Designing dynamically corrected gates robust to multiple noise sources using geometric space curves

Noise-induced gate errors remain one of the main obstacles to realizing a broad range of quantum information technologies. Dynamical error suppression using carefully designed control schemes is critical for overcoming this challenge. Such schemes must be able to correct against multiple noise sources simultaneously afflicting a qubit in order to reach error correction thresholds. Here, we present a general framework for designing control fields that simultaneous suppress both noise in the fields themselves as well as transverse dephasing noise. Using the recently developed Space Curve Quantum Control formalism, in which robust quantum evolution is mapped to closed geometric curves in a multidimensional Euclidean space, we derive necessary and sufficient conditions that guarantee the cancellation of both types of noise to leading order. We present several techniques for solving these conditions and provide explicit examples of error-resistant control fields. Our work also sheds light on the relation between holonomic evolution and the suppression of control field errors.Comment: 12 pages, 4 figure

Dressed states of a strain-driven spin in diamond

Emerging quantum technologies, such as quantum information processing and quantum metrology, require quantum systems that provide reliable toolsets for initialization, readout, and coherent manipulation as well as long coherence times. The coherence of these systems, however, is usually limited by uncontrolled interactions with the surrounding environment. In particular, innovations building on solid-state spin systems like the Nitrogen-Vacancy (NV) center in diamond ordinarily involve the use of magnetic field-sensitive states. In this case, ambient magnetic field fluctuations constitute a serious impediment that shortens the coherence time considerably. Thus, the protection of individual quantum systems from environmental perturbations constitutes a fundamentally important but also a challenging task for the further development of quantum appliances. In this thesis, we address this challenge by extending the widely used approach of dynamical decoupling to protect a quantum system from decoherence. Specifically, we study three-level dressed states that emerge under continuous, `closed-contour' interaction driving. To implement and investigate these dressed states, we exploit well-established methods for coherent microwave and strain manipulation of the NV center spin in a hybrid spin-mechanical system. Our results reveal that this novel continuous decoupling mechanism can overcome external magnetic fluctuations in a robust way. We demonstrate experimentally that the dressed states we created are long-lived and find coherence times nearly two orders of magnitude longer than the inhomogeneous dephasing time of the NV spin, even for moderate driving strengths. To realize direct and efficient access to the coherence-protected dressed states under closed-contour driving, we further demonstrate the use of state transfer protocols for their initialization and readout. In addition to an adiabatic approach, we apply recently developed protocols based on `shortcuts to adiabaticity' to accomplish the initialization process, which ultimately accelerates the transfer speed by a factor of $2.6$ compared to the fastest adiabatic protocol with similar fidelity. Moreover, we show bidirectionality of the accelerated state transfer, which allows us to directly read out the dressed state population and to quantify the transfer fidelity of $\approx$$\,99\,\%$. By employing the methods to prepare and read out the dressed states, we lay the foundation to meet the remaining key requirement for quantum systems -- coherent quantum control. We present direct, coherent manipulation of the dressed states in their own manifold and exploit this for extensive characterization of the dressed states' properties. Thus, our results constitute an elementary step to establish the dressed states as a powerful resource in prospective quantum sensing applications. Harnessing quantum systems like the dressed states as nanoscale sensors of external fields requires the detailed characterization of the local internal environment. In the final part of this thesis, we report on the determination of intrinsic effective fields of individual NV center spins. We study single NVs in high purity diamond and find that local strain dominates over local electric fields. In addition, we experimentally demonstrate and theoretically describe a new technique for performing single spin-based polarization analysis of microwave fields in a tunable, linear basis

Quantum protocols for few-qubit devices

Quantum computers promise to dramatically speed up certain algorithms, but remain challenging to build in practice. This thesis focuses on near-term experiments, which feature a small number (say, 10-200) of qubits that lose the stored information after a short amount of time. We propose various theoretical protocols that can get the best out of such highly limited computers. For example, we construct logical operations, the building blocks of algorithms, by exploiting the native physical behavior of the machine. Moreover, we describe how quantum information can be sent between qubits that are only indirectly connected

