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.     

Quantum spin dynamics in solution applicable to quantum computing

We investigate quantum spin dynamics of spin network systems in a liquid and in a molecular cluster with external magnetic field and discuss the importance of topological spin structures in relation to the quantum computing and quantum mechanical dimensions of the nuclear and the electron spins.     

Optical tailoring of electron spin coherence in quantum dots

We address the precession of an ensemble of electron spins, each confined in a (In, Ga)As/GaAs self-assembled quantum dot. The quantum dot inhomogeneity is directly reflected in the precession of the optically oriented electron spins about an external magnetic field, which is subject to fast dephasing on a nanoseconds time scale. Proper periodic laser excitation allows synchronization of the electron spin precessions with the excitation cycle. The experimental conditions can be tailored such that eventually all (about a million) electron spins that are excited by the laser precess with a single frequency. In this regime the ensemble can be exploited during the single electron spin coherence times being in the microseconds range.     

Stimulated polarization wave process in spin 3/2 chains

Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Recently, it has been demonstrated that, in an idealized one-dimensional Ising spin 1/2 chain with nearest-neighbor interactions and realistic spin 1/2 chain including the natural dipole-dipole interactions, irradiated by a weak resonant transverse field, a wave of flipped spins can be triggered by a single spin flip. Here we focuse on control of polarization wave in chain of spin 3/2, where the nuclear quadrupole interaction is dominant. Results of simulations for 1D spin chains and rings with up to five spins are presented.     

Quantum computation using the 13C nuclear spins near the single NV defect center in diamond

We discuss the possibility of realizing quantum computation on the basis of a cluster of single interacting nuclear spins in solids. This idea seems to be feasible because of the combination of two techniques—Single Molecule Spectroscopy and Optically Detected Electron Nuclear Double Resonance. Compared to the well-known bulk Nuclear Magnetic Resonance (NMR), the proposed method of quantum computation has the advantage that quantum computation is performed with pure spin states and the quantum processor is more easily scalable. At the same time, the advantages of NMR quantum computation are kept: long coherence time and easy construction of quantum gates. As a specific system to implement the above idea, we discuss the ¹³C-nuclear spins in the nearest vicinity of a single nitrogen-vacancy (NV) defect center in diamond, which can be optically detected using the technique of scanning confocal microscopy. Owing to the hyperfine coupling of the ground state electron paramagnetic spin S=1 of the center to ¹³C nuclear spins in a diamond lattice, the states of nuclear spins in the vicinity of the defect-center can be addressed individually. Preliminary consideration shows that it should be possible to address up to 12 individual ¹³C nuclear spins. The dephasing time of the nuclear spin states at low temperatures allows realization up to 10⁵ gates.     

Quantum computing by optical control of electron spins

We review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III–V or II–VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centres in solids, such as P-donors in silicon and nitrogen-vacancy centres in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing between stationary spin qubits in QDs and flying photon qubits in waveguides, rapid initialization of spin qubits and qubit-specific single-shot non-demolition quantum measurement. The rapid qubit initialization may be realized by selectively enhancing certain entropy dumping channels via phonon or photon baths. The single-shot quantum measurement may be in situ implemented through the integrated photonic network. The relevance of quantum non-demolition measurement to large-scale quantum computation is discussed. To illustrate the feasibility and demand, the resources are estimated for the benchmark problem of factorizing 15 with Shor's algorithm.     

Voltage-selective bidirectional polarization and coherent rotation of nuclear spins in quantum dots

We propose and demonstrate that the nuclear spins of the host lattice in GaAs double quantum dots can be polarized in either of two opposite directions, parallel or antiparallel to an external magnetic field. The direction is selected by adjusting the dc voltage. This nuclear polarization manifests itself by repeated controlled electron-nuclear spin scattering in the Pauli spin-blockade state. Polarized nuclei are also controlled by means of nuclear magnetic resonance. This Letter confirms that the nuclear spins in quantum dots are long-lived quantum states with a coherence time of up to 1 ms, and may be a promising resource for quantum-information processing such as quantum memories for electron spin qubits.     

