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Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, omega^dagger H, and S. All of these gates have matrix entries in the ring Z[1/2,i], the smallest subring of the complex numbers containing 1/2 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in Z[1/2,i] can be realized by a quantum circuit over the above gate set using at most one ancilla. In this paper, we give a finite presentation by generators and relations of U_n(Z[1/2,i]), the group of unitary nxn-matrices with entries in Z[1/2,i].
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 controlled-Z gate. We introduce a normal form for real stabilizer circu
Quantum simulators and processors are rapidly improving nowadays, but they are still not able to solve complex and multidimensional tasks of practical value. However, certain numerical algorithms inspired by the physics of real quantum devices prove
We formulate entropic measurements uncertainty relations (MURs) for a spin-1/2 system. When incompatible observables are approximatively jointly measured, we use relative entropy to quantify the information lost in approximation and we prove positive
We investigate whether a trade-off relation between the diagonal elements of the mean square error matrix exists for the two-parameter unitary models with mutually commuting generators. We show that the error trade-off relation which exists in our mo
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