Magnetic-field-assisted manipulation and entanglement of Si spin qubits

Abstract

Architectures of donor-electron based qubits in silicon near an oxide interface are considered theoretically. We find that the precondition for reliable logic and read-out operations, namely the individual identification of each donor-bound electron near the interface, may be accomplished by fine-tuning electric and magnetic fields, both applied perpendicularly to the interface. We argue that such magnetic fields may also be valuable in controlling two-qubit entanglement via donor electron pairs near the interface.PACS numbers: 03.67. Lx, 73.20.Hb, 85.35.Gv, 71.55.Cn Spin qubits in semiconductors (e.g. GaAs, Si) are among the most promising physical systems for the eventual fabrication of a working quantum computer (QC). There are two compelling reasons for this perceived importance of semiconductor spin qubits: (i) electron spin has very long coherence times, making quantum error correction schemes feasible as a matter of principle; (ii) semiconductor structures provide inherently scalable solid state architectures, as exemplified by the astonishing success of the microelectronics technology in increasing the speed and efficiency of logic and memory operations over the last fifty years (i.e. 'Moore's Law'). These advantages of semiconductor quantum computation apply much more to Si than to GaAs, because the electron spin coherence time can be increased indefinitely (up to 100 ms or even longer in the bulk) in Si through isotopic purification [1, 2, 3] whereas in GaAs the electron spin coherence time is restricted only to about 10 µs [1, 2, 4]. It is thus quite ironic that there has been much more substantial experimental progress [4] in electron spin and charge qubit manipulation in the III-V semiconductor quantum dot systems [5] than in the Si:P Kane computer architecture [6]. In addition to the long coherence time, the Si:P architecture has the highly desirable property of microscopically identical qubits which are scalable using the Si microelectronic technology. The main reason for the slow experimental progress in the Kane architecture is the singular lack of qubit-specific quantum control over an electron which is localized around a substitutional P atom in the bulk in a relatively unknown location. This control has turned out to be an impossibly difficult experimental task in spite of impressive developments in materials fabrication and growth in the Si:P architecture using both the 'top-down' and the 'bottom-up' techniques [7]. It is becoming manifestly clear that new ideas are needed in developing quantum control over single qubits in the Si:P QC architecture.In this Letter we suggest such a new idea, establishing convincingly that the use of a magnetic field, along with an electric field, would enable precise identification, manipulation and entanglement of donor qubits in the Si:P quantum computer architecture by allowing control over the spatial location of the electron as it is pulled from its shallow hydrogenic donor state to the Si/SiO 2 interface by an electric field. Additionally, the magnet...

Failure of standard approximations of the exchange coupling in nanostructures

“…Therefore, much attention has been devoted to simple approximations which lead to closed-form analytic expressions for the exchange coupling. 2,12,13 It is, however, not immediately obvious to what extent these approximations yield correct predictions, and where they break down. For example, in a recent work, 12 the validity criterion for such approximations was the requirement that the exchange coupling at zero magnetic field must always be positive.…”

Influence of confining potentials on the exchange coupling in double quantum dots

“…This behavior is well known for the Heitler-London approximation. 11,13 Eventually, the Heitler-London approximation also breaks down for the potential V q and predicts a negative exchange coupling, however, only at lower confinement energies ͑not shown͒. At large confinement energies, the potentials V min and V q Ј give nonnegative, finite values of the exchange coupling at short distances.…”

“…The first three potentials have previously been considered in the literature. 2,5,[7][8][9][10][11][12][13] The following approximations take as starting point the uncoupled dots at large distances, d ӷ r 0 . For the left or right dot centered at r L/R = ͑ϯd ,0͒, the ground state can be written 14 as …”

Quantum control and manipulation of donor electrons in Si-based quantum computing

“…We have also analyzed the effect of a magnetic field applied parallel to the electric field. 17,29 The magnetic field shrinks the electron wavefunction in the direction parallel to the interface.…”

“…We also briefly discuss the effect of a magnetic field applied parallel to the electric field. 18 In Sec. IV we discuss how the 2-qubit operations could be performed with the electrons at the interface state 17 and show new results for the calculation of the exchange calculated with an improved Heitler-London method.…”