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Coherent control of anisotropic hyperfine-coupled electron and nuclear spins for quantum information processing

Clarice D. Aiello, Jieyu Yang, J. S. Hodges, David G. Cory

Published Jan 1, 2009• 0 citations
Publisher
DOI
10.3254/978-1-60750-039-1-519

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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.

•Aug 10, 2015•1 citation
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.