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arXiv:0904.4020 · Physical Review A

Nuclear spin qubits in a trapped-ion quantum computer

Mang Feng, Yuan Xu, Fei Zhou, Dieter Suter

Published May 22, 2009• 9 citations
arXivHTMLPDF

Abstract

Physical systems must fulfill a number of conditions to qualify as useful quantum bits (qubits) for quantum-information processing, including ease of manipulation, long decoherence times, and high fidelity readout operations. Since these conditions are hard to satisfy with a single system, it may be necessary to combine different degrees of freedom. Here we discuss a possible system based on electronic and nuclear spin degrees of freedom in trapped ions. The nuclear spin yields long decoherence times, while the electronic spin, in a magnetic field gradient, provides efficient manipulation, and the optical transitions of the ions assure a selective and efficient initialization and readout.

DOI
10.1103/physreva.79.052331

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Physical systems must fulfill a number of conditions to qualify as useful quantum bits (qubits) for quantum-information processing, including ease of manipulation, long decoherence times, and high fidelity readout operations. Since these conditions are hard to satisfy with a single system, it may be necessary to combine different degrees of freedom. Here we discuss a possible system based on electronic and nuclear spin degrees of freedom in trapped ions. The nuclear spin yields long decoherence times, while the electronic spin, in a magnetic field gradient, provides efficient manipulation, and the optical transitions of the ions assure a selective and efficient initialization and readout.
We outline a complete set of operations for manipulating nuclear spin qubits of trapped-ions stored in high magnetic fields such as required for Penning trapping, where the nuclear and electron spins are largely decoupled due to the dominance of the external field Hamiltonian. The reduced nuclear magnetic moment results in insensitivity to external magnetic fields compared to the use of an electron spin, but also makes the nuclear spin hard to manipulate on fast timescales. To maintain speed, we propose a two-qubit phase gate technique which utilizes the electron spin, but for which the qubit remains protected from magnetic fields through retaining the nuclear encoding. This method works for magnetic-field insensitive qubits at lower fields as well as for both microwave and laser field gradients.
Many approaches have been proposed towards the realization of practical quantum information processing. They include laser manipulation of the energy states in atomic or ion traps, nuclear magnetic resonance in molecules, quantum computation in optical lattices, and in Bose-Einstein condensates. For any of these system to be viable quantum computation, it should have stable and long-lived internal states. In addition it should be possible to quantum- mechanically entangle two or more qubits and the entangled states should be capable of non-local realism phenomena. The ground state and metastable states of low Z atoms especially the single and two-electron atoms and their ions are the most commonly used qubits for quantum information processing systems. Efforts to exhibit these phenomena in high Z elements has been much more challenging. In part because of the high energy needed to ionize the high Z elements into effective one- or two-electron system suitable for quantum information processing. Furthermore the energy difference between two stable states of the High Z elements that are possible qubits states turn to be very high. Preferably the energy difference of two qubits levels should be in the meV to a few tens of electron volts for practical realization of a quantum computing system. In general any two stable terms of an atomic or molecular system with low to moderate energy separation, that do not violate term rules for selection and symmetry, may be viable qubits states.
Storing information in quantum mechanical degrees of freedom and processing it by unitary transformation promises a new class of computers that can efficiently solve problems for which no efficient classical algorithms are known. The most straightforward implementation of this type of information processing uses nuclear spins to store the information and nuclear magnetic resonance for processing it. We discuss the basics of quantum information processing by NMR, with an emphasis on two fields of research: the design and implementation of robust logical gate operations and the loss of quantum information, which is known as decoherence.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
Continuous-variable quantum computing utilizes continuous parameters of a quantum system to encode information, promising efficient solutions to complex problems. Trapped-ion systems provide a robust platform with long coherence times and precise qubit control, enabling the manipulation of quantum information through its motional and electronic degrees of freedom. In this work, quantum operations that can be generated in trapped-ion systems are employed to investigate applications aimed at state preparation in continuous-variable quantum systems.
We review progress on the use of electron spins to store and process quantum information, with particular focus on the ability of the electron spin to interact with multiple quantum degrees of freedom. We examine the benefits of hybrid quantum bits (qubits) in the solid state that are based on coupling electron spins to nuclear spin, electron charge, optical photons, and superconducting qubits. These benefits include the coherent storage of qubits for times exceeding seconds, fast qubit manipulation, single qubit measurement, and scalable methods for entangling spatially separated matter-based qubits. In this way, the key strengths of different physical qubit implementations are brought together, laying the foundation for practical solid-state quantum technologies.