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Rational Hadamard products via Quantum Diagonal Operators
[article]

2008
*
arXiv
*
pre-print

fonctions) of the

arXiv:0810.3641v1
fatcat:767m56lk35b7bnrp3nq2exci7y
*Hadamard**product*by a*rational*fraction. ... We use the remark that, through Bargmann-Fock representation,*diagonal**operators*of the Heisenberg-Weyl algebra are scalars for the*Hadamard**product*to give some properties (like the stability of periodic ... In order to compute the*Hadamard**products*of the elements of the basis (5) , one remarks that the*diagonal**operators*are scalars for the*Hadamard**product*. ...##
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Generating functions for effective Hamiltonians via the symmetrized Hadamard product

2008
*
Journal of Physics A: Mathematical and Theoretical
*

The method is based on the application of the Molien generating function technique and the

doi:10.1088/1751-8113/41/38/382004
fatcat:qxwfewqw4nbolizzggdaiqkcr4
*Hadamard**product*of*rational*functions. ... The latter leads to the representation of the answer in a form of a*rational*function. ... n z n . (2) The following fact is known: the*Hadamard**product*of two*rational*functions is a*rational*function [8, 11, 15, 25] . ...##
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Quantum approximate optimization is computationally universal
[article]

2018
*
arXiv
*
pre-print

The

arXiv:1812.11075v1
fatcat:ogbcoqbnpzgb7npsjl74vfn7j4
*quantum*approximate optimization algorithm (QAOA) applies two Hamiltonians to a*quantum*system in alternation. ... This paper shows that the same alternating procedure can be used to perform universal*quantum*computation: the times for which the Hamiltonians are applied can be programmed to give a computationally universal ... He −it 2 H Z He −it 1 H Z , (9) where H = H 1 ⊗ . . . ⊗ H j . . . is the tensor*product*of single qubit*Hadamard**operations*, is also computationally universal. ...##
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What is random about a quantum random walk?
[article]

2003
*
arXiv
*
pre-print

We use simple deterministic dynamical systems as coins in studying

arXiv:quant-ph/0305026v1
fatcat:m4kaf6ubtjbudastsplmcuoxau
*quantum*walks. ... Introducing multi-Harper maps as deterministic models of random walks we study the effect of coin chaos on the*quantum*walk. ... It has solely been financed by the tax payers of India*via*the agency of the Department of Space, Govt. of India. ...##
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Quantum random walks in one dimension via generating functions

2007
*
Discrete Mathematics & Theoretical Computer Science
*

International audience We analyze nearest neighbor one-dimensional

doi:10.46298/dmtcs.3533
fatcat:72ex56vaynfxpopsj6ens6tbkq
*quantum*random walks with arbitrary unitary coin-flip matrices. ... This unitary composition of*operators*represents one step of the*Hadamard*walk. ... Ambainis et al. focus on the*Hadamard*walk. This is based on the*Hadamard*transformation, a unitary*operator*on l 2 (Σ) whose matrix with respect to the standard basis is U √ 1 2 := 1 √ 2 1 1 1 −1 . ...##
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Bounds on the number of time steps for simulating arbitrary interaction graphs
[article]

2002
*
arXiv
*
pre-print

To express the effect of the control

arXiv:quant-ph/0203061v2
fatcat:44iubkv2pngylgpbzpoexzbiri
*operations*on the coupling matrix J note that any unitary*operation*u ∈ SU (d) corresponds to a rotation on the m-dimensional sphere*via*the relation u † α c α σ α ... Here a*quantum*computer can be any*quantum*system provided that its time evolution can be controlled in a universal way. ...##
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Quantum information processing by weaving quantum Talbot carpets

2015
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

Interpretation of the Talbot effect as a

doi:10.1103/physreva.91.062328
fatcat:xgizpx3my5bxfmwuzogfthqzvq
*quantum*logic*operation*provides a beautiful and interesting way to visualize*quantum*computation through wave propagation and interference. ... Adding a*diagonal*phase gate, we show that a complete set of single quDit gates can be implemented. ...*Diagonal*gates and the*quantum*Fourier transform While free space propagation naturally implements a whole family of single quDit transformations*via*the Talbot effect, some commonly used linear optics ...##
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Introduction to topological quantum computation with non-Abelian anyons

