Electron spins in solids are promising candidates for quantum memories for superconducting qubits because they can have long coherence times, large collective couplings, and many quantum bits can be encoded into the spin-waves of a single ensemble. We demonstrate the coupling of electron spin ensembles to a superconducting transmission-line resonator at coupling strengths greatly exceeding the cavity decay rate and comparable to spin linewidth. We also use the enhanced coupling afforded by the small cross-section of the transmission line to perform broadband spectroscopy of ruby at millikelvin temperatures at low powers. In addition, we observe hyperfine structure in diamond P1 centers and time domain saturation-relaxation of the spins.An eventual quantum computer, like its classical analog, will make use of a variety of physical systems specialized for different tasks. Just as a classical computer uses charge-based transistors for fast processing and magnetic hard drives for long term information storage, a quantum computer might use superconducting qubits for processing [1] and ensembles of electron spins as quantum memories [2,3], linked by single microwave photons. Although other microscopic systems have been proposed for use in a hybrid architecture [4][5][6][7], electron spins complement superconducting qubits particularly well. They feature similar transition frequencies, do not require trapping, and can be packed densely. Furthermore, a single ensemble could be used to store many qubits using holographic encoding techniques [3] demonstrated classically for nuclear [8] and electron [9] spins.In this Letter, we demonstrate the first step toward realizing a solid-state quantum memory: coupling an electron spin ensemble to an on-chip superconducting cavity at powers corresponding to a single cavity photon. We observe megahertz spin-photon interaction strengths in both ruby Cr 3+ spins and N substitution (P1) centers in diamond. A parallel effort by Kubo, et. al.[? ] sees similar coupling to nitrogen vacancy (NV) centers in diamond. In doing so we develop a platform for the study of electron spin resonance (ESR) physics in picoliter mode volumes, millikelvin temperatures, and attowatt powers. Finally, we perform time-resolved saturation/relaxation measurements of the P1 centers, a precursor to full pulsed control of the system. ESR studies the microwave response of electron spins at their resonant frequency in a magnetic field. Samples are conventionally placed inside a 3D high quality-factor (Q) cavity which enhances the sensitivity by confining photons with the spins and extending the interaction time [10]. In this work, several 1D cavities are capacitively coupled to a common feedline on a sapphire chip. We place the spins within the mode volume by fabricating the device on doped sapphire (ruby - Fig. 1a), attaching a substrate on top of an existing device (diamond - Fig. 1b), or simply spin-coating the surface (DPPHnot shown). The single spin-photon coupling is given by g s /2π = m 0 (µ 0 ω/2hV c ) 1/2 ,...

We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper pair box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.

There is a demand for good theoretical understanding of the response of an atomic force microscope cantilever to the extremely nonlinear impacts received while tapping a sample. A model and numerical simulations are presented in this paper which provide a very pleasing comparison with experimental results. The dependence of the cantilever amplitude and phase upon the sample stiffness, adhesion and damping are investigated using these simulations, and it is found that 'topographic' tapping images are not independent of sample properties, nor will it be trivial to measure materials' properties from the tapping data. The simulation can be applied to other probe microscope configurations as well.

Quantum mechanics permits an entity, such as an atom, to exist in a superposition of multiple states simultaneously. Quantum information processing (QIP) harnesses this profound phenomenon to manipulate information in radically new ways [1]. A fundamental challenge in all QIP technologies is the corruption of superposition in a quantum bit (qubit) through interaction with its environment. Quantum bang-bang control provides a solution by repeatedly applying 'kicks' to a qubit [2,3], thus disrupting an environmental interaction. However, the speed and precision required for the kick operations has presented an obstacle to experimental realization. Here we demonstrate a phase gate of unprecedented speed [4, 5] on a nuclear spin qubit in a fullerene molecule, and use it to bang-bang decouple the qubit from a strong environmental interaction. We can thus trap the qubit in closed cycles on the Bloch sphere, or lock it in a given state for an arbitrary period. Our procedure uses operations on a second qubit, an electron spin, in order to generate an arbitrary phase on the nuclear qubit. We anticipate the approach will be vital for QIP technologies, especially at the molecular scale where other strategies, such as electrode switching, are unfeasible.Two well known concepts in overcoming the corruption of information stored within a qubit are decoherence free subspaces [6,7,8,9], and quantum error correcting codes [10,11,12]. The former is the passive solution of restricting oneself to some set of states that, due to symmetries in the system, are largely immune to the dominant types of unwanted coupling. The latter is a sophisticated form of feedback control whereby the effect of unwanted coupling is detected and corrected. Between these limits there is the idea of dynamical suppression of couplingmaking some rapid, low level manipulation of the system so as to actively interfere with the decoherence process. Ideas here often relate to the 'quantum Zeno effect' in which repeated measurement (or some related process) is capable of suppressing the natural evolution of the system [13,14]. As the system evolves from one quantum eigenstate, |0 , to another, |1 , it passes through a * Electronic address: john.morton@materials.ox.ac.uk FIG. 1:A representation of our decoupling scheme, and the physical system to which it is applied. (a) Our decoupling process -shown by the path of the nuclear qubit on its Bloch sphere. The line within the Bloch sphere is a visual guide and does not indicate that the state becomes mixed. The state leaves the two-state space represented by the Bloch sphere, and returns at the indicated point on the opposite side, remaining pure at all times. An RF field is applied to drive state |00 to |01 . However, applying a phase of −1 to |01 during the evolution causes the state to jump to the other side of the Bloch sphere, from which it must evolve back to its initial state. The process can be repeated to prevent the system from ever reaching |01 . (b) A model of the N@C60 molecule. (c) Although this N@C60 ...

Abstract. Given the effectiveness of semiconductor devices for classical computation one is naturally led to consider semiconductor systems for solid state quantum information processing. Semiconductors are particularly suitable where local control of electric fields and charge transport are required. Conventional semiconductor electronics is built upon these capabilities and has demonstrated scaling to large complicated arrays of interconnected devices. However, the requirements for a quantum computer are very different from those for classical computation, and it is not immediately obvious how best to build one in a semiconductor. One possible approach is to use spins as qubits: of nuclei, of electrons, or both in combination. Long qubit coherence times are a prerequisite for quantum computing, and in this paper we will discuss measurements of spin coherence in silicon. The results are encouraging -both electrons bound to donors and the donor nuclei exhibit low decoherence under the right circumstances. Doped silicon thus appears to pass the first test on the road to a quantum computer. IntroductionSemiconductor based qubits (quantum bits) and gates were among the earliest suggestions for physical realizations of quantum information processors [1][2][3][4]. Since those early proposals, numerous groups have tackled various aspects of the problem of defining and constructing quantum logic in a semiconductor. The popularity of semiconducting systems for quantum computers can be directly traced to their popularity for classical electronics. A huge base of knowledge and experience has been built up over the last half-century about all aspects of semiconductors -their chemical purification, crystal growth, defect control, nanostructure fabrication, and so forth. Given their versatility, many different states inside a semiconductor have been proposed as qubits. Some of these include excitons bound in quantum dots [1,2,5,6], the spin of electrons trapped at donors or in quantum dots [4,[7][8][9][10], other low-lying states of impurities [11], and nuclear spins of an either an impurity [3,12] or the host semiconductor [13,14], as well as combinations of one or more of these states.