Spin-based Quantum Computation Research Articles

Transport in graphene nanostructures

Graphene nanostructures are promising candidates for future nanoelectronics and solid-state quantum information technology. In this review we provide an overview of a number of electron transport experiments on etched graphene nanostructures. We briefly revisit the electronic properties and the transport characteristics of bulk, i.e., two-dimensional graphene. The fabrication techniques for making graphene nanostructures such as nanoribbons, single electron transistors and quantum dots, mainly based on a dry etching “paper-cutting” technique are discussed in detail. The limitations of the current fabrication technology are discussed when we outline the quantum transport properties of the nanostructured devices. In particular we focus here on transport through graphene nanoribbons and constrictions, single electron transistors as well as on graphene quantum dots including double quantum dots. These quasi-one-dimensional (nanoribbons) and quasi-zero-dimensional (quantum dots) graphene nanostructures show a clear route of how to overcome the gapless nature of graphene allowing the confinement of individual carriers and their control by lateral graphene gates and charge detectors. In particular, we emphasize that graphene quantum dots and double quantum dots are very promising systems for spin-based solid state quantum computation, since they are believed to have exceptionally long spin coherence times due to weak spin-orbit coupling and weak hyperfine interaction in graphene.

An endohedral fullerene-based nuclear spin quantum computer

We propose a new scalable quantum computer architecture based on endohedral fullerene molecules. Qubits are encoded in the nuclear spins of the endohedral atoms, which posses even longer coherence times than the electron spins which are used as the qubits in previous proposals. To address the individual qubits, we use the hyperfine interaction, which distinguishes two modes (active and passive) of the nuclear spin. Two-qubit quantum gates are effectively implemented by employing the electronic dipolar interaction between adjacent molecules. The electron spins also assist in the qubit initialization and readout. Our architecture should be significantly easier to implement than earlier proposals for spin-based quantum computers, such as the concept of Kane [B.E. Kane, Nature 393 (1998) 133].

Electron Spin Decoherence in Isotope-Enriched Silicon

Silicon is promising for spin-based quantum computation because nuclear spins, a source of magnetic noise, may be eliminated through isotopic enrichment. Long spin decoherence times T2 have been measured in isotope-enriched silicon but come far short of the T2=2T1 limit. The effect of nuclear spins on T2 is well established. However, the effect of background electron spins from ever present residual phosphorus impurities in silicon can also produce significant decoherence. We study spin decoherence decay as a function of donor concentration, 29Si concentration, and temperature using cluster expansion techniques specifically adapted to the problem of a sparse dipolarly coupled electron spin bath. Our results agree with the existing experimental spin echo data in Si:P and establish the importance of background dopants as the ultimate decoherence mechanism in isotope-enriched silicon.

Spin dependent tunneling spectroscopy in 1.2 nm dielectrics

We demonstrate voltage controlled spin dependent tunneling in 1.2 nm effective oxide thickness silicon oxynitride films. Our observations introduce a simple method to link point defect structure and energy levels in a very direct way in materials of great technological importance. We obtain defect energy level resolution by exploiting the enormous difference between the capacitance of the very thin dielectric and the capacitance of the depletion layer of moderately doped silicon. The simplicity of the technique and the robust character of the response make it, at least potentially, of widespread utility in the understanding of defects important in solid state electronics. Since the specific defect observed is generated by high electric field stressing, an important device instability in present day integrated circuitry, the observations are of considerable importance for present day technology. Since the observations involve inherent high sensitivity and tunneling, and since the process can be turned on and off with the application of a narrow range of voltage, our results may also be relevant to the development of spin based quantum computing.

Theory of Anisotropic Exchange in Laterally Coupled Quantum Dots

The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field, the exchange interaction is practically unaffected by spin-orbit coupling, for any interdot coupling, boosting prospects for spin-based quantum computing. The anisotropic exchange appears at finite magnetic fields. A numerically accurate effective spin Hamiltonian for modeling spin-orbit-induced two-electron spin dynamics in the presence of magnetic field is proposed.

