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A Note on the Approximability of Deepest-Descent Circuit Steps [article]

Steffen Borgwardt, Cornelius Brand, Andreas Emil Feldmann, Martin Koutecký
2021 arXiv   pre-print
Linear programs (LPs) can be solved by polynomially many moves along the circuit direction improving the objective the most, so-called deepest-descent steps (dd-steps).  ...  Computing these steps is NP-hard (De Loera et al., arXiv, 2019), a consequence of the hardness of deciding the existence of an optimal circuit-neighbor (OCNP) on LPs with non-unique optima.  ...  Then an (n− rank(A))-approximation of a c-deepest-descent circuit step in P from x 0 can be computed in polynomial time. Proof.  ... 
arXiv:2010.10809v2 fatcat:rrmdycazybb6bcwkziv3fzwv2m

An implementation of steepest-descent augmentation for linear programs [article]

Steffen Borgwardt, Charles Viss
2019 arXiv   pre-print
Steepest-descent augmentation is especially promising, but an implementation of the iterative scheme is a significant challenge.  ...  Generalizing the simplex method, circuit augmentation schemes for linear programs follow circuit directions through the interior of the underlying polyhedron.  ...  One example of a circuit augmentation algorithm is the greedy or deepest-descent augmentation scheme from [10, 11] which requires at most (weakly) polynomially many steps.  ... 
arXiv:1911.08636v1 fatcat:7anhydgdtvaydg4k7ax43pwfg4

On Augmentation Algorithms for Linear and Integer-Linear Programming: From Edmonds--Karp to Bland and Beyond

Jesús A. De Loera, Raymond Hemmecke, Jon Lee
2015 SIAM Journal on Optimization  
and are closely related to research on the diameters of polytopes and the search for a strongly polynomial-time simplex or augmentation algorithm.  ...  Our results also improve on what is known for such algorithms in the context of linear optimization (e.g., generalizing the bounds of Kitahara and Mizuno for the number of steps in the simplex method)  ...  The first author is thankful to the Technical University of Munich for the support and hospitality received during his visit in Spring 2013 as a John von Neumann professor and to the NSF for the support  ... 
doi:10.1137/151002915 fatcat:phyhbcnakfbgtaqnje4cgtypom

Constrained Optimization Applied to the Parameter Setting Problem for Analog Circuits

David Kirk, Kurt W. Fleischer, Lloyd Watts, Alan H. Barr
1991 Neural Information Processing Systems  
Automated parameter setting is an integral part of a goal-based engineering design methodology in which circuits are constructed with parameters enabling a wide range of behaviors, and are then "tuned"  ...  Choosing the proper circuit parameters is important to compensate for manufacturing deviations or adjust circuit performance within a certain range.  ...  All opinions, findings, conclusions, or recommendations expressed in this document are those of the author and do not necessarily reflect the views of the sponsoring agencies.  ... 
dblp:conf/nips/KirkFWB91 fatcat:3qexy3u5ibhafcr5lbgrjeyh2a

Imaging with terahertz pulses

Timothy Dorney, Jon Johnson, Daniel Mittleman, Richard G. Baraniuk, Andrew G. Tescher
2000 Applications of Digital Image Processing XXIII  
This paper provides a brief introduction of the state-of-the art in THz imaging. It also focuses on expanding the potential of this new and exciting field through two major efforts.  ...  The first concentrates on improving the experimental sensitivity of the system. We are exploring an interferometric arrangement to provide a background-free reflection imaging geometry.  ...  ACKNOWLEDGEMENTS We wish to acknowledge the support of the Army Research Office, the Environmental Protection Agency, and the National Science Foundation.  ... 
doi:10.1117/12.411592 fatcat:djvcuvxbxjg2xecjjx2yp72kku

Circuit imbalance measures and linear programming [article]

Farbod Ekbatani, Bento Natura, László A. Végh
2021 arXiv   pre-print
We also present new bounds on the diameter and circuit diameter of polyhedra in terms of the fractional circuit imbalance measure.  ...  The fractional circuit imbalance measure turns out to be a crucial parameter in the context of linear programming, and two integer variants can be used to describe integrality properties of associated  ...  Acknowledgements The authors are grateful to Daniel Dadush for numerous inspiring discussions and joint work on circuit imbalances and linear programming.  ... 
arXiv:2108.03616v2 fatcat:5qquu3nv3zbozjtp73wnkj6hy4

Deep Learning Works in Practice. But Does it Work in Theory? [article]

Lê Nguyên Hoang, Rachid Guerraoui
2018 arXiv   pre-print
Deep learning relies on a very specific kind of neural networks: those superposing several neural layers.  ...  Roughly speaking, we conjecture that the shortest computational descriptions of the universe are algorithms with inherently large computation times, even when a large number of computers are available  ...  on circuits of depth k − 1.  ... 
arXiv:1801.10437v1 fatcat:x4nocianqbhmldaimo3kifg66a

Unified approach to data-driven quantum error mitigation [article]

