Isotopically engineered Si and Ge for spintronics and quantum computation

Si, Ge as well as SiGe structures are the promising materials for spintronics and quantum computation due to the fact that in both crystals only one isotope (²⁹Si and ⁷³Ge) has nuclear spin. As a result, isotope engineering of Si and Ge permits to control the density of nuclear spins and vary the spin coherence time, a crucial parameter in spintronics. In the first part we discuss the NMR study of nuclear spin decoherence in Ge single crystals with different abundance of the ⁷³Ge isotope. It was observed that the slow component of the dephasing process is elongated with depletion of Ge crystal with isotope ⁷³Ge. The second part is devoted to the development of the Kane's model of nuclear spin-based quantum computer, which uses the nuclear spin of ³¹P impurity atoms in a ²⁸Si matrix as quantum bits (qubits). We discuss a new method of placing ³¹P atoms in a ²⁸Si based on neutron-transmutation-doping of isotopically engineered Si and Ge. In the proposed structure, interqubit coupling is due to indirect hyperfine interaction of ³¹P nuclear spins with electrons localized in a ²⁸Si quasi-one-dimensional nanowire, which allows one to control the coupling between distant qubits.     

A quantum computer based on NV centers in diamond: Optically detected nutations of single electron and nuclear spins

In an effort to realize a two-bit processor for a quantum computer on the basis of single nitrogen-vacancy defect centers (NV centers) in diamond, the optically detected nutations of the electron spin of a single NV center in the ground state and of the nuclear spin of a ¹³C atom located at a diamond lattice site nearest to the NV center are studied. The photodynamics of NV and NV + ¹³C centers under different temperatures and optical excitation conditions is discussed. A seven-level model of a center excited by radiation from an Ar⁺ laser at room temperature is proposed. On the basis of this model, the experimental spectra of optically detected electron paramagnetic and electron-nuclear double resonances of single NV and NV + ¹³C centers in diamond nanocrystals, as well as experimental data on the optically detected nutations of the electron and nuclear spins of these centers caused by the actions of pulsed microwave and radiofrequency fields, respectively, are interpreted.     

Defects and impurities in nanodiamonds: EPR, NMR and TEM study

EPR, ¹³C NMR and TEM study of ultradisperse diamond (UDD) samples is reported. The compounds show a high concentration of paramagnetic centers (up to 10²⁰ spin/g), which are due to structural defects (dangling C-C bonds) on the diamond cluster surface. The anomalous reduction in the spin-lattice relaxation time of ¹³C (from several hours in natural diamond to ∼150 ms in UDD clusters) is attributed to the interaction between the unpaired electrons of the paramagnetic centers and nuclear spins. ¹³C NMR line-width reflects the fact that the structure of the UDD surface is distorted in comparison to the ‘bulk’ diamond structure.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: I. The spin Hamiltonian method

Details of the application of the spin Hamiltonian method for studying spin characteristics of a quantum register that includes an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several isotopic atoms ¹³C located at different lattice sites near the vacancy of the NV center. Two methods of finding the hyperfine interaction tensors for these NV + n ¹³C spin systems are considered, one of which is based on the conventional electron spin resonance (ESR) method, while the other involves methods of quantum chemistry. The results of the latter method are compared with ESR data and with spectra of optically detected magnetic resonance (ODMR) and with the character of the modulation of the ODMR echo decay observed in single NV + n ¹³C systems. This comparison shows that the ab initio modeling of the spin characteristics of diamond nanoclusters containing NV centers makes it possible to obtain quantitative spin characteristics of the quantum registers under study.     

Experimental Hamiltonian Learning of an 11-Qubit Solid-State Quantum Spin Register

Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates.However,it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size.Here,we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond.We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment.Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms,and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.     

