupied and valence unoccupied 1-particle states only. This design choice reflects the strong dependence of the optimal correlation length scale of the F12 ansatz on the orbital energies/structure, and helps to avoid the unphysical raising of the ground-state energy if the F12 geminals are used to correlate pairs of all 1-particle states. The improved F12 geminal design is incorporated into the unitary transcorrelation framework to produce a unitary 2-body Hamiltonian that incorporates the short-range dynamical correlation physics for ground and low-energy excited states in a balanced manner. This explicitly correlated effective Hamiltonian reduces the basis set requirement on the correlation-consistent basis cardinal number by 1 or more over the uncorrelated counterpart for the description of ground-state coupled-cluster singles and doubles (CCSD) energies, vertical excitation energies, and harmonic vibrational frequencies of equation-of-motion CCSD low-energy excited states.

Hamiltonians↗
NASA NTRS2017

Recent Advancements in the Infrared Flow Visualization System for the NASA Ames Unitary Plan Wind Tunnels

The following details recent efforts undertaken at the NASA Ames Unitary Plan wind tunnels to design and deploy an advanced, production-level infrared (IR) flow visualization data system. Highly sensitive IR cameras, coupled with in-line image processing, have enabled the visualization of wind tunnel model surface flow features as they develop in real-time. Boundary layer transition, shock impingement, junction flow, vortex dynamics, and buffet are routinely observed in both transonic and supersonic flow regimes all without the need of dedicated ramps in test section total temperature. Successful measurements have been performed on wing-body sting mounted test articles, semi-span floor mounted aircraft models, and sting mounted launch vehicle configurations. The unique requirements of imaging in production wind tunnel testing has led to advancements in the deployment of advanced IR cameras in a harsh test environment, robust data acquisition storage and workflow, real-time image processing algorithms, and evaluation of optimal surface treatments. The addition of a multi-camera IR flow visualization data system to the Ames UPWT has demonstrated itself to be a valuable analyses tool in the study of new and old aircraft/launch vehicle aerodynamics and has provided new insight for the evaluation of computational techniques.

Infrared Thermography↗
NASA NTRS2015

Institutional Schlieren: A Production-Level Wind Tunnel Test Measurement

The following details recent efforts undertaken at the NASA Ames Unitary Plan Wind Tunnel to design and deploy an advanced, institutional, production-level data system for the classical Schlieren-shadowgraph technique. Motivation for the selection of individual system components is discussed along with a software methodology that combines image acquisition and processing into a production-level wind tunnel test measurement. In general terms, a production-level measurement refers to any data system that is seamlessly integrated into the primary wind tunnel data system, and whose data products are available real-time (e.g. force and moment, pressure, temperature data). The advantage of integrating a measurement in such a manner is an immediate increase in data product efficiency, productivity, reliability, and quality. Coupled with these benefits and leveraging recent advancements in high-speed imaging and image processing, automated, synchronized, time-resolved Schlieren-shadowgraph imaging for dynamic flow phenomena is now a reality. This makes possible the synthesis of dynamic off-body imaging with unsteady on-body measurements to produce a uniquely descriptive data product invaluable to the modern researcher.

Shadowgraph↗
NASA NTRS2011

Supersonic Retro-Propulsion Experimental Design for Computational Fluid Dynamics Model Validation

The development of supersonic retro-propulsion, an enabling technology for heavy payload exploration missions to Mars, is the primary focus for the present paper. A new experimental model, intended to provide computational fluid dynamics model validation data, was recently designed for the Langley Research Center Unitary Plan Wind Tunnel Test Section 2. Pre-test computations were instrumental for sizing and refining the model, over the Mach number range of 2.4 to 4.6, such that tunnel blockage and internal flow separation issues would be minimized. A 5-in diameter 70-deg sphere-cone forebody, which accommodates up to four 4:1 area ratio nozzles, followed by a 10-in long cylindrical aftbody was developed for this study based on the computational results. The model was designed to allow for a large number of surface pressure measurements on the forebody and aftbody. Supplemental data included high-speed Schlieren video and internal pressures and temperatures. The run matrix was developed to allow for the quantification of various sources of experimental uncertainty, such as random errors due to run-to-run variations and bias errors due to flow field or model misalignments. Some preliminary results and observations from the test are presented, although detailed analyses of the data and uncertainties are still on going.

