We demonstrate coherent control of two nuclear spins mediated by the magnetic resonance of a hyperfine-coupled electron spin. This control is used to create a double-nuclear coherence in one of the two electron spin manifolds, starting from an initial thermal state, in direct analogy to the creation of an entangled (Bell) state from an initially pure unentangled state. We identify challenges and potential solutions to obtaining experimental gate fidelities useful for quantum information processing in this type of system.
We demonstrate coherent control of two nuclear spins mediated by the magnetic resonance of a hyperfine-coupled electron spin. This control is used to create a double-nuclear coherence in one of the two electron spin manifolds, starting from an initial thermal state, in direct analogy to the creation of an entangled (Bell) state from an initially pure unentangled state. We identify challenges and potential solutions to obtaining experimental gate fidelities useful for quantum information processing in this type of system.
Coupled electron-nuclear spins are promising physical systems for quantum in-formation processing: By combining the long coherence times of the nuclear spins with the ability to initialize, control, and measure the electron spin state, the favor-able properties of each spin species are utilized. This thesis discusses a procedure to initialize these nuclear spin qubits, and presents a vision of how these systems could be used as the fundamental processing unit of a quantum computer. The fo-cus of this thesis is on control of a system in which a single electron spin is coupled to N nuclear spins via resolvable anisotropic hyperfine (AHF) interactions. High-fidelity universal control of this le-Nn system is possible using only excitations on a single electron spin transition. This electron spin actuator control is implemented by using optimal control theory to find the modulation sequences that generate the desired unitary operations. Decoherence and the challenge of making useful qubits from these systems are also discussed. Experimental evidence of control using an electron spin actuator was acquired with a custom-built pulsed electron spin resonance spectrometer. Complex mod-
The ability to perform quantum error correction (QEC) arbitrarily many cycles is a significant challenge for scalable quantum information processing (QIP). Key requirements for multiple-round QEC are a high degree of quantum control, the ability to efficiently characterize both intrinsic and extrinsic noise, and the ability to dynamically and efficiently extract entropy from ancilla qubits. Nuclear Magnetic Resonance (NMR) based quantum devices have demonstrated high control fidelity with up to 12 qubits, and the noise characterizations can be performed using an efficient protocol known as randomized benchmarking. One of the remaining challenges with NMR systems is that qubit initialization is normally only attainable via thermal equilibration. This results in very low polarizations in reasonable experimental conditions. Moving to electron-nuclear coupled spin systems in a single crystal is a promising solution to the ancilla qubit preparation problem. One obvious advantage of incorporating electron spins comes from higher gyromagnetic ratio of the electron which yields about three orders of magnitude larger thermal spin polarization than that of nuclear spins in the same experimental condition. In addition, fast control of nuclear spins is possible provided appropriate level of anisotropic hyperfine interaction strength. The nuclear spins can be polarized even beyond the thermal electron spin temperature using a technique Heat-Bath Algorithmic Cooling (HBAC). With theoretical ideas in hand, the next step is to develop classical instrumentations to control electron-nuclear coupled systems and accomplish high fidelity coherent control. Noise characterizations are also necessary for benchmarking the quality of control over the electron-nuclear spin system. \nI first present example applications of NMR QIP with small number of qubits: Testing a foundational question in quantum mechanics and measuring spectral density of noise in a quantum system. Then I report on our home-built X-band electron spin resonance (ESR) spectrometer and progress in achieving high fidelity coherent control of electron and nuclear spins for QIP. We focus on implementing nuclear spin manipulation via anisotropic hyperfine interaction and microwave (mw) control, but discussions also include electron nuclear double resonance (ENDOR) control techniques. We perform realistic algorithmic simulations to show that an experimental cooling of nuclear spins below electron thermal temperature is feasible, and to present the electron-nuclear spin systems as promising testbeds for scalable QIP.
ESR quantum computing presents faster means to perform gates on nuclear spins than the traditional NMR methods. This means ESR is a test-bed that can potentially be useful in ways that are not possible with NMR. The first step is to demonstrate universal control in the ESR system. This work focuses on spin systems with one electron spin and two nuclear spins. We try to demonstrate control over the nuclear spins using the electron as an actuator. \n \nIn order to perform the experiments, a customized ESR spectrometer was built in the lab. The main advantage of the home-built system is the ability to send arbitrary pulses to the spins. This ability is the key to perform high fidelity controls on the spin system. \n \nA customized low temperature probe was designed and built to have three features necessary for the experiments. First, it is possible to orient the sample, thus to change the spin Hamiltonian of the system, in situ. Second, the combined system is able to perform ESR experiments at liquid nitrogen and liquid helium temperatures and rotate the sample while it is cold. Last, the pulse bandwidth of the microwave resonator, which directly affects the fidelity of the gates, is held constant with respect to the sample temperature. \n \nSimulations of the experiments have been carried out and the results are promising. Preliminary experiments have been performed, the final set of experiments, demonstrating full quantum control of a three-spin system, are underway at present.
