Gradient Ascent Pulse Engineering Algorithm Research Articles

Design of calibration-free RF pulses for T -weighted single-slab 3D turbo-spin-echo sequences at 7T utilizing parallel transmission.

T -weighted turbo-spin-echo (TSE) sequences are a fundamental technique in brain imaging but suffer from field inhomogeneities at ultra-high fields. Several methods have been proposed to mitigate the problem, but were limited so far to nonselective three-dimensional (3D) measurements, making short acquisitions difficult to achieve when targeting very high resolution images, or needed additional calibration procedures, thus complicating their application. Slab-selective excitation pulses were designed for flexible placement utilizing the concept of k -spokes. Phase-coherent refocusing universal pulses were subsequently optimized with the Gradient Ascent Pulse Engineering algorithm and tested in vivo for improved signal homogeneity. Implemented within a 3D variable flip angle TSE sequence, these pulses led to a signal-to-noise ratio (SNR) improvement ranging from 10%to 30% compared to a two-dimensional (2D) T2w TSE sequence employing -shimmed pulses. field inhomogeneities could be mitigated and artifacts from deviations reduced. The concept of universal pulses was successfully applied. We present a pulse design method which provides a set of calibration-free universal pulses (UPs) for slab-selective excitation and phase-coherent refocusing in slab-selective TSE sequences.

Flexible preparation of the W state via the GRAPE algorithm in a nanoring-quantum-dot system

In this paper, we put forward a scheme for flexibly preparing W states in the presence of detunings and asymmetric couplings in a nanoring-quantum-dot (nanoring-QD) system. Based on the gradient ascent pulse engineering algorithm, the coupling strength modulation (CSM) and the energy level modulation (ELM) methods are proposed, respectively. In the CSM method, the waveforms of the coupling strengths are properly designed to compensate for detunings, thus the decline on the fidelity is effectively suppressed. For the asymmetric couplings, a high-fidelity W state can be generated by the ELM method, which alters the energy levels of QDs in a desired manner. Finally, we generalize the current scheme to realize the preparation of N-particle W states in nanoring-QD systems.

Improved quantum computing with higher-order Trotter decomposition

In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ans\"atze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks.

Practical pulse engineering: Gradient ascent without matrix exponentiation

Since 2005, there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as nuclear magnetic resonance quantum information processors. These approaches, which build on the original gradient ascent pulse engineering algorithm, remain computationally intensive because of the need to calculate matrix exponentials for each time step in the control pulse. In this study, we discuss how the propagators for each time step can be approximated using the Trotter–Suzuki formula, and a further speedup achieved by avoiding unnecessary operations. The resulting procedure can provide substantial speed gain with negligible costs in the propagator error, providing a more practical approach to pulse engineering.

Quantum control of nuclear magnetic resonance spin systems

With the development of quantum information science, the active manipulation of quantum systems is becoming an important research frontier. To build realistic quantum information processors, one of the challenges is to implement arbitrary desired operations with high precision on quantum systems. A large number of quantum control methods and relevant numerical techniques have been put forward in recent years, such as quantum optimal control and quantum feedback control. Nuclear magnetic resonance (NMR) spin systems offer an excellent testbed to develop benchmark tools and techniques for controlling quantum systems. In this review paper, we briefly introduce some of the basic control ideas developed for NMR systems in recent years. We first explain, for the liquid spin systems, the physics of various couplings and the causes of relaxation effects. These mechanisms govern the system dynamics, and thus are crucial for constructing rigorous and efficient control models. We also identify three types of available control means: 1) raido-frequency fields as coherent controls; 2) phase cycling, gradient fields and relaxation effects as non-unitary controls; 3) radiation damping effect as feedback control mechanism. Then, we elucidate some important control tasks, which may arise from the conventional NMR spectroscopy (e.g., pulse design and polarization transfer) or from quantum information science (e.g., algorithmic cooling and pseudo-pure state preparation). In the last part, we review some of the most important control methods that are applicable to NMR control tasks. For systems with a relatively small number of spins, it is possible to use analytic optimal control theory to realize the target unitary operations. However, for larger systems, numerical methods are necessary. The gradient ascent pulse engineering algorithm and pulse compiler techniques are the most successful techniques for implementing complicated quantum networks currently. There are some interesting topics of utilizing radiation damping and relaxation effects to achieve more powerful controls. Finally, we give an outline of the possible future work.

Parallel-transmission-enabled three-dimensional T2 -weighted imaging of the human brain at 7 Tesla.

