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At least 235 records · Page 13

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DOE OSTI2020

Approximate quantum circuit synthesis using block encodings

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging them for ancilla qubits via block encodings. This approach combines smaller block encodings, which are easier to synthesize, into quantum circuits for larger operators. Due to the use of block encodings, our technique is not limited to unitary operators and can be applied for the synthesis of arbitrary operators. Overall, we show that operators which can be approximated by a canonical polyadic expression with a polylogarithmic number of terms can be synthesized with polylogarithmic gate complexity with respect to the matrix dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Strong coupling expansion of free energy and BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal models with fundamental hypermultiplets

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625 ) of strong-coupling expansion of non-planar corrections in $ \mathcal{N} $ = 2 4d superconformal models we consider two special theories with gauge groups SU( N ) and Sp(2 N ). They contain N -independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding $ \mathcal{N} $ = 4 SYM theories. These $ \mathcal{N} $ = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS 5 × S 5 superstring. Starting with the localization matrix model representation for the $ \mathcal{N} $ = 2 partition function on S 4 we find exact differential relations between the 1 /N terms in the corresponding free energy F and the $ \frac{1}{2} $ -BPS Wilson loop expectation value $ \left\langle \mathcal{W}\right\rangle $ and also compute their large ’t Hooft coupling ( λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2 N ) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1 /N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and $ \left\langle \mathcal{W}\right\rangle $ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.

1/N expansion↗

DOE OSTI2025

Decoherence dynamics in molecular qubits: Exponential, Gaussian and beyond

In this article, we examine how the structure of system–bath interactions can determine commonly encountered temporal decoherence patterns, such as Gaussian and exponential decay, in molecular and other qubits coupled to a thermal bosonic bath. The analysis, based on a pure dephasing picture that admits analytical treatment, shows that decoherence, in general, is neither purely Gaussian nor exponential but rather the exponential of oscillatory functions, with periods determined by the bath’s frequencies. For initially unentangled qubit-bath states, Gaussian decay is always present at early times. It becomes increasingly dominant with increasing temperature, qubit–bath interaction strength, and bath correlation time. Initial system–bath entanglement that arises due to displacement in the position of the bath states preserves the Gaussian decay. By contrast, strict exponential decay arises only in very specific models that we isolate. However, it becomes dominant for times longer than the bath correlation time or for early times when there is initial entanglement due to momentum displacement of the bath states. For molecular electronic decoherence, the long-time exponential regime plays a limited role as it emerges after most coherence is lost. Thus, the Gaussian decay provides a more suitable (albeit imperfect) model of such decoherence. Furthermore, we discuss the connection between electronic decoherence dynamics and electronic spectroscopic line shape theory, where Gaussian spectral peaks correspond to Gaussian coherence decay and Lorentzian peaks correspond to exponential coherence decay. We find that Gaussian spectral peaks, usually associated with inhomogeneous broadening, can emerge from the entangling unitary system–bath dynamics even when there is no inhomogeneity in the initial conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Magnetic phase transitions in quantum spin-orbital liquids

Here, we investigate the spin and orbital correlations of a superexchange model with spin $\textit{S}$ = 1 and orbital $\textit{L}$ = 1 relevant for $5d^4$ transition-metal Mott insulators, using exact diagonalization and density matrix renormalization group (DMRG). For spin-orbit coupling λ = 0, the orbitals are in an entangled state that is decoupled from the spins. We find two phases with increasing λ: (I) the $\textit{S}$2 phase with two peaks in the structure factor for λ ≤ λ$_{c1}$ ≈ 0.34$\textit{J}$ where $\textit{J}$ is the ferromagnetic exchange; and, (II) the $\textit{S}$1 phase for λ$_{c1}$ < λ ≤ λ$_{c2}$ ≈ 1.2$\textit{J}$ with emergent antiferromagnetic correlations. Both $\textit{S}$1 and $\textit{S}$2 phases are shown to exhibit power-law correlations, indicative of a gapless spectrum. Upon increasing λ > λ$_{c2}$ leads to a product state of local spin-orbital singlets that exhibit exponential decay of correlations, indicative of a gapped phase. We obtain insights into the phases from the well-known Uimin-Lai-Sutherland model in an external field that provides an approximate description of our model within mean-field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

A multilayer multi-configurational approach to efficiently simulate large-scale circuit-based quantum computers on classical machines

