Quantum computers based on rare-earth compounds and PT- and anti-PT symmetric qubits

Hardware of modern quantum computing (QC) platforms is based mainly on superconductors and ion traps. It demands ultra-low temperature and high vacuum. Practicality and scaling up thus remain questionable. This work analyzes the alternative based on the micro- and nanoparticles of the compounds of Rare Earth (RE) elements, such as phosphors NaYF4: X3+ (X stands for Tm, Er, etc.), embedded in polymer matrices. The qubits in these systems correspond to the quantum levels of 4f electrons of RE ions, and they have optical frequencies. Qubit formation is supported by the properties of RE ions: (a) weak interaction with the environment, (b) strong inhomogeneous crystal field, and (c) the ability of neighboring ions, being in some 4f states, to interact with each other through the mechanism of Stark blockade. The latter is required for quantum conditional gate operations, such as Controlled NOT (CNOT – the basic block of a quantum computer circuit). Optical spectroscopy indicated that CNOT gate can be implemented, for instance, using the transitions in for-level system of Tm3+ ions |3H6> (ground state), |3H4> (state 0), |1D2> (state 1), and |1I6> (auxiliary state 1’) activated with conventional tunable lasers at 451, 653, 798, and 1459 nm. We also considered the PT- and anti-PT-symmetry on the decoherence rate of the qubits. PT-symmetric Hamiltonian H(x) has its real part symmetric versus x-coordinate, and the anti-PT-symmetric one is anti-symmetric. Anti-PT symmetric qubits tend to be more decoherence stable than the others. It was suggested that the anti-PT-symmetry can be introduce via coupling of the qubits to anti-PT-symmetric cavities using RE-doped compounds as gain media.