Silicon-based Quantum Computer Research Articles

On the nuclear magnetic resonance frequency of phosphorus donor atom in a silicon-based quantum computer

The nuclear magnetic resonance (NMR) frequency of a single qubit structure of Kane’s solid-state quantum computer is investigated by using the perturbation theory. With higher-order excited states (up to 3d modes) included in our calculation, the perturbation frequencies and energies are obtained numerically. To compute for arbitrary A gate geometries, the perturbation potential inside the qubit structure is determined through an electromagnetic simulation method. Calculations show that the potential distributions for realistic A gate geometries are far from linear ones. Our results show that the A gate voltage has a much more effective control over the NMR frequency of the phosphorus nucleus than that previously shown. Using our method, arbitrary A gate structures of any shapes or geometries can be engineered for the realization of a solid-state scalable quantum computer. We also investigate an alternative A gate structure using SiGe as the insulation barrier. Our study shows that this A gate structure o...

Qubit addressing using hyperfine-interaction control by an electric field in a magnetic crystal

We demonstrate experimentally the hyperfine-interaction control by an electric field, which is the operating principle of the addressable qubit operation in a silicon-based solid-state quantum computer in a new quantum computer system, a magnetic crystal. The transferred hyperfine field at a ${\mathrm{F}}^{\ensuremath{-}}$ nucleus caused by neighboring ${\mathrm{Mn}}^{2+}$ electron spins in an antiferromagnetic ${\mathrm{MnF}}_{2}$ single crystal was measured by $^{19}\mathrm{F}$ nuclear magnetic resonance (NMR) with an external electric field applied along the [110] crystal direction. The electric field splits the $^{19}\mathrm{F}$ NMR peak into two resolved lines that come from the F nuclei located at geometrically equivalent sites. A line splitting of 56 kHz was achieved at an electric field of 3.4 V/$\ensuremath{\mu}$m. One of the ${\mathrm{F}}^{\ensuremath{-}}$ nuclear spins could be flipped selectively by a composite radio-frequency pulse while leaving the other unchanged, thereby demonstrating qubit addressing via electric field control of the hyperfine interaction.

Visualizing a silicon quantum computer

Quantum computation is a fast-growing, multi-disciplinary research field. The purpose of a quantum computer is to execute quantum algorithms that efficiently solve computational problems intractable within the existing paradigm of ‘classical’ computing built on bits and Boolean gates. While collaboration between computer scientists, physicists, chemists, engineers, mathematicians and others is essential to the project's success, traditional disciplinary boundaries can hinder progress and make communicating the aims of quantum computing and future technologies difficult. We have developed a four minute animation as a tool for representing, understanding and communicating a silicon-based solid-state quantum computer to a variety of audiences, either as a stand-alone animation to be used by expert presenters or embedded into a longer movie as short animated sequences. The paper includes a generally applicable recipe for successful scientific animation production.

Spin-dependent scattering off neutral antimony donors in Si28 field-effect transistors

We report measurements of spin-dependent scattering of conduction electrons by neutral donors in accumulation-mode field-effect transistors formed in isotopically enriched silicon. Spin-dependent scattering was detected using electrically detected magnetic resonance where spectra show resonant changes in the source-drain voltage for conduction electrons and electrons bound to donors. We discuss the utilization of spin-dependent scattering for the readout of donor spin states in silicon based quantum computers.

IMPLEMENTATION OF QUANTUM LOGIC OPERATIONS AND CREATION OF ENTANGLEMENT BETWEEN TWO NUCLEAR SPIN QUBITS WITH CONSTANT INTERACTION

We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear–electron hyperfine and electron–electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Controlled-NOT gate. The exchange interaction is constant, and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper, parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.

Optical Detection and Ionization of Donors in Specific Electronic and Nuclear Spin States

We resolve the remarkably sharp bound exciton transitions of highly enriched 28Si using a single-frequency laser and photoluminescence excitation spectroscopy, as well as photocurrent spectroscopy. Well-resolved doublets in the spectrum of the 31P donor reflect the hyperfine coupling of the electronic and nuclear donor spins. The optical detection of the nuclear spin state, and selective pumping and ionization of donors in specific electronic and nuclear spin states, suggests a number of new possibilities which could be useful for the realization of silicon-based quantum computers.

