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At least 55 records · Page 3

Symmetry Breaking and Error Correction in Open Quantum Systems

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system—a Lindbladian—a unitary symmetry can be imposed in a “weak” or a “strong” way. We characterize the possible $\mathbb{Z}_n$ symmetry-breaking transitions for both cases. In the case of $\mathbb{Z}_2$, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Further, our study forges a connection between driven-dissipative phase transitions and error correction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ~10 9 two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. Furthermore, this work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Recent advancements in chiral spintronics: from molecular-level insights to device applications. A prospect based on the interplay between physical and chemical properties of chiral systems

This review discusses recent advancements in chiral-based spin-electronic devices achieved using suitable combinations of organic, inorganic and hybrid materials. The focus is on how chirality can be effectively used to control spin in practical applications, particularly in spintronic sensors and consumer devices. Interestingly, the underlying mechanism for this control is the chiral-induced spin selectivity (CISS) effect, which links the structural chirality of a material to its spin-selective electronic transport properties. The CISS effect arises from the observation that charge transmission in chiral systems is spin selective. Experimental evidence suggests a relationship between electron spin and the structural handedness of the material. In conclusion, this unique structure-transport relationship can be exploited to design a wide range of spintronics devices, including memory, transistors, logic gates and molecular q-bits.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A formal model of asynchronous communication and its use in mechanically verifying a biphase mark protocol

In this paper we present a formal model of asynchronous communication as a function in the Boyer-Moore logic. The function transforms the signal stream generated by one processor into the signal stream consumed by an independently clocked processor. This transformation 'blurs' edges and 'dilates' time due to differences in the phases and rates of the two clocks and the communications delay. The model can be used quantitatively to derive concrete performance bounds on asynchronous communications at ISO protocol level 1 (physical level). We develop part of the reusable formal theory that permits the convenient application of the model. We use the theory to show that a biphase mark protocol can be used to send messages of arbitrary length between two asynchronous processors. We study two versions of the protocol, a conventional one which uses cells of size 32 cycles and an unconventional one which uses cells of size 18. We conjecture that the protocol can be proved to work under our model for smaller cell sizes and more divergent clock rates but the proofs would be harder.

Moore, J. Strother↗

Fuel-Efficient Descent and Landing Guidance Logic for a Safe Lunar Touchdown

The landing of a crewed lunar lander on the surface of the Moon will be the climax of any Moon mission. At touchdown, the landing mechanism must absorb the load imparted on the lander due to the vertical component of the lander's touchdown velocity. Also, a large horizontal velocity must be avoided because it could cause the lander to tip over, risking the life of the crew. To be conservative, the worst-case lander's touchdown velocity is always assumed in designing the landing mechanism, making it very heavy. Fuel-optimal guidance algorithms for soft planetary landing have been studied extensively. In most of these studies, the lander is constrained to touchdown with zero velocity. With bounds imposed on the magnitude of the engine thrust, the optimal control solutions typically have a "bang-bang" thrust profile: the thrust magnitude "bangs" instantaneously between its maximum and minimum magnitudes. But the descent engine might not be able to throttle between its extremes instantaneously. There is also a concern about the acceptability of "bang-bang" control to the crew. In our study, the optimal control of a lander is formulated with a cost function that penalizes both the touchdown velocity and the fuel cost of the descent engine. In this formulation, there is not a requirement to achieve a zero touchdown velocity. Only a touchdown velocity that is consistent with the capability of the landing gear design is required. Also, since the nominal throttle level for the terminal descent sub-phase is well below the peak engine thrust, no bound on the engine thrust is used in our formulated problem. Instead of bangbang type solution, the optimal thrust generated is a continuous function of time. With this formulation, we can easily derive analytical expressions for the optimal thrust vector, touchdown velocity components, and other system variables. These expressions provide insights into the "physics" of the optimal landing and terminal descent maneuver. These insights could help engineers to achieve a better "balance" between the conflicting needs of achieving a safe touchdown velocity, a low-weight landing mechanism, low engine fuel cost, and other design goals. In comparing the computed optimal control results with the preflight landing trajectory design of the Apollo-11 mission, we noted interesting similarities between the two missions.

guidance logic↗

GLOBEC: Global Ocean Ecosystems Dynamics: A component of the US Global Change Research Program

