Quantum computation is a promising technology owing to the unique physical nature of quantum systems. Quantum computers have the potential to be as much as exponentially more efficient than today’s most powerful classical computer at certain tasks. One of the major challenges the scientific community must overcome, arises due to the intrinsic tendency of quantum information to be highly susceptible to environmental noise. This thesis presents work in developing and characterizing methods for precision quantum control in the presence of decoherence inducing noise, using trapped 171Yb+ ions as a model experimental platform. A flexible , robust microwave system is used to access the 12.6 GHz hyperfine qubit manifold in the outer S-shell orbital. The low phase noise characteristics of a microwave oscillator allow free-evolution coherence times in excess of three seconds, and operational fidelities F > 99.99%, characterized by randomized benchmarking. Starting from this relatively clean baseline, control techniques may be implemented in order to simulate a variety of realistic, time-dependent noise models, via arbitrary IQ modulation of the microwave source. A formalism for calculating the spectral noise filter functions of piece-wise constant control sequences is developed. The efficacy of this formalism is demonstrated by experimentally characterizing a variety of control protocols in the presence of engineered noise.
Quantum computation is a promising technology owing to the unique physical nature of quantum systems. Quantum computers have the potential to be as much as exponentially more efficient than today’s most powerful classical computer at certain tasks. One of the major challenges the scientific community must overcome, arises due to the intrinsic tendency of quantum information to be highly susceptible to environmental noise. This thesis presents work in developing and characterizing methods for precision quantum control in the presence of decoherence inducing noise, using trapped 171Yb+ ions as a model experimental platform. A flexible , robust microwave system is used to access the 12.6 GHz hyperfine qubit manifold in the outer S-shell orbital. The low phase noise characteristics of a microwave oscillator allow free-evolution coherence times in excess of three seconds, and operational fidelities F > 99.99%, characterized by randomized benchmarking. Starting from this relatively clean baseline, control techniques may be implemented in order to simulate a variety of realistic, time-dependent noise models, via arbitrary IQ modulation of the microwave source. A formalism for calculating the spectral noise filter functions of piece-wise constant control sequences is developed. The efficacy of this formalism is demonstrated by experimentally characterizing a variety of control protocols in the presence of engineered noise.
We present novel techniques for modelling and mitigating the effects of time-dependent noise created by interactions between a quantum system and its environment, and by errors in applied controls. Our scope encompasses quantum storage and nontrivial QIP tasks in both single- and multi-qubit systems, with a particular focus on control operations applied to trapped-ion qubits. The work begins with the introduction of a computationally efficient approach to characterizing the impact of time-dependent noise in single-qubit systems, in terms of the spectral characteristics of the noise and a set of generalized control filter functions. In conjunction with brute-force numerical simulation, we show that this novel analytical technique can used to model the evolution of a noisy single-qubit system subject to an arbitrary piecewise-constant control sequence, and to accurately predict the effects of experimentally engineered noise in single-qubit trapped ion systems. We also obtain a number of new and important results that extend the range of utility of state-preserving dynamical decoupling control sequences. These device-independent results provide a means to create a practically useful high-fidelity, long-time quantum memory in both single- and multi-qubit systems. We go on to explain how, given the freedom to arbitrarily and quasi-instantaneously change the phase of the interaction between a system of qubits and a finite collection of oscillators, frequency-specific phase modulation protocols can be implemented that decouple the qubits from targeted oscillator modes at pre-determined times. This technique can be used to generate fast, high-fidelity multi-qubit entangling operations in, for example, ion trap QIP devices.
We develop and demonstrate a technique to engineer universal unitary baths in quantum systems. Using the correspondence between unitary decoherence due to ambient environmental noise and errors in a control system for quantum bits, we show how a wide variety of relevant classical error models may be realized through in-phase or in-quadrature modulation on a vector signal generator producing a resonant carrier signal. We demonstrate our approach through high-bandwidth modulation of the 12.6-GHz carrier appropriate for trapped 171Yb+ ions. Experiments demonstrate the reduction of coherent lifetime in the system in the presence of both engineered dephasing noise during free evolution and engineered amplitude noise during driven operations. In both cases, the observed reduction of coherent lifetimes matches well with quantitative models described herein. These techniques form the basis of a toolkit for quantitative tests of quantum control protocols, helping experimentalists characterize the performance of their quantum coherent systems.
