Abstract
The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating classical computer gates. As for optical as well as magnetic systems, those gates are obtained as quantum evolutions. Despite, in certain cases they are attained as an asymptotic series of evolution effects. The current work exploits the direct sum of the evolution operator on a non-local basis for the driven bipartite Heisenberg-Ising model to construct a set of equivalent universal gates as straight evolutions for this interaction. The prescriptions to get these gates are reported as well as a general procedure to evaluate their performance.
Highlights
Quantum computation and quantum information are modern developments taking advantage from the Quantum Mechanics features to propose technological applications
We propose and develop a set of universal gates constructed for bipartite magnetic systems ruled by the anysotropic Heisenberg-Ising interaction with strengths Jk along each direction and including driven magnetic fields Bih on each qubit i = 1, 2 in only one of the x, y, z directions (h = 1, 2, 3): Hh =
Exact control for time independent magnetic fields has been used here to reduce the evolution blocks to pertinent blocks to reproduce the gates D alternative to B, but other kinds of control could be introduced [10,18], whose control schemes are well known for the SU (2) dynamics
Summary
Quantum computation and quantum information are modern developments taking advantage from the Quantum Mechanics features to propose technological applications. In this work we explode last property to show that an alternative set of universal gates can be constructed These gates operate on these subspaces defined by the pairs of Bell states as a privileged grammar instead or alternatively to the computational basis (through the block forms depicted there). For the Bell states basis, an analog set of gates could be alternative to the last universal set These gates operates on the entire quantum information space of the bipartite system: D = {(11 ⊗ Sπ/8 2 )B , (11 ⊗ Sπ/4 2 )B , The process of translation is shown in the Figure 1
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