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An Efficient Quantum Algorithm and Circuit to Generate Eigenstates Of SU(2) and SU(3) Representations

Electronic Theses of Indian Institute of Science

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Title An Efficient Quantum Algorithm and Circuit to Generate Eigenstates Of SU(2) and SU(3) Representations
 
Creator Sainadh, U Satya
 
Subject Quantum Mechanics
Quantum Algorithms
Eigenstates - Special Unitary (SU) Group Representations
Quantum Circuits
Special Unitary (SU) Group Representations
Computational Complexity
Schur Transform
Eigenstate - SU(2)
Eigenstate - SU(3)
High Energy Physics
 
Description Many quantum computation algorithms, and processes like measurement based quantum computing, require the initial state of the quantum computer to be an eigenstate of a specific unitary operator. Here we study how quantum states that are eigenstates of finite dimensional irreducible representations of the special unitary (SU(d)) and the permutation (S_n) groups can be efficiently constructed in the computational basis formed by tensor products of the qudit states. The procedure is a unitary transform, which first uses Schur-Weyl duality to map every eigenstate to a unique Schur basis state, and then recursively uses the Clebsch - Gordan transform to rotate the Schur basis state to the computational basis. We explicitly provide an efficient quantum algorithm, and the corresponding quantum logic circuit, to generate any desired eigenstate of SU(2) and SU(3) irreducible representations in the computational basis.
 
Contributor Patel, Apoorva D
 
Date 2018-04-18T09:46:38Z
2018-04-18T09:46:38Z
2018-04-18
2013
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3425
http://etd.iisc.ernet.in/abstracts/4292/G25929-Abs.pdf
 
Language en_US
 
Relation G25929