Turing's notion of oracle machine is influential in diverse fields like computation, communication as well as philosophy. It has long been a fascinating open issue on construction of a real working oracle machine. Here, we address physical implementation of a quantum oracle machine which resolves the quantum optimal control problem. We show that the most computationally challenging part of gradient ascent pulse engineering, namely computing the fidelity and gradient for input control pulse, can be accomplished by the process of physical evolution and measurement on the quantum system being controlled. The quantum system outputs the desired information for gradient iteration at a constant and affordable cost thus can be treated as an oracle. By posing queries to and receiving messages from the oracle, classical computing devices update the control parameters until an optimum is achieved. To demonstrate the idea in experiment, we use a nine-spin nuclear magnetic resonance system, on which we have succeeded in preparing a seven-correlated quantum state without involving simulating the large Hilbert space evolution.
Turing's notion of oracle machine is influential in diverse fields like computation, communication as well as philosophy. It has long been a fascinating open issue on construction of a real working oracle machine. Here, we address physical implementation of a quantum oracle machine which resolves the quantum optimal control problem. We show that the most computationally challenging part of gradient ascent pulse engineering, namely computing the fidelity and gradient for input control pulse, can be accomplished by the process of physical evolution and measurement on the quantum system being controlled. The quantum system outputs the desired information for gradient iteration at a constant and affordable cost thus can be treated as an oracle. By posing queries to and receiving messages from the oracle, classical computing devices update the control parameters until an optimum is achieved. To demonstrate the idea in experiment, we use a nine-spin nuclear magnetic resonance system, on which we have succeeded in preparing a seven-correlated quantum state without involving simulating the large Hilbert space evolution.
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.
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.
Quantum information processing is a multi-disciplinary science involving physics, mathematics, computer science, and even quantum chemistry. It is centred around the idea of manipulating physical systems at the quantum level, either for simulation of physical systems, or numerical computation. Although it has been known for almost a decade that a quantum computer would enable the solution of problems deemed infeasible classically, constructing one has been beyond today's capabilities. In this work we explore one proposed implementation of a quantum computer: Nuclear Magnetic Resonance (NMR) spectroscopy. We also develop a numerical software tool, a pulse sequence compiler, for use in the implementation of quantum computer programs on an NMR quantum computer. Our pulse sequence compiler takes as input the specifications of the molecule used as a quantum register, the desired quantum gate, and experimental data on the actual effects of RF pulses on a sample of the molecule, and outputs an optimum set of pre and post 'virtual' gates that minimize the error induced.
Quantum optimal control, a powerful toolbox for engineering an optimal control field modulation that most precisely implements a desired quantum operation in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The gradient ascent pulse engineering (GRAPE) algorithm is a widely used method in quantum optimal control, which has achieved great success in different physical platforms. However, its computational complexity increases exponentially with the number of qubits, making it challenging to be implemented for large-scale quantum systems. To mitigate this issue, we present the iterative GRAPE algorithm (iGRAPE), which reduces the optimization problem into a series of lower-dimensional subproblems by incorporating disentanglement operations. Our numerical simulations on physical platforms such as nuclear magnetic resonance and superconducting quantum systems demonstrate that iGRAPE significantly enhances state preparation speed. Specifically, compared to GRAPE, iGRAPE achieves up to a five-fold acceleration in preparing Greenberger--Horne--Zeilinger states using a 12-qubit implementation, and up to a 13-fold acceleration for arbitrary state preparation with eight qubits. To further validate our findings, we conduct experimental validation of iGRAPE on a four-qubit nuclear magnetic resonance system. Overall, iGRAPE offers an efficient solution for implementing optimal control in large-scale quantum systems, holding great potential for advancing quantum technologies during the noisy intermediate-scale quantum era.
