Considering qutrits as the foundational unit for quantum information — rather than qubits — opens up exciting possibilities for encoding data in higher-dimensional spaces. It is the link with the QM, QFT and quantum computing maybe if the 3 level systems are considered instead of binary qubits. That can permit to naturally consider the phase,inputs , outputs ,and space representations with the positions, momentum and volumes,. If the primary informations are in this logic , so the quantum states can be represented in a continuous context . The multidimenisonal phase space and this uncertainty so become relevant . We know that the phases are essential for the quantum computing in checking the interactions of states, , so the superpositions of qutrits also . The angles become intriguing and rotations also .The transformations are more complex and moimate the universe maybe and the spherical volumes and oscillations, motions, rotations,......It seems possible with the coordinates sets and calculations and geonetric transformations and phases shifts and error correction mechanisms. So the qutrits gates and phase space and circuits with the error resistances can appear.
The relevance is the encodings with the volumes and phases interferences , that could permit to filter or amplify the states, The specific regions of phases can permit the input and output .
The mapping of these inputs and outputs with topological and geometrical tramsformations become relevant with the coordinates and these transformations. The logical operations and calculations with the position, momentum and volumes for the qutrit states become relevant also for the changes preserving the volumes and it is taking like a protection of quantum informations like gates.
For the representation of circuits with the qutrit phase spaces. it is complex with the gates for the rotations, translations, momemtum changes, and even volume changes , for the density it is an other possible story, The fact to buil circuits in hhigher diemnsional gaytes with concrete quantum algorythms could permit to reduce the circuits , it seems interesting for the machine learning and simulations , maybe for the cryptography also,The fact to encode and transform in these higher dimensional spaces can improve the actual models and their efficiency with even better quantum error corrections and better storages with better resistances,