Measurement of a heavy-hole hyperfine interaction in InGaAs quantum dots using resonance fluorescence

We measure the strength and the sign of hyperfine interaction of a heavy hole with nuclear spins in single self-assembled quantum dots. Our experiments utilize the locking of a quantum dot resonance to an incident laser frequency to generate nuclear spin polarization. By monitoring the resulting Overhauser shift of optical transitions that are split either by electron or exciton Zeeman energy with respect to the locked transition using resonance fluorescence, we find that the ratio of the heavy-hole and electron hyperfine interactions is -0.09 ± 0.02 in three quantum dots. Since hyperfine interactions constitute the principal decoherence source for spin qubits, we expect our results to be important for efforts aimed at using heavy-hole spins in quantum information processing.     

Coupling Distant Spins of Surface-State Electrons by Manipulating Their Collective Vibrations

The system of electrons on liquid helium is an interesting candidate to implement quantum computation, due to the long coherence times of the qubits encoded by the electronic spins. In order to implement the quantum logic operations between the spins, we propose here a configuration, similarly to the cooled ions in a trap, to couple the distant electrons via manipulating their center of mass （CM） vibrations. First, we show that the electrons could be confined in a common harmonic oscillator potential by using an electrostatic field. Then, with a single current pulse （applied on the micro-electrode below the liquid helium） the distant electronic spins can be coupled simultaneously to the CM mode. Finally, by adiabatically eliminating the CM mode, effective interaction between the distant spins is induced for implementing the desired quantum computing.     

Concepts of spin quantum computing

Quantum computing is based on two-state quantum systems called qubits. Recent proposals for quantum computing included nuclear spin 1/2 as qubits and implementations of several quantum algorithms were demonstrated by applying liquid-state NMR. Here I want to lay out some of the concepts of spin quantum computing including nuclear and electron spins. This article is intended to serve a dual purpose. It should on one hand introduce the reader who is not familiar with magnetic resonance to the spin quantum computing terminology and the concepts of pulsed magnetic resonance. At the same time I want to introduce the NMR expert to the recent developments in quantum computing.     

Rapid and robust spin state amplification

Electron and nuclear spins have been employed in many of the early demonstrations of quantum technology. However, applications in real world quantum technology are limited by the difficulty of measuring single spins. Here we show that it is possible to rapidly and robustly amplify a spin state using a lattice of ancillary spins. The model we employ corresponds to an extremely simple experimental system: a homogenous Ising-coupled spin lattice in one, two, or three dimensions, driven by a continuous microwave field. We establish that the process can operate at finite temperature (imperfect initial polarization) and under the effects of various forms of decoherence.     

Verification of a new quantum simulation approach through its application to two-dimensional Ising lattices

A new quantum simulation approach has been applied in the present work to the two-dimensional (2D) ferromagnetic and antiferromagnetic Ising lattices to calculate their magnetic structures, magnetizations, free energies and specific heats in the absence of an external magnetic field. Surprisingly, no size effects could be observed in our simulations performed for the Ising lattices of different sizes. Most importantly, our calculated spontaneous thermally averaged spins for the two kinds of systems are exactly same as those evaluated with quantum mean field theory, and the magnetic structures simulated at all chosen temperatures are perfectly ferromagnetic or antiferromagnetic, verifying the correctness and applicability of our quantum model and computational algorithm. On the other hand, if the classical Monte Carlo (CMC) method is applied to the ferromagnetic 2D Ising lattice with S=1, it is able to generate correct magnetization well consistent with Onsager's theory; but in the case of S=1/2, the computational results of CMC are incomparable to those predicted with the quantum mean field theory, giving rise to very much reduced magnetization and considerably underestimated Curie temperature. The difficulty met by the CMC method is mainly caused by its improperly calculated exchange energy of the randomly selected spin in every simulation step, especially immediately below the transition temperature, where the thermal averages of spins are much less than 1/2, however they are assigned to ±1/2 by CMC to evaluate the exchange energies of the spins, such improper manipulation is obviously impossible to lead the code to converge to the right equilibrium states of the spin systems.     

