Solid state and condensed matter systems, such as diamond impurities, superconductors, quantum dots, and ion traps, constitute important physical platforms for various applications in quantum information processing (QIP). However, it has consistently been shown that all such modern platforms suffer from non-equilibrium behavior on timescales that are relevant for many important QIP tasks. The causes range from intrinsic non-equilibrium dynamics (e.g. in diamond) to the presence of various impurities with their own internal dynamics (e.g. in superconductors and quantum dots) or variations in the control fields used to stabilize the quantum matter (e.g. in ion traps). When reserving degrees of freedom for QIP in any physical medium, it is therefore important to track and adapt to the non-equilibrium behavior of the rest of relevant degrees of freedom (a.k.a. the environment). In particular, if the environment noise is parameterized by some underlying physical model, then the non-equilibrium behavior will generally yield temporal variations in the noise parameters relevant for QIP. This dissertation proposes a general adaptive refinement to standard QIP (specifically for quantum error correction) by allocating appropriate environment degrees of freedom for use as real-time quantum sensors (a.k.a. spectator systems). This will provide classical side-information about the environment noise parameters in real-time, which is then used to stabilize the performance of the particular QIP task at hand. The main results of this work can be divided into two parts: (1) proposing a realistic physical model for the joint implementation of spectator systems with QIP systems, and (2) studying the fundamental physical limitations of the spectator-based approach, particularly for quantum error correction. This dissertation provides a multi-disciplinary approach to QIP, by attempting to breach the current gap between the mainly mathematical approach to QIP and related physical questions, which ultimately need to be addressed for its realization.
Solid state and condensed matter systems, such as diamond impurities, superconductors, quantum dots, and ion traps, constitute important physical platforms for various applications in quantum information processing (QIP). However, it has consistently been shown that all such modern platforms suffer from non-equilibrium behavior on timescales that are relevant for many important QIP tasks. The causes range from intrinsic non-equilibrium dynamics (e.g. in diamond) to the presence of various impurities with their own internal dynamics (e.g. in superconductors and quantum dots) or variations in the control fields used to stabilize the quantum matter (e.g. in ion traps). When reserving degrees of freedom for QIP in any physical medium, it is therefore important to track and adapt to the non-equilibrium behavior of the rest of relevant degrees of freedom (a.k.a. the environment). In particular, if the environment noise is parameterized by some underlying physical model, then the non-equilibrium behavior will generally yield temporal variations in the noise parameters relevant for QIP. This dissertation proposes a general adaptive refinement to standard QIP (specifically for quantum error correction) by allocating appropriate environment degrees of freedom for use as real-time quantum sensors (a.k.a. spectator systems). This will provide classical side-information about the environment noise parameters in real-time, which is then used to stabilize the performance of the particular QIP task at hand. The main results of this work can be divided into two parts: (1) proposing a realistic physical model for the joint implementation of spectator systems with QIP systems, and (2) studying the fundamental physical limitations of the spectator-based approach, particularly for quantum error correction. This dissertation provides a multi-disciplinary approach to QIP, by attempting to breach the current gap between the mainly mathematical approach to QIP and related physical questions, which ultimately need to be addressed for its realization.
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.
Recent advances in coherent manipulation and control have led to new opportunities to study non-equilibrium dynamics in quantum many-body systems. Using a variety of experimental platforms ranging from cold atoms and ions to solid-state spin defects, small building blocks of fully controllable quantum systems can be assembled into a strongly interacting many-body system. With this approach, one can gain new insights into fundamental questions in basic science such as the mechanism of quantum thermalization or the existence of exotic phases of matter out of equilibrium. At the same time, a fully controllable large-scale quantum device has promising applications for high precision sensing, secure communication, and quantum information processing.\nThis thesis describes recent progress in engineering quantum dynamics that is robust against various imperfections such as environmental noise, disorder, or imprecise controls. We find that non-equilibrium quantum states of strongly interacting systems can be protected from imperfections upon appropriate external manipulations such as time-dependent periodic controls, engineered coherent or dissipative interactions, or an introduction of strong quenched disorder. Furthermore, under certain conditions, these imperfections can be utilized to stabilize non-trivial quantum states. Our results challenge conventional wisdom of statistical mechanics, shedding light on the microscopic mechanisms of thermalization.\nWe also discuss how engineered dynamics can be harnessed for applications such as quantum metrology, simulations, or information processing.