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor $(^{31}\mathrm{P})$ doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

Influence of qubit displacements on quantum logic operations in a silicon-based quantum computer with constant interaction

The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using controlled-NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a controlled-NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small.

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighbouring P donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position and inter donor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, whilst the magnitude of the double occupancy probability can affect the error rate.

Magnetic susceptibility of exchange-disordered antiferromagnetic finite chains

The low-temperature behavior of the static magnetic susceptibility $\chi(T)$ of exchange-disordered antiferromagnetic spin chains is investigated. It is shown that for a relatively small and even number of spins in the chain, two exchange distributions which are expected to occur in nanochains of P donors in silicon lead to qualitatively distinct behaviors of the low-temperature susceptibility. As a consequence, magnetic measurements might be useful to characterize whether a given sample meets the requirements compatible with Kane's original proposalfor the exchange gates in a silicon-based quantum computer hardware. We also explore the dependence of $\chi(T)$ on the number of spins in the chain as it increases towards the thermodynamic limit, where any degree or distribution of disorder leads to the same low-temperature scaling behavior. We identify a crossover regime where the two distributions of disorder may not be clearly differentiated, but the characteristic scaling of the thermodynamic limit has not yet been reached.

Si atom wire growth for quantum information processing

We report on the experimental realization of straight atomic wires of Si on a vicinal Si(111) substrate. Atomic-kink-free steps with an identical structure are formed on the clean substrate by prolonged annealing around 800 °C. The direction of the annealing DC current that is effective to extend the straight step region is the so-called kink-up direction. Furthermore, the step-edge structure obtained is serendipitously suitable for the exclusive growth of the single adatom wires by molecular beam epitaxy. An isotopic version of such a structure is expected to be the most basic building block for a silicon-based quantum computer.

SILICON-BASED NUCLEAR SPIN QUANTUM COMPUTER

We review the basic physics and operation principles of the silicon-based quantum computer proposed by Kane, one of the most promising solid-state quantum computer proposals. We describe in some details how single- and two-qubit operations and readout measurements can, in principle, be performed for the Kane quantum computer. In addition, we also mention briefly its recent theoretical progress and development.

Enhancing semiconductor device performance using ordered dopant arrays

As the size of semiconductor devices continues to shrink, the normally random distribution of the individual dopant atoms within the semiconductor becomes a critical factor in determining device performance--homogeneity can no longer be assumed. Here we report the fabrication of semiconductor devices in which both the number and position of the dopant atoms are precisely controlled. To achieve this, we make use of a recently developed single-ion implantation technique, which enables us to implant dopant ions one-by-one into a fine semiconductor region until the desired number is reached. Electrical measurements of the resulting transistors reveal that device-to-device fluctuations in the threshold voltage (Vth; the turn-on voltage of the device) are less for those structures with ordered dopant arrays than for those with conventional random doping. We also find that the devices with ordered dopant arrays exhibit a shift in Vth, relative to the undoped semiconductor, that is twice that for a random dopant distribution (- 0.4 V versus -0.2 V); we attribute this to the uniformity of electrostatic potential in the conducting channel region due to the ordered distribution of dopant atoms. Our results therefore serve to highlight the improvements in device performance that can be achieved through atomic-scale control of the doping process. Furthermore, ordered dopant arrays of this type may enhance the prospects for realizing silicon-based solid-state quantum computers.

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.

