Highly tunable exchange in donor qubits in silicon

Abstract

In this article we have investigated the electrical control of the exchange coupling (J) between donor-bound electrons in silicon with a detuning gate bias, crucial for the implementation of the two-qubit gate in a silicon quantum computer. We found that the asymmetric 2P-1P system provides a highly tunable exchange curve with mitigated J-oscillation, in which 5 orders of magnitude change in the exchange coupling can be achieved using a modest range of electric field (3 MV/m) for~15-nm qubit separation. Compared with the barrier gate control of exchange in the Kane qubit, the detuning gate design reduces the gate density by a factor of~2. By combining large-scale atomistic tight-binding method with a full configuration interaction technique, we captured the full two-electron spectrum of gated donors, providing state-of-the-art calculations of exchange energy in 1P-1P and 2P-1P qubits.npj Quantum Information (2016) 2, 16008; doi:10.1038/npjqi.2016.8; published online 12 April 2016 INTRODUCTION Donor qubits in silicon are promising candidates for spin-based quantum computation as they have exceptionally long T 1 (refs 1-3) and T 2 times 4-6 and offer both electron and nuclear spins for encoding quantum information 5-8 utilising commonly used silicon device technology. With recent demonstration of single qubits in silicon with both electronic and nuclear spins of donors, 5,7 the next biggest challenge is to demonstrate two-qubit gates based on the exchange interaction. Ideally, the exchange coupling J in a two-qubit gate needs to be tuned electrically by several orders of magnitude between an 'Off' and an 'On' state within a small and realisable bias range. To achieve this, the popular Kane architecture uses a J-gate between two phosphorus donors to tune the J-coupling. Recently A-gates that tune the hyperfine interaction for individual qubits have been demonstrated. 9 However, in the long run such a J-and A-gate architecture leads to a high gate density, requiring ultra-small gate widths to minimise electrical cross-talk between gates, and precise donor positioning relative to gates. Moreover, the tunability of the exchange coupling is limited both by the electric field range the J-gate can produce and by the field ionisation of the electrons to the surface. Previous calculations have also shown that the J-coupling oscillates as a function of donor separation due to crystal momentum states, 10 and is therefore sensitive to atomic-scale placement errors. All these issues lead to severe constraints in the implementation of a two-qubit gate in donors.In this work, we introduce an alternative design for an exchange gate in a two-qubit donor system, which allows flexibility in device fabrication and in tuning the exchange coupling. In principle, this new design can (1) eliminate the need for additional J-gates between the donors, (2) function with a range of donor separations, (3) provide an~5 orders of magnitude J-tunability within a modest E-field range of~3 MV/m and lowered 'Off' state exchange and (4) mitigate th...

Valley Filtering in Spatial Maps of Coupling between Silicon Donors and Quantum Dots

“…Tunneling and exchange in a coupled donor/QD system differs from two donors [18,19,21,[24][25][26] because the QD is a superposition of ±z valleys only, and the donor is a six-valley superposition as evidenced by latticeaperiodic components in the Fourier transforms of STM tunnel current maps ( Fig. 3c).…”

“…Experimentally measuring these oscillations is difficult since it would require to ability to change the valley phase of the QD wavefunction, or directly measuring < 0.5 meV values of exchange with direct transport, which is not possible in our scheme at 4.2 K . The QD state in the calculation was calibrated so that full configuration interaction (FCI) wavefunctions [26,77] reproduce experimentally measured spectra. A 5 nm STM tip radius was found to reproduce the bias where 0e → 1e and 1e → 2e QD transitions occur, away from the donor.…”

Excited states of defect linear arrays in silicon: A first-principles study based on hydrogen cluster analogs

“…For two electrons in a single donor (D − ), ATB calculations followed by a self-consistent Hartree method were used to account for the electron-electron interaction in a mean-field way, while neglecting exchange [34,35]. A full configurationinteraction (FCI) computation has been performed for D − with single-electron wave functions obtained from the atomistic tight-binding method [36,37].…”

A computational workflow for designing silicon donor qubits

“…Tight-binding (TB) [36,37] and densityfunctional tight binding (DFTB) [38] methods that make use of these approximations are computationally attractive alternatives for electronic structure modeling of silicon donor qubit devices. Whereas TB methods have been used extensively for modeling silicon donor systems [31,32,[39][40][41][42][43], DFTB methods have not yet been extensively applied.…”