Quantum alternating operator ansatz for the preparation and detection of long-lived singlet states in NMR

Designing efficient and robust quantum control strategies is vital for developing quantum technologies. One recent strategy is the Quantum Alternating Operator Ansatz (QAOA) sequence that alternatively propagates under two noncommuting Hamiltonians, whose control parameters can be optimized to generate a gate or prepare a state. Here, we describe the design of a QAOA sequence to prepare long-lived singlet states (LLSs) from the thermal state in NMR. With extraordinarily long lifetimes exceeding the spin-lattice relaxation time constant T1, LLSs have been of great interest for various applications, from spectroscopy to medical imaging. Accordingly, designing sequences for efficiently preparing LLS in a general spin system is crucial. Using numerical analysis, we study the efficiency and robustness of our QAOA sequence over a wide range of errors in the control parameters. Using a two-qubit NMR register, we conduct an experimental study to benchmark our QAOA sequence against other prominent methods of LLS preparation and observe superior performance, especially under noisy conditions. Finally, we numerically demonstrate the applicability of our QAOA sequence beyond two-qubit registers, specifically for polychromatic excitation of delocalized LLS in a six-proton system.