Spin qubit in silicon quantum dots is a promising platform to achieve large scale quantum computation due to its small feature size and mature techniques already existing in the semiconductor industry. To perform useful computation, one needs to implement the surface code, which requires qubits with an error rate below surface code threshold 1% [1]. Currently spin qubit in Si/SiGe has achieved high fidelity single- [2] and twoqubit gates [3] with error rate below this error threshold. We now want to further explore the possibility to further improve two-qubit gate fidelities.

The device used is a linear quantum dot array defined in isotopically enriched silicon/silicon-germanium heterostructure. A few metrics of this device are the Rabi oscillation coherence time $T_{2}^{Rabi} \sim 50 $ $\mu$s, spin coherence time $T^{*}_{2} \sim 7 $ $\mu$s, randomized benchmarking (RB) fidelities $F_{2Q,unc} \sim 99.8\% $ for single-qubit unconditional gates and $F_{CNOT} \sim 99.5\% $ for two-qubit $CNOT$ gate [3]. Since both the unconditional single-qubit gates and two-qubit gates are implemented with same physical pulses, we believe we could increase two-qubit gate fidelity to a higher value of $F_{CNOT}\sim F_{2Q,unc} \sim 99.8\%$.

To do this we will need more knowledge on noise source which reduce the two-qubit gate fidelity. Gate set tomography (GST), which gives a detailed report on gate errors [4], is used to obtain a full report on twoqubit gate errors. A set of error generators which represent different error processes and the associated error strengths is returned by GST [5]. By comparing simulated two-qubit gates with the GST measured errors we can pinpoint control parameters that is causing errors. After narrowing down the contributing control parameters, calibration or optimization experiment can be designed and improve gate fidelities. For example, if the main contributing error is over- or under-rotation of the gates, we could perform calibration sequence on gate pulse amplitude to yield best sequence fidelity. If the error is not due to a single parameter but a set of parameters instead, we could use optimization algorithm such as Nelder-Mead algorithm to search over the parameter space and obtain an optimized parameter set which gives the best gate fidelity.

References

[1] A. G. Fowler, A. C. Whiteside, and L. C. L. Hollenberg, Phys. Rev. Lett. 108, 180501 (2012).

[2] K. Takeda, J. Kamioka, T. Otsuka, et. al., Science Advances, vol. 2, p. e1600694 (2016)

[3] A. Noiri, K. Takeda, T. Nakajima, T. et al., Nature 601, 338–342 (2022)

[4] Blume-Kohout, R., Gamble, J., Nielsen, E. et al., Nat Commun 8, 14485 (2017).

[5] Robin Blume-Kohout, Marcus P. da Silva, et. al., PRX Quantum 3, 020335 (2022)