Here, a multilayer multi-configurational theory framework is adapted to simulate circuit-based quantum computers. Quantum addition of superpositions of an exponential number of summands is performed in polynomial time with high accuracy. We demonstrate numerically accurate calculations including up to one million qubits for entangling benchmarks. Simulation cost can be assessed by entropy-based entanglement measures. For the considered systems, we show that the entanglement only grows weakly with the system size. The present simulations demonstrate how quantum algorithms in low-entropy regimes can be used efficiently on classically simulated quantum computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Ground-state phase diagram and superconductivity of the doped Hubbard model on six-leg square cylinders

Here, we have studied the ground state properties of Hubbard model on long six-leg square cylinders with doped hole concentration per site 5.55%≤δ≤12.5% using density-matrix renormalization group. By keeping a large number of states for long system sizes, we find that the nature of the ground state is remarkably sensitive to the presence of next-nearest-neighbor electron hopping t'. In the positive t' side, we find a robust d-wave superconducting (SC) phase characterized by coexisting quasi-long-range SC and charge density wave (CDW) correlations. Without t' the ground state forms an insulating stripe phase with long-range CDW order but short-range spin-spin and SC correlations. In stark contrast to four-leg cylinders, our results show that the lightly doped Hubbard model on six-leg cylinders remains insulating in the negative t' side where the SC correlations decay exponentially with short correlation lengths. In the larger negative t' side, the doped holes form a novel holon Wigner crystal with one doped hole per emergent unit cell and short-range spin-spin correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

A Novel Multiphysics Multiscale Multiporosity Shale Gas Transport Model for Geomechanics/Flow Coupling in Steady and Transient States

Summary A novel multiphysics multiscale multiporosity shale gas transport (M3ST) model was developed to investigate shale gas transport in both transient and steady states. The microscale model component contains a kerogen domain and an inorganic matrix domain, and each domain has its own geomechanical and gas transport properties. Permeabilities of various shale cores were measured in the laboratory using a pulse decay permeameter (PDP) with different pore pressure and confining stress combinations. The PDP-measured apparent permeability as a function of pore pressure under two effective stresses was fitted using the microscale M3ST model component based on nonlinear least squares fitting (NLSF), and the fitted model parameters were able to provide accurate model predictions for another effective stress. The parameters and petrophysical properties determined in the steady state were then used in the transient-state, continuum-scale M3ST model component, which performed history matching of the evolutions of the upstream and downstream gas pressures. In addition, a double-exponential empirical model was developed as a powerful alternative to the M3ST model to fit laboratory-measured apparent permeability under various effective stresses and pore pressures. The developed M3ST model and the research findings in this study provided critical insights into the role of the multiphysics mechanisms, including geomechanics, fluid dynamics and transport, and the Klinkenberg effect on shale gas transport across different spatial scales in both steady and transient states.

Engineering↗

DOE OSTI2024

Quantifying Quantum Chaos through Microcanonical Distributions of Entanglement

A characteristic feature of “quantum chaotic” systems is that their eigenspectra and eigenstates display universal statistical properties described by random matrix theory (RMT). However, eigenstates of local systems also encode structure beyond RMT. To capture this feature, we introduce a framework that allows us to compare the properties of eigenstates in local systems with those of pure random states. In particular, our framework defines a notion of distance between quantum state ensembles that utilizes the Kullback-Leibler divergence to compare the microcanonical distribution of entanglement entropy (EE) of eigenstates with a reference RMT distribution generated by pure random states (with appropriate constraints). This notion gives rise to a quantitative metric for quantum chaos that not only accounts for averages of the distributions but also higher moments. The differences in moments are compared on a highly resolved scale set by the standard deviation of the RMT distribution, which is exponentially small in system size. As a result, the metric can distinguish between chaotic and integrable behaviors and, in addition, quantify and compare the of chaos (in terms of proximity to RMT behavior) between two systems that are assumed to be chaotic. We implement our framework in local, minimally structured, Floquet random circuits, as well as a canonical family of many-body Hamiltonians, the mixed-field Ising model (MFIM). Importantly, for Hamiltonian systems, we find that the reference random distribution must be appropriately constrained to incorporate the effect of energy conservation in order to describe the ensemble properties of midspectrum eigenstates. The metric captures deviations from RMT across all models and parameters, including those that have been previously identified as strongly chaotic, and for which other diagnostics of chaos such as level spacing statistics look strongly thermal. In Floquet circuits, the dominant source of deviations is the second moment of the distribution, and this persists for all system sizes. For the MFIM, we find significant variation of the KL divergence in parameter space. Notably, we find a small region where deviations from RMT are minimized, suggesting that “maximally chaotic” Hamiltonians may exist in fine-tuned pockets of parameter space. Published by the American Physical Society 2024

