Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule

Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. The gradient measurement is possible when the underlying device can realize all Pauli rotations in the expansion of the Hamiltonian whose coefficients depend on the parameter. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.

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Time-dependent Hamiltonian simulation with L1-norm scaling

Quantum ◽

10.22331/q-2020-04-20-254 ◽

2020 ◽

Vol 4 ◽

pp. 254 ◽

Cited By ~ 2

Author(s):

Dominic W. Berry ◽

Andrew M. Childs ◽

Yuan Su ◽

Xin Wang ◽

Nathan Wiebe

Keyword(s):

Quantum Dynamics ◽

Time Dependent ◽

L1 Norm ◽

Linear Combinations ◽

New Techniques ◽

Dyson Series ◽

Hamiltonian Simulation ◽

Simulation Algorithms ◽

Near Term ◽

Parameters Of Interest

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the L1 norm ∫0tdτ‖H(τ)‖max, whereas the best previous results scale with tmaxτ∈[0,t]‖H(τ)‖max. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. These algorithms could potentially be applied to semi-classical simulations of scattering processes in quantum chemistry.

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Noisy atomic magnetometry in real time

New Journal of Physics ◽

10.1088/1367-2630/ac3b71 ◽

2021 ◽

Author(s):

Julia Amoros-Binefa ◽

Jan Kolodynski

Keyword(s):

Real Time ◽

Continuous Measurement ◽

Quantum Evolution ◽

Atomic Spin ◽

Atomic Magnetometry ◽

Stochastic Parameter ◽

Stochastic Fluctuations ◽

The Magnetic Field ◽

General Method ◽

Do So

Abstract Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing, they attain a quantum-enhanced scaling of sensitivity both as a function of time, t, and the number of atoms involved, N. In our work, we rigorously study how such conclusions based on Kalman filtering methods change when inevitable imperfections are taken into account: in the form of collective noise, as well as stochastic fluctuations of the field in time. We prove that even an infinitesimal amount of noise disallows the error to be arbitrarily diminished by simply increasing N, and forces it to eventually follow a classical-like behaviour in t. However, we also demonstrate that, "thanks" to the presence of noise, in most regimes the model based on a homodyne-like continuous measurement actually achieves the ultimate sensitivity allowed by the decoherence, yielding then the optimal quantum-enhancement. We are able to do so by constructing a noise-induced lower bound on the error that stems from a general method of classically simulating a noisy quantum evolution, during which the stochastic parameter to be estimated—here, the magnetic field—is encoded. The method naturally extends to schemes beyond the linear-Gaussian regime, in particular, also to ones involving feedback or active control.

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Image Analysis of Intramembrane Particles in Freeze-Fractured Biomembranes Using Computer Simulation Techniques

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100114694 ◽

1975 ◽

Vol 33 ◽

pp. 214-215

Author(s):

D.J. Benefiel ◽

R.S. Weinstein

Keyword(s):

Membrane Proteins ◽

Freeze Fracture ◽

Integral Membrane Proteins ◽

Systematic Evaluation ◽

Intramembrane Particles ◽

Modeling Methods ◽

Simulation Techniques ◽

Freeze Fracture Electron Microscopy ◽

Fracture Electron ◽

Computer Simulation Techniques

Intramembrane particles (IMP or MAP) are components of most biomembranes. They are visualized by freeze-fracture electron microscopy, and they probably represent replicas of integral membrane proteins. The presence of MAP in biomembranes has been extensively investigated but their detailed ultrastructure has been largely ignored. In this study, we have attempted to lay groundwork for a systematic evaluation of MAP ultrastructure. Using mathematical modeling methods, we have simulated the electron optical appearances of idealized globular proteins as they might be expected to appear in replicas under defined conditions. By comparing these images with the apearances of MAPs in replicas, we have attempted to evaluate dimensional and shape distortions that may be introduced by the freeze-fracture technique and further to deduce the actual shapes of integral membrane proteins from their freezefracture images.

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Σ =13 tilt grain boundary in silicon bicrystal

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100175946 ◽

1990 ◽

Vol 48 (4) ◽

pp. 562-563

Author(s):

M.J. Kim ◽

Y.L. Chen ◽

R.W. Carpenter ◽

J.C. Barry ◽

G.H. Schwuttke

Keyword(s):

Grain Boundary ◽

Grain Boundaries ◽

Rotation Axis ◽

Czochralski Method ◽

High Resolution Electron Microscopy ◽

Image Simulation ◽

Simulation Techniques ◽

Resolution Electron ◽

The Common ◽

Tilt Grain Boundary

The structure of grain boundaries (GBs) in metals, semiconductors and ceramics is of considerable interest because of their influence on physical properties. Progress in understanding the structure of grain boundaries at the atomic level has been made by high resolution electron microscopy (HREM) . In the present study, a Σ=13, (510) <001>-tilt grain boundary in silicon was characterized by HREM in conjunction with digital image processing and computer image simulation techniques.The bicrystals were grown from the melt by the Czochralski method, using preoriented seeds. Specimens for TEM observations were cut from the bicrystals perpendicular to the common rotation axis of pure tilt grain boundary, and were mechanically dimpled and then ion-milled to electron transparency. The degree of misorientation between the common <001> axis of the bicrystal was measured by CBED in a Philips EM 400ST/FEG: it was found to be less than 1 mrad. HREM was performed at 200 kV in an ISI-002B and at 400 kv in a JEM-4000EX.

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Analyzing the Potential Benefit of Microcomputer Use for Teaching Figurative Language

American Journal of Speech-Language Pathology ◽

10.1044/1058-0360.0102.36 ◽

1992 ◽

Vol 1 (2) ◽

pp. 36-43 ◽

Cited By ~ 5

Author(s):

Marilyn A. Nippold ◽

Ilsa E. Schwarz ◽

Molly Lewis

Keyword(s):

Language Learning ◽

Children And Adolescents ◽

Standardized Tests ◽

Figurative Language ◽

Language Intervention ◽

School Age Children ◽

Educational Materials ◽

Language Learning Disabilities ◽

Promising Application ◽

Experience Difficulty

Microcomputers offer the potential for increasing the effectiveness of language intervention for school-age children and adolescents who have language-learning disabilities. One promising application is in the treatment of students who experience difficulty comprehending figurative expressions, an aspect of language that occurs frequently in both spoken and written contexts. Although software is available to teach figurative language to children and adolescents, it is our feeling that improvements are needed in the existing programs. Software should be reviewed carefully before it is used with students, just as standardized tests and other clinical and educational materials are routinely scrutinized before use. In this article, four microcomputer programs are described and evaluated. Suggestions are then offered for the development of new types of software to teach figurative language.

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