A promise of ultra high field MRI is to produce images of the human brain with higher spatial resolution due to an increased signal to noise ratio. Yet, the shorter radiofrequency wavelength induces an inhomogeneous distribution of the transmit magnetic field and thus challenges the applicability of MRI sequences which rely on the spin excitation homogeneity. In this work, the ability of parallel-transmission to obtain high-quality T2 -weighted images of the human brain at 7 Tesla, using an original pulse design method is evaluated. Excitation and refocusing square pulses of a SPACE sequence were replaced with short nonselective transmit-SENSE pulses individually tailored with the gradient ascent pulse engineering algorithm, adopting a kT -point trajectory to simultaneously mitigate B1 (+) and ΔB0 nonuniformities. In vivo experiments showed that exploiting parallel-transmission at 7T with the proposed methodology produces high quality T2 -weighted whole brain images with uniform signal and contrast. Subsequent white and gray matter segmentation confirmed the expected improvements in image quality. This work demonstrates that the adopted formalism based on optimal control, combined with the kT -point method, successfully enables three-dimensional T2 -weighted brain imaging at 7T devoid of artifacts resulting from B1 (+) inhomogeneity.

Cooperative pulses for pseudo-pure state preparation

Using an extended version of the optimal-control-based gradient ascent pulse engineering algorithm, cooperative (COOP) pulses are designed for multi-scan experiments to prepare pseudo-pure states in quantum computation. COOP pulses can cancel undesired signal contributions, complementing and generalizing phase cycles. They also provide more flexibility and, in particular, eliminate the need to select specific individual target states and achieve the fidelity of theoretical limit by flexibly choosing appropriate number of scans and duration of pulses. The COOP approach is experimentally demonstrated for three-qubit and four-qubit systems.

Design of non-selective refocusing pulses with phase-free rotation axis by gradient ascent pulse engineering algorithm in parallel transmission at 7 T

At ultra-high magnetic field (⩾7T), B1 and ΔB0 non-uniformities cause undesired inhomogeneities in image signal and contrast. Tailored radiofrequency pulses exploiting parallel transmission have been shown to mitigate these phenomena. However, the design of large flip angle excitations, a prerequisite for many clinical applications, remains challenging due the non-linearity of the Bloch equation. In this work, we explore the potential of gradient ascent pulse engineering to design non-selective spin-echo refocusing pulses that simultaneously mitigate severe B1 and ΔB0 non-uniformities. The originality of the method lays in the optimization of the rotation matrices themselves as opposed to magnetization states. Consequently, the commonly used linear class of large tip angle approximation can be eliminated from the optimization procedure. This approach, combined with optimal control, provides additional degrees of freedom by relaxing the phase constraint on the rotation axis, and allows the derivative of the performance criterion to be found analytically. The method was experimentally validated on an 8-channel transmit array at 7T, using a water phantom with B1 and ΔB0 inhomogeneities similar to those encountered in the human brain. For the first time in MRI, the rotation matrix itself on every voxel was measured by using Quantum Process Tomography. The results are complemented with a series of spin-echo measurements comparing the proposed method against commonly used alternatives. Both experiments confirm very good performance, while simultaneously maintaining a low energy deposition and pulse duration compared to well-known adiabatic solutions.

Optimal spin-state transition in singly occupied quantum dots network

We present a general model to study the spin-state transition in a network of singly occupied lateral quantum dots. The perturbative expansion of the extended Hubbard model is used to describe the dynamics of confined electrons as an effective spin Hamiltonian in the strong correlation regime. To optimize the transition, we apply the gradient ascent pulse engineering algorithm to control the exchange couplings constrained to the manifolds evaluated by Heitler-London approximation. The method is applicable to an arbitrary number of quantum dots in any arrangement. Results of the method applied to the case of triple quantum dot are presented for linear and triangular topologies.

Robust control of entanglement in a nitrogen-vacancy center coupled to aC13nuclear spin in diamond

We address a problem of generating a robust entangling gate between electronic and nuclear spins in the system of a single nitrogen-vacany centre coupled to a nearest Carbon-13 atom in diamond against certain types of systematic errors such as pulse-length and off-resonance errors. We analyse the robustness of various control schemes: sequential pulses, composite pulses and numerically-optimised pulses. We find that numerically-optimised pulses, produced by the gradient ascent pulse engineering algorithm (GRAPE), are more robust than the composite pulses and the sequential pulses. The optimised pulses can also be implemented in a faster time than the composite pulses.