Berry, Scott A.↗
NASA NTRS1999

Cone-Probe Rake Design and Calibration for Supersonic Wind Tunnel Models

A series of experimental investigations were conducted at the NASA Langley Unitary Plan Wind Tunnel (UPWT) to calibrate cone-probe rakes designed to measure the flow field on 1-2% scale, high-speed wind tunnel models from Mach 2.15 to 2.4. The rakes were developed from a previous design that exhibited unfavorable measurement characteristics caused by a high probe spatial density and flow blockage from the rake body. Calibration parameters included Mach number, total pressure recovery, and flow angularity. Reference conditions were determined from a localized UPWT test section flow survey using a 10deg supersonic wedge probe. Test section Mach number and total pressure were determined using a novel iterative technique that accounted for boundary layer effects on the wedge surface. Cone-probe measurements were correlated to the surveyed flow conditions using analytical functions and recursive algorithms that resolved Mach number, pressure recovery, and flow angle to within +/-0.01, +/-1% and +/-0.1deg , respectively, for angles of attack and sideslip between +/-8deg. Uncertainty estimates indicated the overall cone-probe calibration accuracy was strongly influenced by the propagation of measurement error into the calculated results.

Won, Mark J.↗
NASA NTRS1999

Experimental Investigation of a Point Design Optimized Arrow Wing HSCT Configuration

The M2.4-7A Arrow Wing HSCT configuration was optimized for straight and level cruise at a Mach number of 2.4 and a lift coefficient of 0.10. A quasi-Newton optimization scheme maximized the lift-to-drag ratio (by minimizing drag-to-lift) using Euler solutions from FL067 to estimate the lift and drag forces. A 1.675% wind-tunnel model of the Opt5 HSCT configuration was built to validate the design methodology. Experimental data gathered at the NASA Langley Unitary Plan Wind Tunnel (UPWT) section #2 facility verified CFL3D Euler and Navier-Stokes predictions of the Opt5 performance at the design point. In turn, CFL3D confirmed the improvement in the lift-to-drag ratio obtained during the optimization, thus validating the design procedure. A data base at off-design conditions was obtained during three wind-tunnel tests. The entry into NASA Langley UPWT section #2 obtained data at a free stream Mach number, M(sub infinity), of 2.55 as well as the design Mach number, M(sub infinity)=2.4. Data from a Mach number range of 1.8 to 2.4 was taken at UPWT section #1. Transonic and low supersonic Mach numbers, M(sub infinity)=0.6 to 1.2, was gathered at the NASA Langley 16 ft. Transonic Wind Tunnel (TWT). In addition to good agreement between CFD and experimental data, highlights from the wind-tunnel tests include a trip dot study suggesting a linear relationship between trip dot drag and Mach number, an aeroelastic study that measured the outboard wing deflection and twist, and a flap scheduling study that identifies the possibility of only one leading-edge and trailing-edge flap setting for transonic cruise and another for low supersonic acceleration.

Narducci, Robert P.↗
NASA NTRS1958

Aerodynamic characteristics at mach numbers from 2.5 to 3.5 of a canard bomber configuration designed for supersonic cruise flight

Resilts have been obtained from an investigation in the Langley Unitary Plan wind tunnel at Mach numbers from 2.5 to 3.5 of a canard-type configuration designed for supersonic cruise flight. Tests extended over an angle-of-attack range from about -4 deg to 11 deg and an angle-of-sideslip range from -4 deg to 6 deg. For the present tests, the results indicate that forebody deflection was an efficient means of providing a sizable positive pitching-moment shift with little or no increase in drag. The test configuration had a trimmed lift-drag ratio of approximately 6.0 at Mach numbers near 3.0 and at a Reynolds number of 2.52 X 10(exp 6). The configuration was both longitudinally and directionally stable. The lift-drag ratios are believed to be somewhat low in as much as the models used for the present tests had large-grain size transition strips fixed to the various surfaces and these strips added wave drag. Also, the model boundary-layer diverter is oversized with respect to a full-scale configuration and therefore contributes additional drag.

Carmel, M. M.↗