GLOBEC (GLOBal ocean ECosystems dynamics) is a research initiative proposed by the oceanographic and fisheries communities to address the question of how changes in global environment are expected to affect the abundance and production of animals in the sea. The approach to this problem is to develop a fundamental understanding of the mechanisms that determine both the abundance of key marine animal populations and their variances in space and time. The assumption is that the physical environment is a major contributor to patterns of abundance and production of marine animals, in large part because the planktonic life stages typical of most marine animals are intrinsically at the mercy of the fluid motions of the medium in which they live. Consequently, the authors reason that a logical approach to predicting the potential impact of a globally changing environment is to understand how the physical environment, both directly and indirectly, contributes to animal abundance and its variability in marine ecosystems. The plans for this coordinated study of of the potential impact of global change on ocean ecosystems dynamics are discussed.

Source record↗

Global models: Robot sensing, control, and sensory-motor skills

Robotics research has begun to address the modeling and implementation of a wide variety of unstructured tasks. Examples include automated navigation, platform servicing, custom fabrication and repair, deployment and recovery, and science exploration. Such tasks are poorly described at onset; the workspace layout is partially unfamiliar, and the task control sequence is only qualitatively characterized. The robot must model the workspace, plan detailed physical actions from qualitative goals, and adapt its instantaneous control regimes to unpredicted events. Developing robust representations and computational approaches for these sensing, planning, and control functions is a major challenge. The underlying domain constraints are very general, and seem to offer little guidance for well-bounded approximation of object shape and motion, manipulation postures and trajectories, and the like. This generalized modeling problem is discussed, with an emphasis on the role of sensing. It is also discussed that unstructured tasks often have, in fact, a high degree of underlying physical symmetry, and such implicit knowledge should be drawn on to model task performance strategies in a methodological fashion. A group-theoretic decomposition of the workspace organization, task goals, and their admissible interactions are proposed. This group-mechanical approach to task representation helps to clarify the functional interplay of perception and control, in essence, describing what perception is specifically for, versus how it is generically modeled. One also gains insight how perception might logically evolve in response to needs of more complex motor skills. It is discussed why, of the many solutions that are often mathematically admissible to a given sensory motor-coordination problem, one may be preferred over others.

Schenker, Paul S.↗

Computational Methods for Structural Mechanics and Dynamics, part 1

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Stroud, W. Jefferson↗

Semicoherent symmetric quantum processes: Theory and applications

Discovering pragmatic and efficient approaches to construct ε-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior ε-approximations are invaluable, in that they enable the compilation of classical and quantum algorithm modeling of, e.g., dynamical and thermodynamic quantum properties. In parallel, symmetries are powerful tools concisely describing the fundamental laws of nature; the symmetric underpinnings of physical laws have consistently provided profound insights and substantially increased predictive power. In this work, we consider the interplay between the ε-approximate processes and the exact symmetries in a semicoherent context—where measurements occur at each logical clock cycle. Here we draw inspiration from Pascual Jordan's groundbreaking formulation of nonassociative, but commutative, symmetric algebraic form. Our symmetrized formalism is then applied in various domains such as quantum random walks, real-time evolutions, variational algorithm ansatzes, and efficient entanglement verification. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics in settings where coherence is a limited resource.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

36 MATERIALS SCIENCE↗

Differential geometric approaches to momentum-based formulations for fluids [Slides]

This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Logical gates embedding in artificial spin ice

The realization and study of arrays of interacting magnetic nanoislands, such as artificial spin ices, have reached mature levels of control that allow design and demonstration of exotic, collective behaviors not seen in natural materials. Advances in the direct manipulation of their local, binary moments also suggest a use as nanopatterned, interacting memory media, for computation within a magnetic memory. Recent experimental work has demonstrated the possibility of building logic gates from clusters of interacting magnetic domains, and yet the possibility of large scale integration of such gates can prove problematic even at the theoretical level. Here we introduce theoretically complete sets of logical gates, in principle realizable in an experiment, and we study the feasibility of their integration into tree-like circuits. By evaluating the fidelity control parameter between their collective behavior and their expected logic functionality we determine conditions for integration. Also, we test our numerical results against the presence of disorder in the couplings, showing that the design gate structure is robust to small coupling perturbations, and thus possibly to small imperfections in the fabrication of the islands.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Efficient Simulation of Logical Magic State Preparation Protocols

