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Register a new userHamiltonian Engineering with Constrained Optimization for Quantum Sensing and Control
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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$^{text -}$ centers. Such a scheme is of interest for NV$^text{-}$ magnetometers which have reached the NV$^text{-}$-NV$^text{-}$ 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.
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Engineering desired Hamiltonian in quantum many-body systems is essential for applications such as quantum simulation, computation and sensing. Conventional quantum Hamiltonian engineering sequences are designed using human intuition based on perturbation theory, which may not describe the optimal solution and is unable to accommodate complex experimental imperfections. Here we numerically search for Hamiltonian engineering sequences using deep reinforcement learning (DRL) techniques and experimentally demonstrate that they outperform celebrated sequences on a solid-state nuclear magnetic resonance quantum simulator. As an example, we aim at decoupling strongly-interacting spin-1/2 systems. We train DRL agents in the presence of different experimental imperfections and verify robustness of the output sequences both in simulations and experiments. Surprisingly, many of the learned sequences exhibit a common pattern that had not been discovered before, to our knowledge, but has an meaningful analytical description. We can thus restrict the searching space based on this control pattern, allowing to search for longer sequences, ultimately leading to sequences that are robust against dominant imperfections in our experiments. Our results not only demonstrate a general method for quantum Hamiltonian engineering, but also highlight the importance of combining black-box artificial intelligence with understanding of physical system in order to realize experimentally feasible applications.
We give an overview of different paradigms for control of quantum systems and their applications, illustrated with specific examples. We further discuss the implications of fault-tolerance requirements for quantum process engineering using optimal control, and explore the possibilities for architecture simplification and effective control using a minimum number of simple switch actuators.
Understanding how to tailor quantum dynamics to achieve a desired evolution is a crucial problem in almost all quantum technologies. We present a very general method for designing high-efficiency control sequences that are always fully compatible with experimental constraints on available interactions and their tunability. Our approach reduces in the end to finding control fields by solving a set of time-independent linear equations. We illustrate our method by applying it to a number of physically-relevant problems: the strong-driving limit of a two-level system, fast squeezing in a parametrically driven cavity, the leakage problem in transmon qubit gates, and the acceleration of SNAP gates in a qubit-cavity system.
Quantum systems can be exquisite sensors thanks to their sensitivity to external perturbations. This same characteristic also makes them fragile to external noise. Quantum control can tackle the challenge of protecting quantum sensors from environmental noise, while leaving their strong coupling to the target field to be measured. As the compromise between these two conflicting requirements does not always have an intuitive solution, optimal control based on numerical search could prove very effective. Here we adapt optimal control theory to the quantum sensing scenario, by introducing a cost function that, unlike the usual fidelity of operation, correctly takes into account both the unknown field to be measured and the environmental noise. We experimentally implement this novel control paradigm using a Nitrogen Vacancy center in diamond, finding improved sensitivity to a broad set of time varying fields. The demonstrated robustness and efficiency of the numerical optimization, as well as the sensitivity advantaged it bestows, will prove beneficial to many quantum sensing applications.
Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.
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