Defect-induced dimer pinning on the Si(0 0 1) surface

Room-temperature STM images frequently show regions of antisymmetric dimer ordering surrounding certain types of defect on the Si(0 0 1) surface. While it has been generally believed that any defect asymmetric with respect to the dimer row would induce this dimer pinning effect, recent experimental results have shown that this is not the case. We present a model, based on a nearest-neighbour Ising treatment of the surface, which allows the extent of pinning caused by a dimer to be predicted from ab initio calculations. We use this model to predict the pinning extent for three phosphorus-containing structures important in a proposed silicon-based quantum computer fabrication scheme, and identify one of these asymmetric features as causing no appreciable pinning. In addition, we use ab initio calculations to identify the effects governing the interaction between neighbouring dimers.

The Road to a Silicon Quantum Computer

We discuss prospects for building a silicon-based quantum computer with phosphorous donor qubits. A specific architecture is proposed for initial demonstrations; and the advantages and difficulties of thisapproach are described along with a plan for systematic development and calibration of the individualcomponents.

Electron exchange coupling for single-donor solid-state spin qubits

Inter-valley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighbouring phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wavefunctions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys. Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighbouring donors that have been implanted into the silicon substrate using an 15keV ion beam in the so-called 'top down' fabrication scheme for a Kane solid-state quantum computer. In addition we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wavefunctions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighbouring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller.

Towards the atomic-scale fabrication of a silicon-based solid state quantum computer

The construction of a scalable quantum computer in silicon, using single phosphorus atoms as qubits, presents a significant technological challenge. This paper describes recent results from a ‘bottom-up’ strategy to incorporate individual phosphorus atoms in silicon with atomic precision using a combination of advanced scanning tunnelling lithography techniques followed by low temperature silicon molecular beam epitaxial overgrowth. To date we have demonstrated (i) placement of individual phosphorus molecules at predetermined sites in the silicon surface using a hydrogen resist strategy, (ii) spatially controlled phosphorus incorporation into the silicon surface, (iii) minimisation of surface segregation by low temperature silicon encapsulation and (iv) complete electrical activation of the donors. Whilst these results bode well for the fabrication of silicon devices with atomically precise dopant profiles, we discuss the challenges that remain before a few qubit P in Si quantum computer prototype can be realised.

Critical issues in the formation of atomic arrays of phosphorus in silicon for the fabrication of a solid-state quantum computer

We present recent progress towards the fabrication of a silicon-based quantum computer, via a ‘bottom up’ strategy, which exploits a combination of scanning tunneling microscopy (STM) and molecular beam epitaxy. Following our recent success in the fabrication of an atomic array of P atoms in silicon we now address the critical issues leading to the encapsulation of this array in silicon. Exposing Si(0 0 1) to a low PH 3 dose at room temperature results in the formation of a number of species on the surface. We use bias dependent STM to characterise these species and identify PH x ( x=2,3) moieties and hemihydrides as the dominant surface adsorbates. We show that by controlled annealing we can incorporate single P atoms into the surface layer. We use STM lithography to depassivate regions of a H:Si(0 0 1) surface in order to confine the above adsorption/incorporation processes to nanometer sized areas.

Strain effects on silicon donor exchange: Quantum computer architecture considerations

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 infrastructure of the powerful Si technology. Quantitative understanding of and precise physical control over donor (e.g. Phosphorus) exchange are crucial elements in the physics underlying the proposed Si-based quantum computer hardware. An important potential problem in this context is that inter-valley interference originating from the degeneracy in the Si conduction band edge causes fast oscillations in donor exchange coupling, which imposes significant constraints on the Si quantum computer architecture. In this paper we consider the effect of external strain on Si donor exchange in the context of quantum computer hardware. We study donor electron exchange in uniaxially strained Si, since strain partially lifts the valley degeneracy in the bulk. In particular, we focus on the effects of donor displacements among lattice sites on the exchange coupling, investigating whether inter-valley interference poses less of a problem to exchange coupling of donors in strained Si. We show, using the Kohn-Luttinger envelope function approach, that fast oscillations in exchange coupling indeed disappear for donor pairs that satisfy certain conditions for their relative positions, while in other situations the donor exchange coupling remains oscillatory, with periods close to interatomic spacing. We also comment on the possible role of controlled external strain in the design and fabrication of Si quantum computer architecture.