Coherent manipulation of three spin qubits in a GdW₃₀ single-ion magnet

Implementing quantum computation with spins faces the challenge of increasing the number of qubits while keeping errors under control. Even the simplest algorithm implies coupling two or more qubits in a controlled manner. However, dipolar interactions are also an important source of decoherence [1]. Here, we explore a way to scale up quantum resources, without introducing additional decoherence, by integrating several electron spin qubits in a single magnetic ion with spin S > ½. This approach is illustrated with a [Gd(H₂O)P₅W₃₀O₁₁₀]^12- polyoxometalate single-ion magnet [2]. Electron paramagnetic resonance experiments have been performed on molecules diluted in a crystal of the diamagnetic isostructural derivative [Y(H₂O)P₅W₃₀O₁₁₀]^12-. The seven allowed transitions between the 2S+1=8 spin states have been separately addressed and its spin coherence T₂ and spin-lattice relaxation T₁ rates measured. Rabi oscillations have been observed for all transitions. The spin states of each Gd³⁺ ion can then be mapped onto the states of three addressable qubits (or, alternatively, of a d = 8-level molecular “qudit”), for which the seven allowed transitions form a universal set of operations. Within this scheme, one of the coherent oscillations observed experimentally provides an implementation of a controlled-controlled-NOT (or Toffoli) three-qubit gate. We also propose a way to implement a simple quantum error correction code using this single-ion "processor". Our findings [3] open prospects for developing more complex and robust quantum computation schemes based on molecular spin qubits.

[1] A. Morello et al, Phys. Rev. Lett., 97, 207206 (2006).
[2] M. J. Martínez-Pérez et al, Phys Rev. Lett. 108, 247213 (2012).
[3] M. D. Jenkins et al, Phys. Rev. B 95, 064423 (2017).