Universal enhancement of the optical readout fidelity of single electron spins at nitrogen-vacancy centers in diamond

Precise readout of spin states is crucial for any approach toward physical realization of a spin-based quantum computer and for magnetometry with single spins. Here, we report a method to strongly improve the optical readout fidelity of electron spin states associated with single nitrogen-vacancy (NV) centers in diamond. The signal-to-noise ratio is enhanced significantly by performing conditional flip-flop processes between the electron spin and the nuclear spin of the NV center's nitrogen atom. The enhanced readout procedure is triggered by a short preparatory pulse sequence. As the nitrogen nuclear spin is intrinsically present in the system, this method is universally applicable to any nitrogen-vacancy center. Besides the readout method, our studies included coherent control over a single nitrogen nuclear spin for the first time.

Gate-inducedg-factor control and dimensional transition for donors in multivalley semiconductors

The dependence of the g-factors of semiconductor donors on applied electric and magnetic fields is of immense importance in spin based quantum computation and in semiconductor spintronics. The donor g-factor Stark shift is sensitive to the orientation of the electric and magnetic fields and strongly influenced by the band-structure and spin-orbit interactions of the host. Using a multimillion atom tight-binding framework the spin-orbit Stark parameters are computed for donors in multi-valley semiconductors, silicon and germanium. Comparison with limited experimental data shows good agreement for a donor in silicon. Results for gate induced transition from 3D to 2D wave function confinement show that the corresponding g-factor shift in Si is experimentally observable.

Ultrafast Optical Spin Echo for Electron Spins in Semiconductors

Spin-based quantum computing and magnetic resonance techniques rely on the ability to measure the coherence time T(2) of a spin system. We report on the experimental implementation of all-optical spin echo to determine the T(2) time of a semiconductor electron-spin system. We use three ultrafast optical pulses to rotate spins an arbitrary angle and measure an echo signal as the time between pulses is lengthened. Unlike previous spin-echo techniques using microwaves, ultrafast optical pulses allow clean T(2) measurements of systems with dephasing times (T_{2};{*}) fast in comparison to the time scale for microwave control. This demonstration provides a step toward ultrafast optical dynamic decoupling of spin-based qubits.

Spin-based quantum computers made by chemistry: hows and whys

This introductory review discusses the main problems facing the attempt to build quantum information processing systems (like quantum computers) from spin-based qubits. We emphasize ‘bottom-up’ attempts using methods from chemistry. The essentials of quantum computing are explained, along with a description of the qubits and their interactions in terms of physical spin qubits. The main problem to be overcome in this whole field is decoherence—it must be considered in any design for qubits. We give an overview of how decoherence works, and then describe some of the practical ways to suppress contributions to decoherence from spin bath and oscillator bath environments, and from dipolar interactions. Dipolar interactions create special problems of their own because of their long range. Finally, taking into account the problems raised by decoherence, by dipolar interactions, and by architectural constraints, we discuss various strategies for making chemistry-based spin qubits, using both magnetic molecules and magnetic ions.

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.

Real time exponentially weighted recursive least squares adaptive signal averaging for enhancing the sensitivity of continuous wave magnetic resonance

This study involves the use of adaptive signal processing techniques to improve the sensitivity of continuous wave electrically detected magnetic resonance. The approach should be of widespread utility in continuous wave magnetic resonance experiments of all kinds. We utilize adaptive signal averaging to expedite the averaging process usually performed in magnetic resonance experiments. We were capable of reducing the noise variance in a single trace by a factor of 11.3 which is equivalent to reduction in time by the same factor. This factor can be quite significant especially when signal averaging must be performed over the span of many hours to days. This technique may also be tailored to conventional electron spin resonance experiments and other techniques where signal averaging is utilized. The approach may offer promise in the eventual development of spin based quantum computing.

Driven coherent oscillations of a single electron spin in a quantum dot

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.

Finite-element analysis of a silicon-based double quantum dot structure

We present the results of a finite-element solution of the Laplace equation for the silicon-based trench-isolated double quantum-dot and the capacitively-coupled single-electron transistor device architecture. This system is a candidate for charge and spin-based quantum computation in the solid state, as demonstrated by recent coherent-charge oscillation experiments. Our key findings demonstrate control of the electric potential and electric field in the vicinity of the double quantum-dot by the electric potential applied to the in-plane gates. This constitutes a useful theoretical analysis of the silicon-based architecture for quantum information processing applications.