Enhancement of electron spin coherence by optical preparation of nuclear spins

We study a large ensemble of nuclear spins interacting with a single electron spin in a quantum dot under optical excitation and photon detection. At the two-photon resonance between the two electron-spin states, the detection of light scattering from the intermediate exciton state acts as a weak quantum measurement of the effective magnetic (Overhauser) field due to the nuclear spins. In a coherent population trapping state without light scattering, the nuclear state is projected into an eigenstate of the Overhauser field operator, and electron decoherence due to nuclear spins is suppressed: We show that this limit can be approached by adapting the driving frequencies when a photon is detected. We use a Lindblad equation to describe the driven system under photon emission and detection. Numerically, we find an increase of the electron coherence time from 5 to 500 ns after a preparation time of 10 micros.     

Spin–orbit interaction induced current dip in a single quantum dot coupled to a spin

Experiments on semiconductor quantum dot systems have demonstrated the coupling between electron spins in quantum dots and spins localized in the neighboring area of the dots. Here we show that in a magnetic field the electrical current flowing through a single quantum dot tunnel-coupled to a spin displays a dip at the singlet–triplet anticrossing point which appears due to the spin–orbit interaction. We specify the requirements for which the current dip is formed and examine the properties of the dip for various system parameters, such as energy detuning, spin–orbit interaction strength, and coupling to leads. We suggest a parameter range in which the dip could be probed.     

Knight-field-enabled nuclear spin polarization in single quantum dots

We demonstrate dynamical nuclear-spin polarization in the absence of an external magnetic field by resonant circularly polarized optical excitation of a single electron or hole charged quantum dot. Optical pumping of the electron spin induces an effective inhomogeneous magnetic (Knight) field that determines the direction along which nuclear spins could polarize and enables nuclear-spin cooling by suppressing depolarization induced by nuclear dipole-dipole interactions. Our experiments constitute a first step towards a quantum measurement of the Overhauser field.     

Entanglement versus correlations in spin systems

We consider pure quantum states of N>1 spins or qubits and study the average entanglement that can be localized between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this localizable entanglement, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.     

Reversal of coherent‐state spins in square magnetic nanodots induced by a magnetic microwave field

We study the coherent state excitation of spins in square nanodots induced by a magnetic microwave field. We present a new mechanism of spin reversal in nanodots. That is, the microwave field directly induces the reversal of the coherent‐state spins instead of indirectly through the magnetic vortex. We obtain the space distribution of coherent‐state spins in terms of a quantum theory, and calculate the time of spin reversal. This spin‐reversal process may be used to serve as a storage mechanism of binary information.     

Dynamics of quantum dot nuclear spin polarization controlled by a single electron

We present measurements of the buildup and decay of nuclear spin polarization in a single semiconductor quantum dot. Our experiment shows that we polarize the nuclei in a few milliseconds, while their decay dynamics depends drastically on external parameters. We show that a single electron can very efficiently depolarize nuclear spins in milliseconds whereas in the absence of the electron the nuclear spin lifetime is on the scale of seconds. This lifetime is further enhanced by 1-2 orders of magnitude by quenching the nonsecular nuclear dipole-dipole interactions with a magnetic field of 1 mT.     

Controllable anisotropic exchange coupling between spin qubits in quantum dots

The exchange coupling between quantum dot spin qubits is isotropic, which restricts the types of quantum gates that can be formed. Here, we propose a method for controlling anisotropic interactions between spins arranged in a bus geometry. The symmetry is broken by an external magnetic field, resulting in XXZ-type interactions that can efficiently generate maximally entangled Greenberger-Horne-Zeilinger states or universal gate sets for exchange-only quantum computing. We exploit the XXZ couplings to propose a qubit scheme, based on double dots.