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At least 235 records · Page 13

Semantic embedding for quantum algorithms

The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation’s realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ansätze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

Physics↗

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗

Paradigm transition in cosmic plasma physics

New discoveries in cosmic plasma physics are described, and their applications to solar, interstellar, galactic, and cosmological problems are discussed. The new discoveries include the existence of double layers in magnetized plasmas and in the low magnetosphere, and energy transfer by electric current in the auroral circuit. It is argued that solar flares and the solar wind-magnetosphere interaction should not be interpreted in terms of magnetic merging theories, and that electric current needs to be explicitly taken account of in understanding these phenomena. The filamentary structure of cosmic plasmas may be caused by electric currents in space, and the pinch effect may have a central role to play in the evolutionary history of interstellar clouds, stars, and solar systems. Space may have a cellular structure, with the cell walls formed by thin electric current layers. Annihilation may be the source of energy for quasars and the Hubble expansion, and the big bang cosmology may well be wrong.

Alfven, H.↗

Quantum Information for Particle Theorists

Lectures given at the Theoretical Advanced Study Institute (TASI 2020), 1-26 June 2020. The topics covered include quantum circuits, entanglement, quantum teleportation, Bell inequalities, quantum entropy and decoherence, classical versus quantum measurement, the area law for entanglement entropy in quantum field theory, and simulating quantum field theory on a quantum computer. Along the way we confront the fundamental sloppiness of how we all learned (and some of us taught) quantum mechanics in college. Links to a Python notebook and Mathematica notebooks will allow the reader to reproduce and extend the calculations, as well as perform five experiments on a quantum simulator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Simplified Theory of the Magneto

This paper contains part of the results of ignition investigations being made for the National Advisory Committee for Aeronautics at the Bureau of Standards, and describes a type of circuit which has been found useful for representing the action of high-tension magneto. While this equivalent circuit is relatively simple, and consequently can be used as a basis for deriving definite mathematical formulas for induced voltages and similar quantities, it has been found experimentally to correspond quite closely in its performance with the highly complicated electrical circuits of an actual magneto. In the paper formulas are given for the voltage induced in the secondary under various conditions of operation, and a number of numerical examples are worked out showing the application of the equations to a variety of practical problems.

Silsbee, F B↗

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)↗

Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. Here, the underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hierarchical hybrid control of manipulators: Artificial intelligence in large scale integrated circuits

Both in practical engineering and in control of muscular systems, low level subsystems automatically provide crude approximations to the proper response. Through low level tuning of these approximations, the proper response variant can emerge from standardized high level commands. Such systems are expressly suited to emerging large scale integrated circuit technology. A computer, using symbolic descriptions of subsystem responses, can select and shape responses of low level digital or analog microcircuits. A mathematical theory that reveals significant informational units in this style of control and software for realizing such information structures are formulated.

Greene, P. H.↗

Effects of high doping levels on silicon solar cell performance

Open-circuit voltages measured in silicon solar cells made from 0.01 ohm-cm material are 150 mV lower than voltages calculated from simple diffusion theory and cannot be explained by poor diffusion lengths or surface leakage currents. An analytical study was made to determine whether high doping effects, which increase the intrinsic carrier concentration, could account for the low observed voltages and to determine the limits on voltage and efficiency imposed by high doping effects. The results indicate that the observed variation of voltage with base resistivity is predicted by these effects. A maximum efficiency of 19% (AMO) and a voltage of 0.7 volts were calculated for 0.1 ohm-cm cells assuming an optimum diffused layer impurity profile.

Godlewski, M. P.↗

RF model of the distribution system as a communication channel, phase 2. Volume 2: Task reports

Based on the established feasibility of predicting, via a model, the propagation of Power Line Frequency on radial type distribution feeders, verification studies comparing model predictions against measurements were undertaken using more complicated feeder circuits and situations. Detailed accounts of the major tasks are presented. These include: (1) verification of model; (2) extension, implementation, and verification of perturbation theory; (3) parameter sensitivity; (4) transformer modeling; and (5) compensation of power distribution systems for enhancement of power line carrier communication reliability.