Fast holonomic quantum computation based on solid-state spins with all-optical control

Holonomic quantum computation is a quantum computation strategy that promises some built-in noise-resilience features. Here, we propose a scheme for nonadiabatic holonomic quantum computation with nitrogen-vacancy center electron spins, which are characterized by fast quantum gates and long qubit coherence times. By varying the detuning, amplitudes, and phase difference of lasers applied to a nitrogen-vacancy center, one can directly realize an arbitrary single-qubit holonomic gate on the spin. Meanwhile, with the help of cavity-assisted interactions, a nontrivial two-qubit holonomic quantum gate can also be induced. The distinct merit of this scheme is that all the quantum gates are obtained via an all-optical geometric manipulation of the solid-state spins. Therefore, our scheme opens the possibility for robust quantum computation using solid-state spins in an all-optical way.     

Quantum information processing and metrology with color centers in diamonds

The Nitrogen Vacancy （NV） center is becoming a promising qubit for quantum information processing. The defect has a long coherence time at room temperature and it allows spin state initialized and read out by laser and manipulated by microwave pulses. It has been utilized as a ultra sensi- tive probe for magnetic fields and remote spins as well. Here, we review the recent progresses in experimental demonstrations based on NV centers. We first introduce our work on implementation of the Deutsch- Jozsa algorithm with a single electronic spin in diamond. Then the quantum nature of the bath around the center spin is revealed and continuous wave dynamical decoupling has been demonstrated. By applying dynamical decoupling, a multi-pass quantum metrology protocol is realized to enhance phase estimation. In the final, we demonstrated NV center can be regarded as a ultra-sensitive sensor spin to implement nuclear magnetic resonance （NMR） imaging at nanoscale.     

Entanglement assisted metrology

We propose a new approach to the measurement of a single spin state, based on nuclear magnetic resonance (NMR) techniques and inspired by the coherent control over many-body systems envisaged by quantum information processing. A single target spin is coupled via the magnetic dipolar interaction to a large ensemble of spins. Applying radio frequency pulses, we can control the evolution so that the spin ensemble reaches one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. We first describe this measurement process using quantum gates; then we show how equivalent schemes can be defined in terms of the Hamiltonian and thus implemented under conditions of real control, using well established NMR techniques. We demonstrate this method with a proof of principle experiment in ensemble liquid state NMR and simulations for small spin systems.     

Study of diamond film by dynamic nuclear polarization-enhanced13C nuclear magnetic resonance spectroscopy

Three chemical vapor deposited diamond films were studied by dynamic nuclear polarization (DNP)-enhanced high-resolution solid-state¹³C nuclear magnetic resonance (NMR) spectroscopy. Enhanced¹³C direct-polarization spectra of diamond films were obtained by irradiating the samples with microwaves at or near electron spin resonance Larmor frequency of carbon center free radicals. No NMR signal for sp² hybridized carbons could be observed. From the curve of the DNP enhancement as a function of frequency, it is found that the dominant DNP mechanism is the solid-state effect. The¹³C cross-polarization spectrum, which is an evidence for existence of the proton defect in the lattice of diamond films, is much broader than the¹³C single pulse spectrum. The reason is discussed shortly.     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

Resonant polarization transfer from electron spins to nuclear spins-or to muon spins-in semiconductors

A review is given of newly developed pulsed Electron Spin Resonance (ESR) methods for dynamic polarization of nuclear spins. The application of two of these methods, Nuclear Orientation Via Electron spin Locking (NOVEL) and the Integrated Solid Effect (ISE), for the polarization of nuclear spins in semiconductors is discussed in more detail. It is proposed to use these methods to study the ESR spectrum of unpaired electrons in the vicinity of muons that are bound in a solid. Thus, ESR would be observed with a sensitivity which is enhanced by about ten orders of magnitude compared to conventional ESR.     

Quantum readout and fast initialization of nuclear spin qubits with electric currents

Nuclear spin qubits have the longest coherence times in the solid state, but their quantum readout and initialization is a great challenge. We present a theory for the interaction of an electric current with the nuclear spins of donor impurities in semiconductors. The theory yields a sensitivity criterion for quantum detection of nuclear spin states using electrically detected magnetic resonance, as well as an all-electrical method for fast nuclear spin qubit initialization.     