Semiconductor quantum dots for electron spin qubits

We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates.

Simulation of Si:P spin-based quantum computer architecture

We present a systematic and realistic simulation for single and double phosphorous donors in a silicon-based quantum computer design. A two-valley equation is developed to describe the ground state of phosphorous donors in strained silicon quantum well (QW), with the central cell effect treated by a model impurity potential. We find that the increase of quantum well confinement leads to shrinking charge distribution in all 3 dimensions. Using an unrestricted Hartree-Fock method with Generalized Valence Bond (GVB) single-particle wave functions, we are able to solve the two-electron Sch${\ddot o}$dinger equation with quantum well confinement and realistic gate potentials. The effects of QW width, gate voltages, donor separation, and donor position are calculated and analyzed. The gate tunability and gate fidelity are defined and evaluated, for a typical QC design. Estimates are obtained for the duration of $\sqrt{SWAP}$ gate operation and the required accuracy in voltage control. A strong exchange oscillation is observed as both donors are shifted along [001] axis but with their separation unchanged. Applying a gate potential tends to suppress the oscillation. The exchange oscillation as a function of donor position along [100] axis is found to be completely suppressed as the donor separation is decreased. The simulation presented in this paper is of importance to the practical design of an exchange-based silicon quantum computer.

Single-spin measurement using spin–orbital entanglement

Single-spin measurement represents a major challenge for spin-based quantum computation. In this paper, we propose a new method for measuring the spin of a single electron confined in a quantum dot (QD). Our strategy is based on entangling (using unitary gates) the spin and orbital degrees of freedom. An ‘orbital qubit’, defined by a second, empty QD, is used as an ancilla and is prepared in a known initial state. Measuring the orbital qubit will reveal the state of the (unknown) initial spin qubit, hence reducing the problem to the easier task of single charge measurement. Since spin-charge conversion is done with unit probability, single-shot measurement of an electronic spin can be, in principle, achieved. We evaluate the robustness of our method against various sources of error and discuss possible implementations.

Electrical readout of a spin qubit without double occupancy

We identify a mechanism to read out a single solid-state electron spin using an all-electrical spin-to-charge conversion in a closed system. Our scheme uses three donors and two electron spins, one spin is the qubit, the other is a reference. The population in the third, originally ionized, donor is monitored with an electrometer. Energy-dependent tunneling of the reference spin to the ionized donor is used to determine the state of the qubit. In contrast to previous methods [e.g., B. E. Kane, Nature (London) 393, 133 (1998)] we avoid double electron occupancy of any site within the system, thereby eliminating the possibility of unwanted electron loss from the system. The single spin readout scheme described here is applicable to both electron and nuclear spin based quantum computer architectures.

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.

Spin-Based Quantum Dot Quantum Computing in Silicon

The spins of localized electrons in silicon are strong candidates for quantum information processing because of their extremely long coherence times and the integrability of Si within the present microelectronics infrastructure. This paper reviews a strategy for fabricating single electron spin qubits in gated quantum dots in Si/SiGe heterostructures. We discuss the pros and cons of using silicon, present recent advances, and outline challenges.

Exchange interaction between three and four coupled quantum dots: Theory and applications to quantum computing

Several prominent proposals have suggested that spins of localized electrons could serve as quantum computer qubits. The exchange interaction has been invoked as a means of implementing two qubit gates. In this paper, we analyze the strength and form of the exchange interaction under relevant conditions. We find that, when several spins are engaged in mutual interactions, the quantitative strengths or even qualitative forms of the interactions can change. A variety of interaction forms can arise depending on the symmetry of the system. It is shown that the changes can be dramatic within a Heitler-London model. Hund-M\"ulliken calculations are also presented, and support the qualitative conclusions from the Heitler-London model. The effects need to be considered in spin-based quantum computer designs, either as a source of gate error to be overcome or a new interaction to be exploited.