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-
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-
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.
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.
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.
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.
Abstract Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit SWAP SWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity ( F=100−6+0 F = 10 0 − 6 + 0 %) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to ∣⇓⇓⇓⟩ ⇓ ⇓ ⇓ , we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of $${T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}$$ T 2 * = 12 μ s .
Quantum computing set a goal to harness the quantum laws of physics and create \ncomputers more powerful than ever imagined. Different technologies can be chosen to implement quantum bits (qubits), each with their advantages and drawbacks. The idea of combining different technologies then seems natural in order to come up with an optimal quantum computer. \n \nIn this sense, Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR) seem to be the perfect marriage. Indeed, while electron spins can perform quantum gates within nanoseconds, they have to fight very fast decoherence phenomena, the nuclear spins, on the other hand, require longer electromagnetic pulses to be rotated but can be controlled longer without loss of quantum information. Using electron spins as actuators and nuclear spins as memory then appears as the optimal use of this hybrid system. Another fact accounting for this association is that the control of the system through the electron spin requires techniques very similar to the well-known NMR ones. \n \nThis work focuses on characterizing as precisely as possible the Hamiltonian of a hybrid spin system in a solid-state single crystal, especially the electron-nuclear interactions, to perform high-fidelity control in a home-built pulsed ESR spectrometer. Using this knowledge, we show that we can choose the orientation of the magnetic field with respect to our crystal to obtain optimal experimental conditions. Indeed, with a good knowledge of the Hamiltonian of the system, we want demonstrate high-fidelity quantum control. \n \nThe final aim of this work is to dynamically supply highly polarized ancilla qubits that can be used in a Quantum Error Correction (QEC) experiment by implementing heat bath algorithmic cooling using a cold electron spin bath. This is an important step towards demonstrating the viability of spin systems for building quantum computers.