Optimal control of topological quantum systems

Topological quantum computation provides an architecture for encoding quantum information in such a way as to be theoretically robust to local noise. Logical qubits are encoded in topological degrees of freedom typically in spin-lattice models. Excitations in the spin-lattice models manifest as anyons, generalisations of bosons and fermions that exist in two dimensions. Proposals for experimental realisation of these topological systems have previously relied on perfect anyon creation in a time independent-manner or in the case of time-dependent proposals have primarily relied on adiabatic, therefore slow, dynamics. The aim of this thesis is to use quantum control to create anyons and encode logical qubits in topological systems without the requirement for adiabaticity and long timescales. First, we demonstrate the creation of abelian anyons using time-dependent controls in the toric code model, a system that is useful as a quantum memory. We show that this may be done within arbitrarily short timescales at the expense of larger magnitude control pulses. Additionally, we investigate the robustness of our protocol in the face of theoretical errors in anyon creation. Secondly, we investigate the creation of non-abelian anyons in the Kitaev honeycomb model. By fermionising a time-dependent version of the model we demonstrate how optimal control theory can allow for anyon creation in faster-than-adiabatic time. Moreover, we show that the particular method we develop to achieve this scales only linearly in the number of spins in the lattice. Thirdly, we investigate defect creation in the surface code, a generalisation of the toric code that does not require periodic boundary conditions. Optimal quantum control is used to show how defects may be created faster than with the typical adiabatic procedures. Additionally, a method using mapping of dynamical Lie algebras is used to demonstrate that optimal control techniques may be extended to operations whose dynamics require solving in a large Hilbert space.Open Acces

Hybrid spin-nanomechanics with single spins in diamond mechanical oscillators

Hybrid spin-oscillator systems, formed by single spins coupled to mechanical oscillators, have attracted ever-increasing attention over the past few years, triggered largely by the prospect of employing such devices as high-performance nanoscale sensors or transducers in multi-qubit networks. Provided the spin-oscillator coupling is strong and robust, such systems can even serve as test-beds for studying macroscopic objects in the quantum regime. In this thesis we present a novel hybrid spin-oscillator system that consists of a diamond cantilever whose mechanical motion couples to the spin degree of freedom of embedded NV centers through crystal strain. This thesis starts with a characterization of the coupling strength between NV spin and resonator motion. Static cantilever bending experiments reveal spin-strain coupling constants of several GHz per unit of strain, corresponding to a single phonon coupling strength $g_0 \approx$\,Hz. Although we demonstrate that our hybrid system resides deep in the resolved sideband regime, our current experimental conditions prevent bringing the diamond resonator to its motional ground state, since spin decoherence rate and mechanical heating rate exceed $g_0$ by several orders of magnitude. However, cooling the resonator, even to its motional ground state, is possible if cantilever dimensions are reduced to the nanometer scale and corresponding experiments are performed at cryogenic temperatures. While spin-strain coupling is not favorable for such experiments in the quantum regime, it offers many other exciting features. In the second part of this thesis, we report on the implementation of a novel continuous decoupling scheme that protects the NV spin from environmental noise, increasing both Rabi oscillation decay time and inhomogeneous coherence time by two orders of magnitude. The remarkable coherence protection is explained by the robust, drift-free strain-coupling mechanism and the narrow linewidth of the high-quality diamond mechanical oscillators. A major finding of this thesis is the demonstration of coherent spin manipulation with transverse AC strain fields, which is presented in the third part of this thesis. We show that AC strain driving not only addresses a magnetic dipole forbidden transition, but also allows working in the strong driving regime, in which the induced spin rotation frequency exceeds the initial spin splitting. Few systems have reached this regime, despite the appeal of studying dynamics beyond the rotating wave approximation. Additionally, continuous strain driving enhances the NV’s spin coherence time by decoupling it from environmental magnetic noise. In the last part of this thesis, we combine coherent MW and strain spin driving to realize a three-level $\nabla$-system in the NV ground state by coherently addressing all three spin transitions. Our studies of the spin dynamics not only confirm the theoretical prediction that the global phase (i.e.\,the relative phase of the three driving fields) governs the occurring spin dynamics, but also that closed-contour driving shields the NV's spin from environmental noise without applying complicated decoupling schemes. The corresponding decoupling mechanism is well explained by the effect of noise on the $\nabla$-system Hamiltonian. Based on our findings, we believe our closed-contour interaction scheme will have future applications in sensing and quantum information processing, for example as a phase sensor or as a test-bed for state transfer protocols