Precise control of quantum systems is vital to scientific and technological progress, including the realisation of quantum computation and simulation, record-breaking timekeeping and positioning applications. Control of quantum systems is hampered by the effects of random environmental or hardware noise, which leads to unknown deviations from the system's desired evolution. This thesis presents a set of interaction-focussed methods for improving precision control, tailored to the problems of quantum error suppression and stabilisation of oscillators, which share a common basic structure. These methods are based on a theoretical framework called the filter-transfer function formalism, which expresses the convolution of user-applied control and random noise in the language of spectral filtering. This powerful and accessible approach is experimentally verified in this thesis, and is used to formulate novel control techniques and improve on existing ones. This thesis experimentally demonstrates the effectiveness of novel composite pulse schemes for suppressing error in quantum bits. Furthermore, the thesis derives and demonstrates a novel predictive technique for stabilising oscillators by means of combining multiple frequency measurements against a quantum reference. The thesis therefore advances the theoretical understanding of a frequency-domain formalism for noise-affected quantum systems, on which basis it presents and demonstrates novel and improved techniques for mitigating the effects of such noise on the user's precision control over the system.
This PhD thesis reports on the development of a wide variety of theoretical and experimental capabilities in the field of quantum information processing using trapped ions. The presentation is organized in two distinct parts. The first part presents a series of published articles containing theoretical results, and their experimental validation, advancing a range of tools and techniques in error-resilient quantum control and robust verification procedures. One of the fundamental challenges in realizing a general purpose quantum computer is the management of error in fragile quantum systems. A familiar aspect of this challenge is decoherence, a process by which the system looses its stored quantum information, rendering it useless for subsequent computation. This collection of works focuses on reducing sources of quantum decoherence and precisely quantifying residual errors in real quantum systems dominated by realistic temporally-correlated noise processes, of central importance in any future architecture for quantum computing. The second part focuses on the design, construction and characterization of a complex experimental system capable of supporting a broad calls of quantum simulation experiments with hundreds of spin qubits using 9Be+ ions in a Penning trap. The trap design is optimized to suppress non-harmonic trapping potentials while providing wide optical access for engineering enhanced spin-motion coupling across large ion crystals. A superconducting magnet, equipped with a fully closed-cycle dual LN2/LHe recondensor, provides the magnetic field for trapping and produces the 55-GHz Zeeman-split qubit states suitable for microwave control. A custom UV laser system for driving the relevant transitions in neutral and ionized beryllium, as well as UV-compatible fibers and in-bore optomechanics for delivering microwave and laser beams to the trap, is presented. The thesis concludes with a brief outlook towards future theoretical and experimental studies, and extensions of the experimental setup
Quantum-enabled technologies promise advancements across a huge range of industrial, metrological and medical applications and are already demonstrating significant impacts, especially in the realm of sensing and metrology. While the extreme sensitivity of quantum systems to their environment is fueling those applications, it also represents a major hurdle to technologies which require long-term stability such as quantum computing and quantum simulations. In addition to the inherent decoherence phenomenon, the challenge associated with controlling a quantum system accurately and precisely, does in fact impede all of the aforementioned applications. Such techniques have therefore been subject to extensive research in both the academic and industrial sector and as a result, sophisticated quantum control techniques are emerging in order to understand, characterize and mitigate errors in quantum systems. This thesis presents how quantum control techniques can be employed to characterize and suppress both control imperfections and environmental noise in quantum systems, using experiments with trapped ions as a model quantum platform. We demonstrate two distinct but interrelated approaches that leverage either time-domain or frequency-domain information about the noise. In the first approach, we show how supervised learning algorithms can efficiently extract time-domain correlations from time-stamped sequences of projective measurements on a qubit. This information can then be used to perform real-time predictive control in which we autonomously pre-compensate anticipated qubit noise in order to stabilize the system. The second approach deploys provably optimal narrowband controls in order to characterize the specific spectral components of noise experienced by a qubit. Here, frequency-shifted Slepian functions permit reconstruction of system noise with maximum out-of-band rejection, and full spectrum reconstruction is enabled using techniques based on multitaper and Bayesian methods.
This thesis describes the development of technology and experimental techniques for scalable trapped-ion quantum computing. An architecture for scalable quantum computing is presented in which 171Yb+ ions are trapped in linear R.F. Paul traps and their hyper-fine states are used to form qubits. Quantum logical operations can be carried out by applying R.F. and microwave fields. This thesis presents significant improvements in the experimental setup used for quantum computing, as well as new theoretical developments and experimental demonstrations of new high- fidelity quantum control methods. A new procedure for carrying out high- delity two qubit gates using static magnetic eld gradients and resonant microwave elds is presented. It is shown that this has the potential to enable signi cantly improved delities compared to current methods. Improved methods for measurement and statistical analysis in trapped-ion experiments are also shown. These should enable more accurate measurement of two-qubit gate delities, which becomes increasingly important as delities increase. A new system for generating arbitrary R.F. and microwave waveforms is presented, including a bespoke software control system allowing the user to de ne custom pulse sequences, which represents a signi cant improvement in the scalability of the quantum control system. Experimental developments towards a system for carrying out on-chip trapped-ion quantum logic in a static magnetic eld gradient are also presented. A new technique for generating multi-level control methods is introduced, based on reducing a multi-level system to an e ective two-level system. High- delity quantum control methods generated using this technique, which form a will form a key part of the scalable quantum computing architecture, are implemented experimentally.