Angus Lowe, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, Lukasz Cincio
2020 arXiv   pre-print
For the problem of estimating the energy of an 8-qubit Ising model system, vnCDR improves the absolute energy error by a factor of 33 over the unmitigated results and by factors 20 and 1.8 over ZNE and  ...  For the problem of correcting observables from random quantum circuits with 64 qubits, vnCDR improves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively.  ...  (Clifford data) Choose a set of circuits S = {V i } m i=1 based on U which will be used to form the training set T in step 3.  ... 
arXiv:2011.01157v1 fatcat:wkwm5wbdnzgy7c4jrdnqs6vie4

On Circuit Diameter Bounds via Circuit Imbalances [article]

Daniel Dadush, Zhuan Khye Koh, Bento Natura, László A. Végh
2022 arXiv   pre-print
We show that the circuit diameter of a system {x ∈ℝ^n: Ax=b, 0≤ x≤ u} for A ∈ℝ^m × n is bounded as O(m min{m, n-m}log(m+ κ_A)+n log n), where κ_A is the circuit imbalance measure of the constraint matrix  ...  We study the circuit diameter of polyhedra, introduced by Borgwardt, Finhold, and Hemmecke (SIDMA, 2015) as a relaxation of the combinatorial diameter.  ...  This can be compared with the bounds O(nL A,b ) using deepest descent augmentation steps in [DLHL15, DLKS19] , where L A,b is the encoding length of (A, b).  ... 
arXiv:2111.07913v2 fatcat:ouucc7guzvakzidxmyqgvmj2r4

Generic Security Analysis Framework for Quantum Secure Direct Communication [article]

Zhangdong Ye, Dong Pan, Zhen Sun, Chunguang Du, Liuguo Yin, Guilu Long
2021 arXiv   pre-print
With these properties considered, we predict the robust framework would open up a broad avenue of the development in the field.  ...  In this paper, we establish a new framework of the security analysis driven by numerics where all the practical problems may be taken into account naturally.  ...  A |C) − H(E A |W B )] ρ ABCEW . (5) Note that the second term of the right hand side of Eq  ... 
arXiv:2011.14546v3 fatcat:wncqfmduljexdoa43m7yxqwpzm

A learning framework for winner-take-all networks with stochastic synapses [article]

Hesham Mostafa, Gert Cauwenberghs
2018 arXiv   pre-print
In this paper, we show that a biologically motivated model based on multi-layer winner-take-all (WTA) circuits and stochastic synapses admits an approximate analytical description.  ...  This allows us to use the proposed networks in a variational learning setting where stochastic backpropagation is used to optimize a lower bound on the data log likelihood, thereby learning a generative  ...  Research Corporation (NERC), a wholly owned subsidiary of the Semiconductor Research Corporation (SRC), through Extremely Energy Efficient Collective Electronics (EXCEL), an SRC-NRI Nanoelectronics Research  ... 
arXiv:1708.04251v2 fatcat:nx2ykqle2nhgngjntfwcgzpkbm

Galileo Probe Mass Spectrometer experiment

H.B. Niemann, D.N. Harpold, S.K. Atreya, G.R. Carignan, D.M. Hunten, T.C. Owen
1992 Space Science Reviews  
The Galileo Probe Mass Spectrometer (GPMS) is a Probe instrument designed to measure the chemical and isotopic composition including vertical variations of the constituents in the atmosphere of Jupiter  ...  The measurement will be performed by in situ sampling of the ambient atmosphere in the pressure range from approximately 150 mbar to 20 bar.  ...  At the General Electric Co. we thank V. Geracy, L. Milton and their team members for the hybrid circuit fabrication.  ... 
doi:10.1007/bf00216852 fatcat:bdxn7b6w7jgiliq3yblf5wt6uq

Robust quantum compilation and circuit optimisation via energy minimisation [article]

Tyson Jones, Simon C Benjamin
2022 arXiv   pre-print
We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. B|in> = A|in>.  ...  We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable 'blind' compilation i.e. harnessing a device whose  ...  We note other recent efforts to perform approximate recompilation of quantum circuits.  ... 
arXiv:1811.03147v5 fatcat:3yzm4b7llnbshlemt2vnhvi33q

Galileo Probe Mass Spectrometer Experiment [chapter]

H. B. Niemann, D. N. Harpold, S. K. Atreya, G. R. Carignan, D. M. Hunten, T. C. Owen
1992 The Galileo Mission  
The instrument weighs 13.2 kg and the average power consumption is 13 W. The instrument follows a sampling sequence of 8192 steps and a sampling rate of two steps per second.  ...  The measurement will be performed by in situ sampling of the ambient atmosphere in the pressure range from approximately 150 mbar to 20 bar.  ...  At the General Electric Co. we thank V. Geracy, L. Milton and their team members for the hybrid circuit fabrication.  ... 
doi:10.1007/978-94-011-2512-3_5 fatcat:xva6s2a4fzaz7fthxjrnacv7cu

Robust quantum compilation and circuit optimisation via energy minimisation

Tyson Jones, Simon C. Benjamin
2022 Quantum  
We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e.  ...  We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable 'blind' compilation i.e. harnessing a device whose  ...  We note other recent efforts to perform approximate recompilation of quantum circuits.  ... 
doi:10.22331/q-2022-01-24-628 fatcat:itsdvmlboreopno4zerq5q4aky
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