Quantum information processing is exceptionally sensitive to errors, posing a significant challenge to the development of practical quantum technologies. Conventional error correction codes, while effective, often rely on pre-defined error profiles that may not accurately represent the true error distribution within a quantum system. This research investigates an adaptive information theory framework designed to dynamically adjust error correction parameters based on the specific error profile of the quantum system, thereby improving error detection and resilience. The core mechanism centers around a feedback loop that continuously monitors the error rate and optimizes the correction parameters to minimize the impact of errors. The proposed approach offers a more flexible and potentially superior solution compared to static error correction methods, addressing a key limitation in current quantum error correction strategies. This work explores the design of a novel system that can adapt to varying error characteristics, leading to enhanced robustness and improved performance in quantum information processing.
The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely on the apriori knowledge of the environment noise parameters to achieve their best performance. However, such parameters are likely to drift in time in the context of implementing long-time quantum memories. This necessitates using a "spectator" system, which estimates the noise parameter in real-time, then feed-forwards the outcome to the recovery protocol as a classical side-information. The memory qubits and the spectator system hence comprise the building blocks for a real-time (i.e. drift-adapting) quantum memory. In this article, I consider spectator-based (incomplete knowledge) recovery protocols as a real-time parameter estimation problem (generally with nuisance parameters present), followed by the application of the "best-guess" recovery map to the memory qubits, as informed by the estimation outcome. I present information-theoretic and metrological bounds on the performance of this protocol, quantified by the diamond distance between the "best-guess" recovery and optimal recovery outcomes, thereby identifying the cost of adaptation in real-time quantum memories. Finally, I provide fundamental bounds for multi-cycle recovery in the form of recurrence inequalities. The latter suggests that incomplete knowledge of the noise could be an advantage, as errors from various cycles can cohere. These results are illustrated for the approximate [4,1] code of the amplitude-damping channel and relations to various fields are discussed.
All real-world quantum systems interact with their surrounding environment to some extent. No matter how weak the coupling that prevents the system from being isolated, the evolution of an open quantum system is eventually plagued by non-unitary features, such as decoherence and dissipation. Decoherence is a quantum effect where the system loses its ability to exhibit coherent behavior. Nowadays, decoherence stands as a serious obstacle in quantum information processing. As the manipulation of quantum coherence in experiments has progressed, the need to better understand, control, and utilize dissipative non-equilibrium dynamics of quantum systems has grown in importance. This has ranged from fundamental questions associated with the quantum-to-classical transition and quantum thermodynamics innovation in quantum optics and cavity/circuit quantum electrodynamics. Current studies of many-body dynamics, ultracold atoms in optical lattices, trapped ions, superconducting systems, nanoelectro-mechanical systems, and quantum fields under the influence of external conditions offer new challenges to address questions regarding quantum systems far from equilibrium. On the theoretical side, quantum trajectory-based methods could be the key to both quantum nanodevice design and exploration of new regimes of quantum mechanics and quantum measurement, as well as applications to various quantum technologies.
Quantum information processing offers unprecedented capabilities, but the inherent fragility of quantum systems necessitates sophisticated error correction techniques. Traditional quantum error correction methods often rely on pre-defined error correction codes, which struggle to adapt to the dynamic nature of the quantum environment. This paper proposes a novel adaptive quantum noise correction algorithm designed to dynamically adjust error correction parameters based on environmental fluctuations. The algorithm leverages a feedback loop that continuously assesses the quantum system's state and adjusts the correction process accordingly. This approach significantly enhances the algorithm's efficiency and robustness, potentially enabling the realization of more complex and reliable quantum computations. We present a detailed analysis of the algorithm's performance, demonstrating its effectiveness in mitigating noise and achieving improved fidelity.