
Generators and Relations for the Group O_n(ℤ[1/2])
We give a finite presentation by generators and relations for the group ...
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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 U_n(ℤ [1/2, i])
Consider the universal gate set for quantum computing consisting of the ...
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The category TOF
We provide a complete set of identities for the symmetric monoidal categ...
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A Straightforward Method to Judge the Completeness of a Polymorphic Gate Set
Polymorphic circuits are a special kind of circuits which possess some d...
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Bisimulations for DelimitedControl Operators
We propose a survey of the behavioral theory of an untyped lambdacalcul...
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Scaled Relative Graph of Normal Matrices
The Scaled Relative Graph (SRG) by Ryu, Hannah, and Yin (arXiv:1902.0978...
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Generators and Relations for Real Stabilizer Operators
Real stabilizer operators, which are also known as real Clifford operators, are generated, through composition and tensor product, by the Hadamard gate, the Pauli Z gate, and the controlledZ gate. We introduce a normal form for real stabilizer circuits and show that every real stabilizer operator admits a unique normal form. Moreover, we give a finite set of relations that suffice to rewrite any real stabilizer circuit to its normal form.
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