Entanglement is one of the most technologically important quantum phenomena and its con-trolled creation brings us a step closer to the realisation of a quantum computer. Hybrid electron and nuclear spin systems which combine long nuclear decoherence times with the high polarisation and rapid processing times of electron spins are considered reliable candidates for the representation of the fundamental building block of a quantum computer, the qubit. In the literature electron spins quite often play the role of a mediator which can access, manipulate and couple states with long coherence times, beneficial for storing quantum information. Despite the fact that an electron spin can be a useful resource for nuclear spin systems, its permanent presence can be a source of decoherence. The use of transient photoexcited electron spins provide an additional advantage and once the operations which involve the electron spin are completed, the electron spin can decay and not interfere further with the evolution of the system. In this thesis we report magnetic resonance experiments and density functional theory calculations for the demonstration of nuclear - nuclear entanglement using photoexcited triplet states. We study homonuclear and heteronuclear fullerene derivatives and we identify in each case the relevant parameters that can lead to high fidelity entangling operations. The hyperfine interaction in a homonuclear system is the key parameter which determines the degree of entanglement between the nucelar spins according to a recent theoretical proposal. We measure and calculate the hyperfine interaction in homonuclear systems with 13C nuclear spins in order to prove the feasibility of this scheme. Further experiments on a fullerene system with two nuclear spins a 31P and a 1H show that entangling operations of high fidelity which involve the demonstration of CNOT gates, are possible within the lifetime of the triplet state.
The goal of this project was to improve our control over nuclear spins in the solid state, and to extend this control to coupled electron-nuclear spins. Our key results are summarized below. 1. We extended the control techniques developed in liquid state NMR quantum information processing to the control of a three-qubit solid state NMR quantum information processor. 2. To explore multi-body spin dynamics and their sensitivity to decoherence, we have measured the decay of NMR multiple quantum coherence intensities in the presence and absence of the dipolar Hamiltonian, in a cubic and a one-dimensional spin system. 3. We also studied the transport of polarization in the one-dimensional fluoroapatite system, both experimentally and theoretically, and created special states in which the polarization is localized to the ends of the chain. This enables both universal Quantum Computing and Quantum Simulation in 1-D systems. 4. We devised a novel scheme for electron-nuclear quantum information processing that exploits the anisotropic hyperfine coupling. This scheme enables universal control over a 1-electron, N-nuclear spin system, addressing only a single electron spin transition. Not having to address the nuclear spins directly significantly speeds up the control. We designed and fabricated a pulsed electron spin resonance spectrometer, along with a cryogenic probe which we used to experimentally implement this scheme on a single crystal sample of irradiated malonic acid. 5. We demonstrated the role of nuclear spin dipolar diffusion in dynamic nuclear polarization (DNP) experiments, in dielectric samples with abundant nuclear spins. We achieved a 29Si polarization of 8.3% at 66 GHz and 1.1 K in single crystal P-doped, the highest ever reported, using DNP.
The highly parallel nature of the fundamental principles of quantum mechanics means that certain key resource-intensive tasks --- including searching, code decryption and medical, chemical and material simulations --- can be computed polynomially or even exponentially faster with a quantum computer. In spite of its remarkably fast development, the field of quantum computing is still young, and a large-scale prototype using any one of the candidate quantum bits (or 'qubits') under investigation has yet to be developed. Spin-based qubits in condensed matter systems are excellent candidates. Spins controlled using magnetic resonance have provided the first, most advanced, and highest fidelity experimental demonstrations of quantum algorithms to date. Despite having highly promising control characteristics, most physical ensembles investigated using magnetic resonance are unable to produce entanglement, a critical missing ingredient for a pure-state quantum computer. Quantum objects are said to be entangled if they cannot be described individually: they remain fundamentally linked regardless of their physical separation. Such highly non-classical states can be exploited for a host of quantum technologies including teleportation, metrology, and quantum computation. Here I describe how to experimentally create, control and characterise entangled quantum ensembles using magnetic resonance. I first explore the relationship between entanglement and quantum metrology and demonstrate a sensitivity enhancement over classical resources using molecular sensors controlled with liquid-state nuclear magnetic resonance. I then examine the computational potential of irreversible relaxation processes in combination with traditional reversible magnetic resonance control techniques. I show how irreversible processes can polarise both nuclear and electronic spins, which improves the quality of qubit initialisation. I discuss the process of quantum state tomography, where an arbitrary quantum state can be accurately measured and characterised, including components which go undetected using traditional magnetic resonance techniques. Lastly, I combine the above findings to initialise, create and characterise entanglement between an ensemble of electron and nuclear spin defects in silicon. I further this by generating pseudo-entanglement between an ensemble of nuclear spins mediated by a transient electron spin in a molecular system. These findings help pave the way towards a particular architecture for a scalable, spin-based quantum computer.