Physics↗

NASA NTRS2004

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗

DOE OSTI2024

Two-fermion negativity and confinement in the Schwinger model

We consider the fermionic (logarithmic) negativity between two fermionic modes in the Schwinger model. Recent results pointed out that fermionic systems can exhibit stronger entanglement than bosonic systems, exhibiting a negativity that decays only algebraically. The Schwinger model is described by fermionic excitations at short distances, while its asymptotic spectrum is the one of a bosonic theory. We show that the two-mode negativity detects this confining, fermion-to-boson transition, shifting from an algebraic decay to an exponential decay at distances of the order of the de Broglie wavelength of the first excited state. We derive analytical expressions in the massless Schwinger model and confront them with tensor network simulations. We also perform tensor network simulations in the massive model, which is not solvable analytically, and close to the Ising quantum critical point of the Schwinger model, where we show that the negativity behaves as its bosonic counterpart. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits

The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L = 14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L = 50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Microbunch rotation in an x-ray free-electron laser using a first-order achromatic bend

Electrons in an x-ray free electron laser (XFEL) develop periodic density fluctuations, known as microbunches, which enable the exponential gain of x-ray power in an XFEL. When an electron beam microbunched at a hard x-ray wavelength is kicked, microbunches are often washed out due to the dispersion and R 56 of the bend. An achromatic (dispersion-free) bend with a small R 56 , however, can preserve microbunches, which rotate to follow the new trajectory of the electron bunch. Rotated microbunches can subsequently interact in a repointed undulator to produce a new beam of off-axis x rays. In this work, we demonstrate hard x-ray multiplexing in the Linac Coherent Light Source hard x-ray undulator line using microbunch rotation through a 10 μ rad first-order-achromatic bend created by transversely offsetting quadrupole magnets in the FODO lattice. Quadrupole offsets are determined analytically from beam-matrix theory. We also discuss the application of microbunch rotation to out-coupling a cavity-based XFEL. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

NASA NTRS1985

Models of the upper atmosphere

Several computer models of the thermosphere are discussed. J70MM, the Jacchia 1970 model with matrix and matrix mean output, and J703X, the Jacchia 1970, 1971, and 1977 models, are of primary interest. The subroutines in these programs were studied in detail, and several mistakes were found and corrected. It is proposed that a weighted average of the three-hour geomagnetic index be used in the models rather than a single index value. The densities (for a given date and time) generated by the J703X program (all three models), using both a single value of the index and weighted averages for three different lag times, are tabulated and discussed. Most of the equations used in the models are the results of empirical curve fits. An attempt was made to generate a theoretical prediction of the thermospheric temperature profile based on a simple physical model of atmospheric heat conduction in a spherically-symmetric shell. The exponential heating theory and the temperature dependence of k are discussed.

Davis, T. M.↗

DOE OSTI2023

Effective description of sub-maximal chaos: stringy effects for SYK scrambling

It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective ‘scramblon’ modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRSDate not supplied

The System Complexity Metric (SCM) Explains Systems Design and is Correlated with Cost and Failure Rate

The human short term memory span and working capacity is limited to three to five items, especially if they are organized complex “chunks” of information. The impression of complexity occurs when a system is simply difficult to understand, where there is no apparent pattern to predict its behavior. Hierarchical systems design can reduce perceived complexity and increase the amount of information that can be managed. The SCM was developed to measure complexity and help compare proposed overall system architectures before detailed design information is available. The SCM is defined as the sum of the number of major nodes, N, in the system block diagram plus the number of one-way interactions, I, between the nodes. SCM = N + I. SCM’s are easily determined by direct inspection of high-level block diagrams of life support systems. Axiomatic design develops a hierarchy of subsystem requirements and designs together in a top-down, back-and-forth process. A coupling matrix is used to control the relationships between the subsystem functions and design concepts. Axiomatic design can improve system design by decoupling requirements and designs. Axiomatic design was applied to the planning of a closed life support system, similar to that used on the International Space Station. A materially open as opposed to a closed system design was created by removing the interconnections required to close the system. The open system had the same number of designed subsystems as the closed system, but it had many fewer interconnections and its SCM was lower by about half. The costs were estimated and the MTBF (Mean Time Before Failure) tabulated for open and closed space life support systems. The estimated costs were linearly proportional to SCM for the wide variations of SCM in life support, but small differences may not be significant. The flight and preflight MTBF’s both declined exponentially with increasing MTBF, faster than MTBF-2, even though the preflight estimated MTBF’s were about ten times higher than the flight MTBF’s.