Rustay, R. C.↗

High Performance Circuit Pastes for Solid Oxide Fuel Cell Applications: Final Technical Report

Using a combination of in-plane electrical conductivity measurements, electrical contact resistance measurements, tensile fracture tests, double shear lap fracture tests, rapid thermal cycling adhesion tests, in situ wetting angle measurements, 3D X-ray tomography, reduction-oxidation (RedOx) cycling, scanning electron microscopy (SEM), energy dispersive x-ray spectroscopy (EDAX), Density Functional Theory (DFT) modeling, Molecular Dynamics (MD) modeling, and Phase Field modeling, this project determined that a new brazing technique developed by the PIs (specifically the use of nickel particles to direct the wetting and spreading of molten silver) could be used to produce well-adhered, >97% dense, electrically-conductive circuits, current collectors, and/or electrical contacts on a variety of ceramic and ceramic-coated substrates (specifically lanthanum strontium manganite, yttria stabilized zirconia, sapphire, Cr2O3-passivated stainless steel, and Al2O3-passivated stainless steel). Compared to other silver-based alternatives, Ag:Ni led to less manufacturing defects and was more tolerant of the extreme environments (isothermal high-temperature aging) and occasional abuse (rapid thermal cycling and RedOx cycling) encountered during Solid Oxide Fuel Cell and/or Solid Oxide Electrolysis Cell operation. Further, in some situations (such as when to produce Ag:Ni electrical contacts to Al2O3-protected stainless steel) the Ni particles also improved operation by acting as chemical getters that removed electrically-insulating, surface-segregating substrate impurities (i.e. by lowering the contact resistance with the underlying substrate).

36 MATERIALS SCIENCE↗

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^8 determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

J Wayne Mullinax↗

Flux-based three-dimensional electrodynamic modeling approach to superconducting circuits and materials

Modeling the behavior of superconducting electronic circuits containing Josephson junctions is crucial for the design of superconducting information processors and devices. In this paper, we introduce DEC-QED, a computational approach for modeling the electrodynamics of superconducting electronic circuits containing Josephson junctions in arbitrary three-dimensional electromagnetic environments. DEC-QED captures the nonlinear response and induced currents in BCS superconductors and accurately captures phenomena such as the Meissner effect, flux quantization, and Josephson effects. Using a spatial coarse-graining formulation based on discrete exterior calculus (DEC), DEC-QED can accurately simulate transient and long-time dynamics in superconductors. Finally, the expression of the entire electrodynamic problem in terms of the gauge-invariant flux field and charges makes the resulting classical field theory suitable for second quantization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Network synthesis

A discussion, with numerous examples, on the application of state variable methods to network analysis and synthesis is reported. The state variable point of view is useful in the design of control circuits for regulators because, unlike frequency domain methods, it is applicable to linear and nonlinear problems. The reported are intended as an introduction to this theory.

Brockett, R. W.↗

Studies of silicon PN junction solar cells

Silicon pn junction solar cells made with low-resistivity substrates show poorer performance than traditional theory predicts. The purpose of this research was to identify and characterize the physical mechanisms responsible for the discrepancy. Attention was concentrated on the open circuit voltage in shallow junction cells of 0.1 ohm-cm substrate resistivity. A number of possible mechanisms that can occur in silicon devices were considered. Two mechanisms which are likely to be of main importance in explaining the observed low values of open-circuit voltage were found: (1) recombination losses associated with defects introduced during junction formation, and (2) inhomogeneity of defects and impurities across the area of the cell. To explore these theoretical anticipations, various diode test structures were designed and fabricated and measurement configurations for characterizing the defect properties and the areal inhomogeneity were constructed.

Lindholm, F. A.↗

Carrier synchronization techniques for unbalanced QPSK signals. I

This paper uses MAP estimation techniques to obtain carrier reconstruction circuits for unbalanced QPSK signals. In addition, the performance analysis of these circuits is carried out to the extent that a loop design can proceed. Numerical results are presented in order to demonstrate the utility of the theory developed. This signal design will be used in the development of the Tracking and Data Relay Satellite System (TDRSS) and the Navigation Satellite Timing and Ranging Global Positioning System (NAVSTAR GPS).

Braun, W. R.↗