Developing space- and time-efficient logical magic state preparation (MSP) protocols will likely be an essential step toward building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for simulating logical MSP protocols under the standard circuit-level noise model. When applied to protocols based on code-switching, magic state cultivation, and magic state distillation, our method yields a complexity polynomial in (i) the number of qubits and (ii) the nonstabilizerness, e.g., stabilizer rank or Pauli rank, of the target encoded magic state. The efficiency of our simulation method is rooted in a curious fact: every circuit-level Pauli error in these protocols propagates to a Clifford error at the end. This property is satisfied by a large family of protocols, including those that repeatedly measure a transversal Clifford that squares to a Pauli. We provide a proof-of-principle numerical simulation that prepares a magic state using such logical Clifford measurements. Our work enables practical simulation of logical MSP protocols without resorting to approximations or resource-intensive state-vector simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum minimal surfaces from quantum error correction

We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow[1]; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining ``areas'' associated to arbitrary logical subsystems, and argue that this definition is ``functionally unique.'' We also formalize a definition of bulk reconstruction that we call ``state-specific product unitary’’ reconstruction. This definition captures the quantum error correction (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases. Our results extend to approximate codes, and even to the ``non-isometric codes'' that seem to describe the interior of a black hole at late times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Formal Methods in the Development of Highly Assured Software for Unmanned Aircraft Systems

In traditional software development methodologies, operational and functional requirements of systems are often specified in structured natural language notations. These restricted notations provide good documentation support, but only provide limited support for semantic analysis. These notations are generally not rich enough to unambiguously specify the requirements of safety-critical systems that, for example, involve complex numerical computations or that interact with the physical environment. Examples of these safety-critical systems are autonomous vehicles such as unmanned aircraft systems. This talk advocates the use of expressive formal logics, such as higher-order logic, to specify the operational and functional requirement of unmanned systems and to prove the correctness of these requirements. Semantic analysis of requirements written in higher-order logic is supported through the use of interactive theorem provers. Formal models serve as ideal reference implementations of functional requirements. Hence, formal logics enable software validation techniques where software implementations can be checked against functional requirements in a mechanical way. The Formal Methods group in the Safety-Critical Avionics Systems Branch at NASA Langley Research Center has conducted research on the development and application of formal verification techniques to safety-critical applications of interest to NASA for more than 30 years. This talk illustrates the use of formal methods in the development of highly-assured autonomous unmanned aircraft systems.

Formal Methods↗

Superaromatics: The key to a unified cosmic dust theory

The theory of Superaromatics, the key to a unified cosmic dust theory, was constructed by analyzing several thousand astronomical features covering every major aspect of astrophysics and astrochemistry relating to dust. To insure consistency between disciplines, the logical structure of the conclusions in each field was checked rather than accepting the current consensus. No substantial contradictory features are known to the author. The analysis falls into seven major parts: (1) kinetics of grain formation and destruction; (2) optical spectra of the interstellar medium (ISM); (3) meteorite interplanetary dust particle (IPD) chemistry; (4) structure and chemistry of the interstellar medium arising from surface catalysis; (6) dynamics of circumstellar and interstellar dust clouds, including galactic morphology; and (7) the chemistry and physics of previously unidentified compounds. Only tentative conclusions are presented here. The principle conclusion is that quantum mechanics as it is normally formulated is incomplete. The probable cause is that it is formulated with complex numbers rather than the more fundamental quaternion system. The manifestation in astrochemistry is that the most stable compounds are superaromatic and exotic enough to confound most classical analysis.

Manuel, Lawrence R.↗

Quantum computation of stopping power for inertial fusion target design

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it—one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [ PRX Quant. 2 , 040332 (2021)], adapting and optimizing those algorithms to estimate observables of interest from the non-Born–Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with an implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Low cost management of replicated data in fault-tolerant distributed systems

Many distributed systems replicate data for fault tolerance or availability. In such systems, a logical update on a data item results in a physical update on a number of copies. The synchronization and communication required to keep the copies of replicated data consistent introduce a delay when operations are performed. A technique is described that relaxes the usual degree of synchronization, permitting replicated data items to be updated concurrently with other operations, while at the same time ensuring that correctness is not violated. The additional concurrency thus obtained results in better response time when performing operations on replicated data. How this technique performs in conjunction with a roll-back and a roll-forward failure recovery mechanism is also discussed.

Joseph, Thomas A.↗