Robust Two-Qubit Gates for Donors in Silicon Controlled by Hyperfine Interactions

Kalra, Rachpon; Laucht, Arne; Hill, Charles D.; Morello, Andrea

doi:10.1103/physrevx.4.021044

Cited by 76 publications

(101 citation statements)

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“…A splitting of 6 MHz could either be caused by a hyperfine-coupled 29 Si on the nearest-neighbor site, 25 or by another 31 P donor, coupled to the donor under measurement by an exchange interaction J ¼ 14 MHz, assuming that the two-electron system is initialized in the j ##i state. 26 An exchange coupling of this magnitude corresponds to an inter-donor separation of $20 nm 27 and is compatible with the expected inter-donor distance from 20 keV P þ 2 molecular implantation. The donor under study is found predominantly in the nuclear j+i state, but other ESR spectra in the nuclear j*i state (data not shown) allowed us to determine the value of the hyperfine coupling A HF ¼ 114.4 MHz.…”

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High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon

et al. 2014

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The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit inversion fidelities for an electron spin qubit bound to a 31 P atom in natural silicon, by applying adiabatic sweeps instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled donor. This work highlights the effectiveness of simple adiabatic inversion techniques for spin control in fluctuating environments. P donor electron 7 and nuclear 8 spins in silicon. In any III-V semiconductor, as well as in natural Si, the fluctuating nuclear spin environment is the main factor limiting spin coherence times 9,10 and, importantly, the fidelity of quantum gate operations, with typical fidelities in the range of 55%-75%. 4,7 This is insufficient for fault-tolerant qubit operations, which require fidelities in excess of 99% even in the most optimistic schemes.11 Group IV semiconductors such as Si and C possess spin-zero nuclear isotopes, which can be artificially enriched to create a nearly spin-free environment for spin qubits. Indeed 28 Si has been termed a "semiconductor vacuum" 12 for this reason. Ensemble spin resonance of 31 P donors in isotopically pure 28 Si has shown extraordinarily long coherence times, T 2e % 10 s for the electron 13 and T 2n % 3 h for the nucleus, 14 and it is certainly an exciting prospect to adopt isotopically pure substrates for nanoscale qubit devices. However, the production of nuclear spin-zero environments in isotopically purified semiconductors other than silicon is relatively undeveloped 15 or impossible because of the lack of suitable isotopes. Therefore, methods to maximize qubit control fidelities in the presence of a nuclear spin environment will remain important.In this Letter, we present how adiabatic frequency sweeps can be utilized to control the spin of an electron bound to a single 31 P donor with high-fidelity, in spite of the fluctuating nuclear spins from the 4.7% 29 Si (spin 1/2) in natural silicon. For an inhomogeneously broadened electron spin resonance (ESR) transition at $36 GHz with a linewidth of $12 MHz, we achieved an average electron spin inversion fidelity as high as F I ¼ 97 6 2%, insensitive to fluctuations of the background nuclear field. The method of adiabatic passage has been widely applied in nuclear magnetic resonance 16 and to some extent also in ESR. 17 Recent progress in high-frequency electronics and the very active research field of spin-based quantum computation have reignited the interest in this topic, with applications as ultra-wideband inversion, 18 geometric phase gates, 19 and even the inversion of single electron spins in diamond. 20,21 Our single qubit, however, is operated at much higher frequencies (36 GHz in the present work) t...

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High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon

et al. 2014

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“…This design can also benefit from improved addressability 2 and longer T 1 times, 3 and can be used in conjunction with the two-qubit scheme proposed in ref. 11. This design can therefore overcome some of the experimental obstacles for realising a two-qubit gate in silicon.…”

Section: Introductionmentioning

confidence: 99%

Highly tunable exchange in donor qubits in silicon

et al. 2016

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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...

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“…More recently, scalable architectures have been proposed to extend single qubit control techniques to larger structures [12,13].…”

Section: Introductionmentioning

confidence: 99%

Hyperfine Stark effect of shallow donors in silicon

et al. 2014

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We present a complete theoretical treatment of Stark effects in bulk doped silicon, whose predictions are supported by experimental measurements. A multi-valley effective mass theory, dealing non-perturbatively with valley-orbit interactions induced by a donor-dependent central cell potential, allows us to obtain a very reliable picture of the donor wave function within a relatively simple framework. Variational optimization of the 1s donor binding energies calculated with a new trial wave function, in a pseudopotential with two fitting parameters, allows an accurate match of the experimentally determined donor energy levels, while the correct limiting behavior for the electronic density, both close to and far from each impurity nucleus, is captured by fitting the measured contact hyperfine coupling between the donor nuclear and electron spin.We go on to include an external uniform electric field in order to model Stark physics: With no extra ad hoc parameters, variational minimization of the complete donor ground energy allows a quantitative description of the field-induced reduction of electronic density at each impurity nucleus. Detailed comparisons with experimental values for the shifts of the contact hyperfine coupling reveal very close agreement for all the donors measured (P, As, Sb and Bi). Finally, we estimate field ionization thresholds for the donor ground states, thus setting upper limits to the gate manipulation times for single qubit operations in Kane-like architectures: the Si:Bi system is shown to allow for A gates as fast as ≈10 MHz.

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Robust Two-Qubit Gates for Donors in Silicon Controlled by Hyperfine Interactions

Cited by 76 publications

References 53 publications

High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon

High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon

Highly tunable exchange in donor qubits in silicon

Hyperfine Stark effect of shallow donors in silicon

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Robust Two-Qubit Gates for Donors in Silicon Controlled by Hyperfine Interactions

Cited by 76 publications

References 53 publications

High-fidelity adiabatic inversion of a 31P electron spin qubit in natural silicon

High-fidelity adiabatic inversion of a 31P electron spin qubit in natural silicon

Highly tunable exchange in donor qubits in silicon

Hyperfine Stark effect of shallow donors in silicon

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High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon

High-fidelity adiabatic inversion of a ³¹P electron spin qubit in natural silicon