Quantum optimal control represents a powerful technique to enhance the performance of quantum experiments by engineering the controllable parameters of the Hamiltonian. However, the computational overhead for the necessary optimization of these control parameters drastically increases as their number grows. We devise a variant of a gradient-free optimal-control method by introducing the idea of phase-modulated driving fields, which allows us to find optimal control fields efficiently. We numerically evaluate its performance and demonstrate the advantages over standard Fourier-basis methods in controlling an ensemble of two-level systems showing an inhomogeneous broadening. The control fields optimized with the phase-modulated method provide an increased robustness against such ensemble inhomogeneities as well as control-field fluctuations and environmental noise, with one order of magnitude less of average search time. Robustness enhancement of single quantum gates is also achieved by the phase-modulated method. Under environmental noise, an XY-8 sequence constituted by optimized gates prolongs the coherence time by $50%$ compared with standard rectangular pulses in our numerical simulations, showing the application potential of our phase-modulated method in improving the precision of signal detection in the field of quantum sensing.
Quantum optimal control represents a powerful technique to enhance the performance of quantum experiments by engineering the controllable parameters of the Hamiltonian. However, the computational overhead for the necessary optimization of these control parameters drastically increases as their number grows. We devise a variant of a gradient-free optimal-control method by introducing the idea of phase-modulated driving fields, which allows us to find optimal control fields efficiently. We numerically evaluate its performance and demonstrate the advantages over standard Fourier-basis methods in controlling an ensemble of two-level systems showing an inhomogeneous broadening. The control fields optimized with the phase-modulated method provide an increased robustness against such ensemble inhomogeneities as well as control-field fluctuations and environmental noise, with one order of magnitude less of average search time. Robustness enhancement of single quantum gates is also achieved by the phase-modulated method. Under environmental noise, an XY-8 sequence constituted by optimized gates prolongs the coherence time by 50 compared with standard rectangular pulses in our numerical simulations, showing the application potential of our phase-modulated method in improving the precision of signal detection in the field of quantum sensing.
Resisting diverse noise effects is crucial for the accurate manipulation of quantum systems. For static or slowly varying noises, many efficient noise mitigation strategies have been developed, such as composite pulses and dynamical decoupling. However, for fast fluctuating noise in the Markovian limit, whether and to what extent coherent quantum control can enhance quantum engineering tasks remains unclear and less explored. Here, we propose a robust quantum optimal control method to tackle Markovian noises. The basic idea is that, regarding the Markovian noise channel as perturbation, we quantitatively characterize the noise-induced error evolution by the perturbative expansion term, and then take them as the objective functions to be suppressed. During optimization, the optimal controls are obtained by maximizing the control target function and meanwhile minimizing the perturbative terms due to Markovian noise order by order. As demonstration examples, we first apply our method to quantum state transfer tasks on two-level and three-level $\mathrm{\ensuremath{\Lambda}}$ systems, then use it to design quantum gates in two-level and three-level ladder systems, all under Markovian noises. The simulation results illustrate that our method can notably enhance quantum state transfer fidelities and have very limited improvement on gate fidelities. The method presented here is versatile and can be extended to enhance the performance of various control tasks under Markovian noise in multilevel or multiqubit quantum systems.
This thesis details work performed on the improvement of experimental control of quantum systems through the use of optimal control theory. We pursue this objective through both conceptual and practical routes. We first devise improved methods of optimal control for quantum systems. We then apply them, as well as more established methods, to experimental situations where robustness to inaccuracy and error is sought. We develop a method for improving the computational efficiency of optimal control theory in the context of quantum control. This approach makes use of the iterative nature of optimisation algorithms, by using perturbation theory to minimise the effort needed to calculate the time propagator associated with a controlled Hamiltonian. We also create a new way of defining a figure of merit when optimising for robustness against error in an experiment. This method specifically applies to errors that have a relatively small effect on the controlled system's Hamiltonian. We compare this with an ensemble method based around randomly sampling several points on the control landscape, and find these methods to be largely equivalent for small errors, with the ensemble method being superior for larger error. On the applied side, we design radio frequency magnetic pulses that create robustness in spin ensembles to inhomogeneous broadening and variations of coupling strength to the control field for two applications. In the first, we create reliable gates in a situation where limitations are imposed on the control that can be applied. In the second application, we design controls for radio frequency magnetic pulses to create a superradiant state in a spin ensemble. Finally, we collaborate with the experiment to measure the electrons electric dipole moment that is being performed at Imperial College London. For this collaboration, we shape the envelope of the radio frequency control pulses used in the experiment to create superpositions of Zeeman and Stark-shifted excited states in YbF molecules. This shaping allows us to impart pre-determined phases to these superpositions, in a manner that is robust to errors in the control pulse envelope. We obtain sets of robust and sensitive pulses that have been sent to the experiment for testing purposes.
