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Rational Hadamard products via Quantum Diagonal Operators
[article]
2008
arXiv
pre-print
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fonctions) of the 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. ...
arXiv:0810.3641v1
fatcat:767m56lk35b7bnrp3nq2exci7y
Generating functions for effective Hamiltonians via the symmetrized Hadamard product
2008
Journal of Physics A: Mathematical and Theoretical
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The method is based on the application of the Molien generating function technique and the 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] . ...
doi:10.1088/1751-8113/41/38/382004
fatcat:qxwfewqw4nbolizzggdaiqkcr4
Quantum approximate optimization is computationally universal
[article]
2018
arXiv
pre-print
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The 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. ...
arXiv:1812.11075v1
fatcat:ogbcoqbnpzgb7npsjl74vfn7j4
What is random about a quantum random walk?
[article]
2003
arXiv
pre-print
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We use simple deterministic dynamical systems as coins in studying 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. ...
arXiv:quant-ph/0305026v1
fatcat:m4kaf6ubtjbudastsplmcuoxau
Quantum random walks in one dimension via generating functions
2007
Discrete Mathematics & Theoretical Computer Science
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International audience We analyze nearest neighbor one-dimensional 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 . ...
doi:10.46298/dmtcs.3533
fatcat:72ex56vaynfxpopsj6ens6tbkq
Bounds on the number of time steps for simulating arbitrary interaction graphs
[article]
2002
arXiv
pre-print
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To express the effect of the control 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. ...
arXiv:quant-ph/0203061v2
fatcat:44iubkv2pngylgpbzpoexzbiri
Quantum information processing by weaving quantum Talbot carpets
2015
Physical Review A. Atomic, Molecular, and Optical Physics
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2014 pre-print arXiv:1412.2710v1 fatcat:yjnen3wspre6piutlrwzwje4pe
Interpretation of the Talbot effect as a 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 ...
doi:10.1103/physreva.91.062328
fatcat:xgizpx3my5bxfmwuzogfthqzvq
Introduction to topological quantum computation with non-Abelian anyons
2018
Quantum Science and Technology
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2018 pre-print arXiv:1802.06176v1 fatcat:yzevgi6pozhwhjwsqaltufmhxyOther Versions
of braids to perform specific 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. ...
doi:10.1088/2058-9565/aacad2
fatcat:53byvb5wjfhpfjukxxcwr5yvoa
3778676.pdf
2019
Figshare
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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 ⊗ | . ...
doi:10.6084/m9.figshare.7588745.v1
fatcat:mkwoqyl665akzpl55t7btu7yy4
Perfect quantum state transfer using Hadamard diagonalizable graphs
2017
Linear Algebra and its Applications
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2017 pre-print arXiv:1610.06094v2 fatcat:bflk7mh2svhhdegvch3shfp2tqOther Versions
Here, we focus on the corresponding Laplacian matrix, and those graphs for which the Laplacian can be 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. ...
doi:10.1016/j.laa.2017.05.037
fatcat:ystcnwhxbzcxjn6sfls4gcddgm
Quantum circuits ofT-depth one
2013
Physical Review A. Atomic, Molecular, and Optical Physics
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This research was also supported by the Intelligence Advanced Research Projects Activity (IARPA) 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. ...
doi:10.1103/physreva.87.042302
fatcat:hzhw6fxpsbc3pfcmmcozbwhxcq
Self-Testing of Universal and Fault-Tolerant Sets of Quantum Gates
2007
SIAM journal on computing (Print)
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The first universal 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. ...
doi:10.1137/s0097539702404377
fatcat:taebrrlf7fhejcagg267hqt7de
Towards topological quantum computer
2018
Nuclear Physics B
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2017 pre-print arXiv:1703.00431v1 fatcat:dqdckmiacbdpjj2mn34aienkxy
One of the principal obstacles on the way to 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. ...
doi:10.1016/j.nuclphysb.2017.11.016
fatcat:hhnisfmibbafrppx6gnea7pdyq
Quantum Automata and Quantum Grammars
[article]
1997
arXiv
pre-print
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We find analogs of several classical theorems, including pumping lemmas, closure properties, 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. ...
arXiv:quant-ph/9707031v1
fatcat:xi7iemcd3vcolgaocn5py62qnq
Quantum automata and quantum grammars
2000
Theoretical Computer Science
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We ÿnd analogs of several classical theorems, including pumping lemmas, closure properties, 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 ...
doi:10.1016/s0304-3975(98)00191-1
fatcat:amjxp3twvzfmre4vtixfnxccna
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