2018
*
Quantum Science and Technology
*

of braids to perform specific

doi:10.1088/2058-9565/aacad2
fatcat:53byvb5wjfhpfjukxxcwr5yvoa
*operations*. ... Topological*quantum*computers promise a fault tolerant means to perform*quantum*computation. ... Acknowledgments 45 ACKNOWLEDGMENTS We acknowledge support from the Australian Research Council (ARC)*via*Discovery Project No. DP170104180. ...##
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3778676.pdf

2019
*
Figshare
*

*Hadamard*coin. ... With the

*Hadamard*coin

*operator*, one can arrive at a matrix representation of the single-step time evolution

*operator*in -space. ... Considering a

*Hadamard*gate, one can write: The initial state of the walker is prepared as: | (0) = |0 ⊗ | . ...

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Perfect quantum state transfer using Hadamard diagonalizable graphs

2017
*
Linear Algebra and its Applications
*

Here, we focus on the corresponding Laplacian matrix, and those graphs for which the Laplacian can be

doi:10.1016/j.laa.2017.05.037
fatcat:ystcnwhxbzcxjn6sfls4gcddgm
*diagonalized*by a*Hadamard*matrix. ...*Quantum*state transfer within a*quantum*computer can be achieved by using a network of qubits, and such a network can be modelled mathematically by a graph. ... INTRODUCTION Accurate transmission of*quantum*states between processors and/or registers of a*quantum*computer is critical for short distance communication in a physical*quantum*computing scheme. ...##
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Quantum circuits ofT-depth one

2013
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

This research was also supported by the Intelligence Advanced Research Projects Activity (IARPA)

doi:10.1103/physreva.87.042302
fatcat:hzhw6fxpsbc3pfcmmcozbwhxcq
*via*Department of Interior National Business Center contract number D11PC20168. The U.S. ... Let us call an*operator*almost classical if it can be written as a*product*of a classical*operator*and a*diagonal**operator*. ... Then E |0 E |+ is a*rational*number. Proof. ...##
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Self-Testing of Universal and Fault-Tolerant Sets of Quantum Gates

2007
*
SIAM journal on computing (Print)
*

The first universal

doi:10.1137/s0097539702404377
fatcat:taebrrlf7fhejcagg267hqt7de
*quantum*gate which*operates*on three qubits was identified by Deutsch [Deu89] . ... The intermediate*quantum*states of this process cannot be used by the program, which cannot perform any other*quantum**operations*either. ... A*quantum*circuit*operates*on n*quantum*bits (qubits), where n is some integer. ...##
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Towards topological quantum computer

2018
*
Nuclear Physics B
*

One of the principal obstacles on the way to

doi:10.1016/j.nuclphysb.2017.11.016
fatcat:hhnisfmibbafrppx6gnea7pdyq
*quantum*computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic*operations*( ... , integrable systems and modern theory of non-perturbative calculations in*quantum*field and string theory. ... This evolution matrix is*diagonal*, since we constructed it in the basis of irreps in the*product*of two spins. ...##
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Quantum Automata and Quantum Grammars
[article]

1997
*
arXiv
*
pre-print

We find analogs of several classical theorems, including pumping lemmas, closure properties,

arXiv:quant-ph/9707031v1
fatcat:xi7iemcd3vcolgaocn5py62qnq
*rational*and algebraic generating functions, and Greibach normal form. ... To study*quantum*computation, it might be helpful to generalize structures from language and automata theory to the*quantum*case. ... We hope that*quantum*grammars and automata will be fruitful areas of research and that they will be useful to people studying*quantum*computation. ...##
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Quantum automata and quantum grammars

2000
*
Theoretical Computer Science
*

We ÿnd analogs of several classical theorems, including pumping lemmas, closure properties,

doi:10.1016/s0304-3975(98)00191-1
fatcat:amjxp3twvzfmre4vtixfnxccna
*rational*and algebraic generating functions, and Greibach normal form. ... To study*quantum*computation, it might be helpful to generalize structures from language and automata theory to the*quantum*case. ... Acknowledgements We are grateful to Bruce Litow, Philippe Flajolet, and Christophe Reutenauer for the proof that the*Hadamard*square of an algebraic series can be transcendental; Bruce Reznick, Jan-Christoph ...
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