A scheme for optimizing quantum gates in quantum computation on decoherence-free subspaces using optimal control theory is presented. Compared with the previous scheme, this scheme possesses the following properties: (i) efficiency in finding control sequences, specifically in a system without controllable exchange interaction where the previous method is difficult to handle; (ii) robustness against control errors; and (iii) showing better performance than the robust GRAPE method under stochastic noise. As an application, we work out the control sequences for the not, quantum phase, and cnot gates.
Quantum information is a growing field showing exciting possibilities for computational speed-up and communications. For the successful implementation of quantum computers, high-precision control is required to reach fault-tolerant thresholds. Control of quantum systems pertains to the manipulation of states and their evolution. In order to minimize the effects of the environment on the control operations of the qubits, control pulses should be made time-optimal. In addition, control pulses should be made robust to noise in the system, dispersion in energies and coupling elements, and uncertain parameters. \n \nIn this thesis, we examine a robust time-optimal gradient ascent technique which is used to develop controls of the motional degrees of freedom for an ensemble of neutral atoms in a one-dimensional optical lattice in the high dispersion regime with shallow trapping potentials. As such, the system is analyzed in the delocalized basis. The system is treated as an ensemble of atoms with a range of possible quasimomenta across the first Brillouin zone. This gives the ensemble of Hamiltonians, indexed by the quasimomenta, a distinct spectra in their motional states and highly inhomogeneous control Hamiltonians. Thus, the optical lattice is seen as a model system for robust control. \n \nWe find optimized control pulses designed using an ensemble modification of gradient-ascent pulse engineering robust to any range of quasimomentum. We show that it is possible to produce rotation controls with fidelities above 90\\% for half of the first Brillouin zone with gate times in the order of several free oscillations. This is possible for a spectrum that shows upwards of 75\\% dispersion in the energies of the band structure. We also show that NOT controls for qubit rotations on the entire Brillouin zone fidelities above 99\\% were possible for 0.6\\% dispersion in energies. The gate times were also in the order of several free oscillations. It is shown that these solutions are palindromic in time due to phase differences in some of the energy couplings when comparing one half of the Brillouin zone to another. We explore the limits of discretized sampling of a continuous ensemble for control.
Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.
Spin ensembles show increasing promise for highly efficient quantum sensing and quantum technologies. However, protecting their coherent properties remains a significant challenge. Dynamical decoupling (DD) typically employs a sequence of fast pulses that aim to reduce the effect of unwanted system-environment interactions. However, the performance of the DD sequences typically suffers in spin ensembles, e.g., due to amplitude and frequency inhomogeneities and control errors. In this work, we compare the performance of an extensive number of DD protocols for coherence protection and quantum sensing in an ensemble of negatively charged NV centers under ambient conditions. We identify the optimal approach that uses rapid adiabatic passage pulses, which are robust to amplitude and frequency inhomogeneity, in combination with the variation of their phases. We experimentally demonstrate an improved signal contrast and an order-of-magnitude increase in memory time with the optimal sequence compared to the widely used XY8 with standard rectangular pulses. We also apply our approach for improved sensing of a weak oscillating field. While our particular demonstration is with NV centers in diamond, the optimized protocol is generally applicable to other spin ensembles and to systems with high amplitude and/or frequency inhomogeneities.