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A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz [article]

Alexander Cowtan and Will Simmons and Ross Duncan
2020 arXiv   pre-print
This is achieved by partitioning Pauli exponential terms into mutually commuting sets. These sets are then diagonalised using Clifford circuits and synthesised using the phase polynomial formalism.  ...  This strategy reduces cx depth by 75.4% on average, and by up to 89.9%, compared to naive synthesis for a variety of molecules, qubit encodings and basis sets.  ...  Diagonalising a commuting set This section describes our method for diagonalising a set of commuting Pauli gadgets.  ... 
arXiv:2007.10515v3 fatcat:uuyeu3y7ejfg5mjnlfv6h23zm4

A comparison of iterative and DFT-Based polynomial matrix eigenvalue decompositions

Fraser K. Coutts, Keith Thompson, Ian K. Proudler, Stephan Weiss
2017 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
The first of these -sequential matrix diagonalisation (SMD) -iteratively decomposes a parahermitian matrix, while the second DFT-based algorithm computes a pointwise in frequency decomposition.  ...  As an extension of the ordinary EVD to polynomial matrices, the PEVD will generate paraunitary matrices that diagonalise a parahermitian matrix.  ...  The method can either return a spectrally majorised decomposition, akin to the example in Fig. 1(b) , or attempt to compute smooth, ideally analytic, eigenvalues as shown in the example of Fig. 1(a)  ... 
doi:10.1109/camsap.2017.8313113 dblp:conf/camsap/CouttsTPW17 fatcat:zoyaq4h4frcb3drzkr3oqngymq

Shortening of Paraunitary Matrices Obtained by Polynomial Eigenvalue Decomposition Algorithms

Jamie Corr, Keith Thompson, Stephan Weiss, Ian Proudler, John McWhirter
2015 2015 Sensor Signal Processing for Defence (SSPD)  
The results presented in this paper compare the effect a simple change in PEVD method can have on the performance of the paraunitary truncation.  ...  This paper extends the analysis of the recently introduced row-shift corrected truncation method for paraunitary matrices to those produced by the state-of-the-art sequential matrix diagonalisation (SMD  ...  Truncated Order and Diagonalisation As previously shown in [13] , the row-shift corrected method has a significant effect on reducing the paraunitary order for the SBR2 method, however with the SMD algorithm  ... 
doi:10.1109/sspd.2015.7288523 fatcat:q6qpnjfmabcvbl6vzkafmxfqhe

Black Box Absolute Reconstruction for Sums of Powers of Linear Forms [article]

Pascal Koiran, Subhayan Saha
2021 arXiv   pre-print
We give a randomized algorithm for the following problem: If a homogeneous polynomial f ∈ K[x_1 , . . . , x_n] (where K ⊆ℂ) of degree d is given as a blackbox, decide whether it can be written as a linear  ...  This yields the first algorithm for this problem over ℂ with polynomial running time in the bit model of computation.  ...  Acknowledgements We would like to thank Mateusz Skomra for useful discussions in the early stages of this work, and Frédéric Magniez for discussions on commutativity testing.  ... 
arXiv:2110.05305v1 fatcat:lnclhzas5jd5ld2bxcndkwa6ve

Performance trade-offs in sequential matrix diagonalisation search strategies

Jamie Corr, Keith Thompson, Stephan Weiss, John G. McWhirter, Ian K. Proudler
2015 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
Abstract-Recently a selection of sequential matrix diagonalisation (SMD) algorithms have been introduced which approximate polynomial eigenvalue decomposition of parahermitian matrices.  ...  2015) Performance trade-offs in sequential matrix diagonalisation search strategies. In: 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).  ...  INTRODUCTION Sequential matrix diagonalisation encompasses a family of iterative algorithms that can factorise a parahermitian matrix into an approximate polynomial matrix eigenvalue decomposition (PEVD  ... 
doi:10.1109/camsap.2015.7383727 dblp:conf/camsap/CorrTWMP15 fatcat:fbr6xhv3gfbijahcvmfuz7c2zi

ATOMDIAT — A program for calculating variationally exact ro-vibrational levels of "floppy" triatomics

Jonathan Tennyson
1983 Computer Physics Communications  
A. van der Avoird for helpful discussions and progranmiing advice. I thank Walter Ravenek for his reading of the manuscript.  ...  Recently, Tennyson and Sutcliffe [7, 8] have developed a general LC-RAMP method for atom-diatom systems. this method is characterised by its use of a body-fixed coordinate and polynomial basis sets for  ...  5] [6] [7] [8] [9] .In particular, the variational treatment of the problem by setting up and diagonalising a secular matrix in the style of Le Roy and Van Kranendonk [1] has been a particular area of  ... 
doi:10.1016/0010-4655(83)90010-3 fatcat:jktk674wejdojf64dw4om2hkru

Complexity and search space reduction in cyclic-by-row PEVD algorithms

Fraser K. Coutts, Jamie Corr, Keith Thompson, Stephan Weiss, Ian K. Proudler, John G. McWhirter
2016 2016 50th Asilomar Conference on Signals, Systems and Computers  
In recent years, several algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced.  ...  The PEVD is a generalisation of the ordinary EVD and uses paraunitary operations to diagonalise a parahermitian matrix.  ...  ACKNOWLEDGEMENT Fraser Coutts is the recipient of a Caledonian Scholarship; we would like to thank the Carnegie Trust for their support.  ... 
doi:10.1109/acssc.2016.7869595 dblp:conf/acssc/CouttsCTWPM16 fatcat:txqvtvyj6zec5anwkx2vnn4m5q

Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms

Fraser K. Coutts, Jamie Corr, Keith Thompson, Stephan Weiss, Ian K. Proudler, John G. McWhirter
2016 2016 24th European Signal Processing Conference (EUSIPCO)  
The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations.  ...  A number of algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced.  ...  ACKNOWLEDGEMENT Fraser Coutts is the recipient of a Caledonian Scholarship; we would like to thank the Carnegie Trust for their support.  ... 
doi:10.1109/eusipco.2016.7760525 dblp:conf/eusipco/CouttsCTWPM16 fatcat:4vrfvcmkrngp5nfsne3kevmvou

Analysing the performance of divide-and-conquer sequential matrix diagonalisation for large broadband sensor arrays

Fraser K. Coutts, Keith Thompson, Stephan Weiss, Ian K. Proudler
2017 2017 IEEE International Workshop on Signal Processing Systems (SiPS)  
The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations.  ...  A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced.  ...  ACKNOWLEDGEMENT Fraser Coutts is the recipient of a Caledonian Scholarship; we would like to thank the Carnegie Trust for their support.  ... 
doi:10.1109/sips.2017.8109976 dblp:conf/sips/CouttsTWP17 fatcat:igc5dmll3jc7za3mve3uj5d7q4

Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices

Soydan Redif, Stephan Weiss, John G. McWhirter
2015 IEEE Transactions on Signal Processing  
In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalisation (SMD) is introduced.  ...  to a polynomial matrix EVD (PEVD).  ...  PEVD VIA POLYNOMIAL MATRIX DIAGONALISATION A.  ... 
doi:10.1109/tsp.2014.2367460 fatcat:rctrz5f7gfa2boyghxc76r5oom

A joint diagonalisation approach for linear stochastic systems

C.F. Li, S. Adhikari, Song Cen, Y.T. Feng, D.R.J. Owen
2010 Computers & structures  
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository.  ...  For the Monte Carlo method, a direct solver based on LU factorization is used; for the joint diagonalisation method and the Neumann expansion method, the relative error is set as 2% in comparison to the  ...  The improved joint diagonalisation method is superior to the basic Neumann expansion method in terms of convergence rate.  ... 
doi:10.1016/j.compstruc.2010.06.013 fatcat:2tr5kg36abh7bdpqrbh5eph4ve

Generalised Polynomial Chaos for a Class of Linear Conservation Laws

Roland Pulch, Dongbin Xiu
2011 Journal of Scientific Computing  
To resolve the stochastic model, the Galerkin technique of the generalised polynomial chaos results in a larger coupled system of PDEs.  ...  Mathematical modelling of dynamical systems often yields partial differential equations (PDEs) in time and space, which represent a conservation law possibly including a source term.  ...  In contrast, the hyperbolicity has been proved if a specific set of basis polynomials is applied, which exhibits a tensor product structure based on the univariate polynomials.  ... 
doi:10.1007/s10915-011-9511-5 fatcat:qo25udfwkncldn4drsipdfoxzy

Surface parametrisation without diagonalisation

Christiaan van de Woestijne
2006 Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06  
The resulting algorithm only uses operations on polynomials (as opposed to rational functions), which keeps all occurring degrees small and avoids spurious factors in the discriminant.  ...  This algorithm uses a diagonalised form of the surface equation. We show, using recent algorithms for quadratic forms, that diagonalisation is not necessary.  ...  This also gives a polynomial time algorithm, in terms of operations in the base ring.  ... 
doi:10.1145/1145768.1145823 dblp:conf/issac/Woestijne06 fatcat:i5v7tgfxxjbvxmoodplwqohksm

Restricted update sequential matrix diagonalisation for parahermitian matrices

Fraser K. Coutts, Keith Thompson, Ian K. Proudler, Stephan Weiss
2017 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations.  ...  Abstract-A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced.  ...  ACKNOWLEDGEMENT Fraser Coutts is the recipient of a Caledonian Scholarship; we would like to thank the Carnegie Trust for their support.  ... 
doi:10.1109/camsap.2017.8313112 dblp:conf/camsap/CouttsTPW17a fatcat:emljemveivh45jilznxc7q42tm

Row-shift corrected truncation of paraunitary matrices for PEVD algorithms

Jamie Corr, Keith Thompson, Stephan Weiss, Ian K. Proudler, John G. McWhirter
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
In particular, arbitrary shifts (delays) of polynomials in one row of a PU matrix yield another PU matrix that admits the same PEVD.  ...  In this paper, we show that the paraunitary (PU) matrices that arise from the polynomial eigenvalue decomposition (PEVD) of a parahermitian matrix are not unique.  ...  Based on the ambiguity identified in Sec. 2, we propose a new truncation method in Sec. 4, that finds a paraunitary matrix with a lower order.  ... 
doi:10.1109/eusipco.2015.7362503 dblp:conf/eusipco/CorrTWPM15 fatcat:5ayyal7fczdt5da2nefjkf72v4
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