An exquisite control over the dynamics of a quantum system is essential for realizing any quantum technology. This thesis presents some practical and efficient strategies for coherent quantum control: a paradigm for controlling quantum dynamics using electromagnetic fields. Coherent control is a common framework for describing the physical implementation of quantum logic gates in several quantum information processing platforms including superconducting qubits and trapped ions. For the purpose of demonstration, however, liquid-state Nuclear Magnetic Resonance (NMR) is used in this thesis as it is an ideal test-bed for developing, testing and benchmarking coherent control tools and techniques. Coherent control was revitalised in 2005 by the development of Gradient Ascent Pulse Engineering (GRAPE), a powerful optimal control technique that is widely used for designing shaped pulses for a variety of tasks. GRAPE, like any other closed-loop optimal control algorithm, requires multiple evaluations of the computationally expensive matrix exponential and the full time-evolution propagator. To this end, I present strategies to sidestep the explicit evaluation of matrix exponentials, thereby offering substantial speed-ups over conventional implementations of the GRAPE algorithm. The results are demonstrated experimentally in NMR, but also in simulations of ultracold molecules and superconducting qubits. Beyond GRAPE, this thesis also considers methods for designing spin-echo sequences for implementing any arbitrary network of controlled-Z gates in a system of qubits with zz-couplings. First, a method based on linear-programming provides near time-optimal sequences in fully-coupled systems having up to a few hundred qubits. Further, an analytic method based on graph colouring finds near time-optimal spin echo sequences in engineered systems with any number of qubits having only nearest and next-nearest neighbour-couplings.
Working on quantum systems entail different interests, for example, working on fundamental \nunderstanding of quantum systems also lay foundation for better quantum computation \ntechniques. A test for whether a system is behaving quantum mechanically or \nclassically is devised by Leggett and Garg in form of inequalities, called Leggett-Garg Inequalities \n(LGI). Such Inequalities are violated by a system whose evolution is governed \nby quantum mechanics. A precise experiment to violate LGIs require a guarantee that the \nmeasurement does not affect the system or its future dynamics. These Inequalities were \nproposed for dichotomic systems,systems which can have two outcomes. Here we present \nan LG experiment on a three-level quantum system, which theoretically have larger quantum \nupper bound than that of a two-level quantum system. This larger violation also \nprovides a bigger buffer to taking in account of the various experimental imperfections. \nPerforming a quantum computing task requires precise level of control to initialize, \nperform and measure the quantum system. With increasing size of the quantum processor \nthe challenge is to maintain optimal control. Nuclear Magnetic Resonance (NMR) has \nalways been a very faithful test-bed for quantum processing ideas. In NMR, we perform \nRadio Frequency (RF) pulses to control and steer the system to the desired state. Most \nused method to derive the exact frequency and amplitude of these pulses for a given \ntask is based on gradient. Although systematic, one have to simulate these pulses on \na classical computer first, which makes the task very inefficient. We report a a way of \nperforming optimization with a hybrid quantum-classical scheme. This scheme helps us \nperform classically harder computational tasks on the quantum processor. We optimize \npulses which drive our system from 7-coherence state to 12-coherence state on a 12-qubit \nNMR processor. \nElectron Spin Resonance (ESR) employs the same techniques as of NMR but having \nadvantage in larger polarization compared to later. Although this does not imply better \ncontrol, cause the frequency at which pulses are required to control an ESR system fall into \nmicrowave region. Microwave frequency are harder to control electronically, thus making \nit harder for performing ESR quantum computing. The hybrid scheme used in NMR \nexperiment relies on some ideal pulses which are needed to be optimized classically. We \nalleviate this requirement by using finite difference method of calculating gradient. We \ncompare these methods with the earlier methods to show the superiority of such a scheme. \nState-to-state transfer pulses are sufficient for most of the quantum computing task, \nbut, an universal quantum information implementation requires state independent pulses. \nThe techniques used in optimizing state-to-state pulses can be modified to optimize for a \nstate independent pulse. We show that this methods scale polynomially with the number \nof qubits and is general in terms of its implementation. We further reduce the resource \nrequirement by using a NMR related implementation.