Hamiltonian engineering with constrained optimization for quantum sensing and control

Abstract

While quantum devices rely on interactions between constituent subsystems and with their environment to operate, native interactions alone often fail to deliver targeted performance. Coherent pulsed control provides the ability to tailor effective interactions, known as Hamiltonian engineering. We propose a Hamiltonian engineering method that maximizes desired interactions while mitigating deleterious ones by conducting a pulse sequence search using constrained optimization. The optimization formulation incorporates pulse sequence length and cardinality penalties consistent with linear or integer programming. We apply the general technique to magnetometry with solid state spin ensembles in which inhomogeneous interactions between sensing spins limit coherence. Defining figures of merit for broadband Ramsey magnetometry, we present novel pulse sequences which outperform known techniques for homonuclear spin decoupling in both spin-1/2 and spin-1 systems. When applied to nitrogen vacancy (NV) centers in diamond, this scheme partially preserves the Zeeman interaction while zeroing dipolar coupling between negatively charged NV − centers. Such a scheme is of interest for NV − magnetometers which have reached the NV − -NV − coupling limit. We discuss experimental implementation in NV ensembles, as well as applicability of the current approach to more general spin bath decoupling and superconducting qubit control.

Sensitivity Optimization for NV-Diamond Magnetometry

“…Therefore, when seeking to extend T * 2 , one should focus on reducing whichever mechanism is dominant until another mechanism becomes limiting. Reference (O'Keeffe et al, 2019) aptly expresses the proper strategy as a "shoot the alligator closest to the boat" approach. For example, if the dephasing due to substitutional nitrogen is decreased by ∼ 10× in a physical experiment, the improvement in T * 2 may only be 2× if, say, strain inhomogeneity becomes a limiting factor; at that point it becomes more fruitful to shift focus towards reducing strain-induced dephasing.…”

Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems

“…In this work, we introduce a comprehensive framework to address these challenges and efficiently design robust, selfcorrecting pulse sequences for dynamic Hamiltonian engineering in interacting spin ensembles using only global control [81][82][83][84][85][86]. Such globally controlled spin ensembles are naturally realized in various systems [52,57,78,[87][88][89][90][91][92][93].…”

Associative memory on qutrits by means of quantum annealing

“…Note that along with the two-spin interaction, which has the form of the Ising interaction or the dipoledipole interaction, three-spin interactions and interactions containing squares of spin operators are required. Methods for obtaining such interactions with the help of rotation operators selective in transitions between the levels of each of the three spins are described in [14,15,20,21].…”

“…As qurits, it is suggested to use, for example, objects with spin S = 1 in magnetic and crystal fields. These include quadrupole nuclei [9,12,13] of deuterium, nitrogen or lithium, as well as NV centers in diamond (paramagnetic color centers formed by an electron on vacancies near the nitrogen atom) [14,15]. The latter variant is preferable because of the presence of a strong dipole-dipole interaction between NV centers, which is necessary for the implementation of conditional operations in quantum algorithms.…”