Controlled coherent dynamics of [VO(TPP)], a prototype molecular nuclear qudit with an electronic ancilla

Abstract

We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system suitable to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds an electronic spin 1/2 coupled through hyperfine interaction to a nuclear spin 7/2, both characterized by remarkable coherence. We demonstrate this by an extensive broadband nuclear magnetic resonance study, which allow us to characterize the nuclear spin-Hamiltonian and to measure the spin dephasing time as a function of the magnetic field. In addition, we combine targeted measurements and numerical simulations to show that nuclear spin transitions conditioned by the state of the electronic qubit can be individually addressed and coherently manipulated by resonant radio-frequency pulses, thanks to the remarkably long coherence times and the effective quadrupolar coupling induced by the strong hyperfine coupling. This approach may open new perspectives for developing new molecular qubit-qudit systems.

Radiofrequency to Microwave Coherent Manipulation of an Organometallic Electronic Spin Qubit Coupled to a Nuclear Qudit

“…The measured n T 2 of ca. 20−30 μs are very competitive if compared to the values obtained for other coupled qubit− qudit systems, 64 thus providing a sound starting point for system manipulation without significant coherence losses. Longer nuclear decay times with respect to e T m (more than 1 order of magnitude) are due to the different origins of the two decoherence processes.…”

“…66 Finally, we remark that an axial quadrupolar tensor P proved to be essential to reproduce the NMR spectra. This term, together with the second-order contribution of the transverse hyperfine coupling (see ref 64), is responsible for the differences between the subsequent nuclear gaps and consequently for the spectral resolution of nearest transitions. This ensures the ability to finely address and manipulate single nuclear transitions (vide infra).…”

“…This energy pattern allows us to individually address by NMR each nuclear spin transition. 63,64 Finally, we report on the possibility of observing both nuclear and electronic Rabi oscillations, indicating the possibility of creating any arbitrary superposition of states, either nuclear or electronic. These properties make [V-(Cp) 2 Cl 2 ] a promising candidate to implement qudit-based quantum algorithms and QEC schemes.…”

“…63 This energy level structure gives full control of the system by radiofrequency (rf) pulses resonant with single-quantum transitions. 64 Among the class of complexes which have not yet been considered for this scope a prominent place is occupied by organometallic systems. In this respect, some of us recently reported the first characterization of electronic spin decoherence in an organometallic titanium-based complex, which shows very appealing properties despite its large number of hydrogen atoms.…”

A perspective on scaling up quantum computation with molecular spins

“…Indeed, the performance of the code can be improved by increasing the number of qudit levels, thus making it possible to correct higher-order dephasing errors. This can be done by considering larger nuclear spins, such as 173 Yb in Yb(trensal) 38 (S ¼ 5/2) or 51 V in VOTPP (S ¼ 7/2), 50 shown in Figs. 3(d) and 3(e).…”