
Generators and relations for U_n(ℤ [1/2, i])
Consider the universal gate set for quantum computing consisting of the ...
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Generators and Relations for Real Stabilizer Operators
Real stabilizer operators, which are also known as real Clifford operato...
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Decomposition of Clifford Gates
In faulttolerant quantum computation and quantum errorcorrection one i...
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Periodicity of lively quantum walks on cycles with generalized Grover coin
In this paper we extend the study of three state lively quantum walks on...
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A Graphical Calculus for Lagrangian Relations
Symplectic vector spaces are the phase space of linear mechanical system...
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Some relations on prefix reversal generators of the symmetric and hyperoctahedral group
The pancake problem is concerned with sorting a permutation (a stack of ...
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Circuit Relations for Real Stabilizers: Towards TOF+H
The real stabilizer fragment of quantum mechanics was shown to have a co...
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Generators and Relations for the Group O_n(ℤ[1/2])
We give a finite presentation by generators and relations for the group O_n(ℤ[1/2]) of ndimensional orthogonal matrices with entries in ℤ[1/2]. We then obtain a similar presentation for the group of ndimensional orthogonal matrices of the form M/√(2)^k, where k is a nonnegative integer and M is an integer matrix. Both groups arise in the study of quantum circuits. In particular, when the dimension is a power of 2, the elements of the latter group are precisely the unitary matrices that can be represented by a quantum circuit over the universal gate set consisting of the Toffoli gate, the Hadamard gate, and the computational ancilla.
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