Spin quantum computation in silicon nanostructures

Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip-flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.     

Developments in quantum information processing by nuclear magnetic resonance: Use of quadrupolar and dipolar couplings

Use of dipolar and quadrupolar couplings for quantum information processing (QIP) by nuclear magnetic resonance (NMR) is described. In these cases, instead of the individual spins being qubits, the 2 ⁿ energy levels of the spin-system can be treated as an n-qubit system. It is demonstrated that QIP in such systems can be carried out using transition-selective pulses, in CH₃CN, ¹³CH₃CN, ⁷Li (I=3/2) and ¹³³Cs (I=7/2), oriented in liquid crystals yielding 2 and 3 qubit systems. Creation of pseudopure states, implementation of logic gates and arithmetic operations (half-adder and subtractor) have been carried out in these systems using transition-selective pulses.     

Preparation of quantum states of two spin-12 particles in the form of the Schmidt decomposition

We consider a system of two spins that are coupled via an isotropic Heisenberg Hamiltonian. For the first time, a two-step method for the preparation of an arbitrary quantum state of two qubits in the form of the Schmidt decomposition is proposed. The simplified version of this method is applied to the physical system of an atom with a nuclear spin 1/2 and one valence electron. As an example, the preparation of two-spin quantum states in the ³¹P system is considered.     

基于金刚石氮-空位色心自旋系综与超导量子电路混合系统的量子节点纠缠

量子纠缠是实现量子计算和量子通信的核心基础,本文提出了在金刚石氮-空位色心(NV centers)自旋系综与超导量子电路耦合的混合系统中实现两个分离量子节点之间纠缠的理论方案.在该混合系统中,把金刚石NV centers自旋系综和与之耦合的超导共面谐振器视为一个量子节点,两个量子节点之间通过一个空的超导共面谐振器连接.具有较长相干时间的NV centers自旋系综作为一个量子存储器,用于制备、存储和发送量子信息;易于外部操控的超导量子电路可执行量子逻辑门操作,快速调控量子信息.为了实现两个分离量子节点之间的纠缠,首先对系统的哈密顿量进行正则变换,将其等价为两个NV centers自旋系综与同一个超导共面谐振器之间的JC耦合;然后采用NV centers自旋-光子混合比特编码的方式,通过调节超导共面谐振器的谐振频率,精确控制体系演化时间,高保真度地实现了两个分离量子节点之间的量子纠缠.本方案还可以进一步扩展和集成,用于构建多节点纠缠的分布式量子网络.     

Dipolar Relaxation of Multiple Quantum NMR Coherences as a Model of Decoherence of Many-Qubit Coherent Clusters

Dipolar relaxation of multiple quantum (MQ) nuclear magnetic resonance (NMR) coherence is investigated on the evolution period of the MQ NMR experiment in chains of ¹⁹F nuclei in a single crystal of calcium fluorapatite. The dependence of the relaxation time of the MQ coherence of the second order on the size of the coherent spin cluster formed on the preparation period is obtained. The dipolar relaxation of MQ NMR coherences is considered as a model for the investigation of decoherence of quantum states of many-qubit spin clusters.     

Towards a spin-ensemble quantum memory for superconducting qubits

This article reviews efforts to build a new type of quantum device, which combines an ensemble of electronic spins with long coherence times, and a small-scale superconducting quantum processor. The goal is to store over long times arbitrary qubit states in orthogonal collective modes of the spin-ensemble, and to retrieve them on-demand. We first present the protocol devised for such a multi-mode quantum memory. We then describe a series of experimental results using NV (as in nitrogen vacancy) center spins in diamond, which demonstrate its main building blocks: the transfer of arbitrary quantum states from a qubit into the spin ensemble, and the multi-mode retrieval of classical microwave pulses down to the single-photon level with a Hahn-echo like sequence. A reset of the spin memory is implemented in-between two successive sequences using optical repumping of the spins.