System Complexity Metric (SCM)↗

DOE OSTI2021

A theoretical approach for transient shock strengthening in high-energy-density laser compression experiments

In high-energy-density shock compression experiments, the desired state of compression is typically achieved by passing shock waves through a sequence of different materials. Here, a theoretical approach for transiently strengthening such shocks passing through interfaces of experimentally relevant impedance ratios is examined. A semi-analytical method based on characteristics analysis is used to solve the problem of a shock passing from one material to another through an intermediate region of non-uniform impedance; by appropriately designing this region, a greater shock strength can be achieved in the second material for a finite duration than in the absence of this region. When a shock passes into a material of higher impedance, the shock strengthening increases to a maximum before decreasing to an asymptotic value as the strength of the incident shock is increased. For shocks passing into materials of decreasing impedance, the shock strengthening increases monotonically as the strength of the incident shock is increased when the impedance ratio is above a critical threshold. Incorporating multiple intermediate materials can further increase the strength of the transmitted shock, with an exponential discretization of intermediate material impedances being the most effective distribution for strengthening strong shocks. The results suggest that up to 25% and 9% increases in pressure behind the leading shock can be achieved for materials of increasing and decreasing impedance, respectively. The technique is applied to the design of laser-driven dynamic compression experiments, and the results of the analysis are verified via comparison to simulations performed with the HYADES hydrodynamics code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Grain detachment and transport clogging during mineral dissolution in carbonate rocks with permeable grain boundaries

In this paper, we explore the effect of permeable grain boundaries on carbonate rock dissolution in order to improve our understanding of grain detachment and migration during reactive flow. To do so we investigated the effects of grain size and enhanced reactivity along grain boundaries on global dissolution kinetics. Variations of permeability and porosity were calculated, and exponential relationships were observed in fractured rocks. Our model employed a reactive transport framework based on the Darcy-Brinkman equation to simulate calcite dissolution in carbonate rocks composed of microporous grains and, included fluid transport along grain boundaries. The model includes fluid flow, solute transport by advection–diffusion, heterogeneous reaction between fluid and minerals and grain detachment with subsequent grain transport in macropores. The migration of solid particles due to dissolution was based on cluster analysis and local movement, and the results show that grain detachment can lead to significant decreases in permeability due to the clogging of transport pathways. Microporous media with smaller grain sizes (fine grains in this study) showed a higher average reaction rate than those with coarser grains. In addition, as the overall rates of geochemical processes are commonly affected by the presence of texture heterogeneities such as fractures, a single fracture (macropore) introduced into a microporous matrix composed of permeable grains and grain boundaries was modelled as a large channel connecting the inlet and outlet of the simulation domain. It was found that macropore clogging by grain detachment temporary decreased permeability, lowering the long-term global reaction rates. Lastly, we observed that increases in flow rate can reduce detachment and fracture clogging by reducing local dissolution along grain boundaries.

58 GEOSCIENCES↗

NASA NTRS2003

Flutter and Divergence Analysis using the Generalized Aeroelastic Analysis Method

The Generalized Aeroelastic Analysis Method (GAAM) is applied to the analysis of three well-studied checkcases: restrained and unrestrained airfoil models, and a wing model. An eigenvalue iteration procedure is used for converging upon roots of the complex stability matrix. For the airfoil models, exact root loci are given which clearly illustrate the nature of the flutter and divergence instabilities. The singularities involved are enumerated, including an additional pole at the origin for the unrestrained airfoil case and the emergence of an additional pole on the positive real axis at the divergence speed for the restrained airfoil case. Inconsistencies and differences among published aeroelastic root loci and the new, exact results are discussed and resolved. The generalization of a Doublet Lattice Method computer code is described and the code is applied to the calculation of root loci for the wing model for incompressible and for subsonic flow conditions. The error introduced in the reduction of the singular integral equation underlying the unsteady lifting surface theory to a linear algebraic equation is discussed. Acknowledging this inherent error, the solutions of the algebraic equation by GAAM are termed 'exact.' The singularities of the problem are discussed and exponential series approximations used in the evaluation of the kernel function shown to introduce a dense collection of poles and zeroes on the negative real axis. Again, inconsistencies and differences among published aeroelastic root loci and the new 'exact' results are discussed and resolved. In all cases, aeroelastic flutter and divergence speeds and frequencies are in good agreement with published results. The GAAM solution procedure allows complete control over Mach number, velocity, density, and complex frequency. Thus all points on the computed root loci can be matched-point, consistent solutions without recourse to complex mode tracking logic or dataset interpolation, as in the k and p-k solution methods.

Edwards, John W.↗