Significant experimental advances in single-electron silicon spin qubits have opened the possibility of realizing long-range entangling gates mediated by microwave photons. Recently proposed iSWAP gates, however, require tuning qubit energies into re
sonance and have limited fidelity due to charge noise. We present a novel photon-mediated cross-resonance gate that is consistent with realistic experimental capabilities and requires no resonant tuning. Furthermore, we propose gate sequences capable of suppressing errors due to quasistatic noise for both the cross-resonance and iSWAP gates.
The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause complications. He
re, we present a widely applicable method for obtaining smooth pulses which is not based on a sampling approach and does not need any assumptions with regards to the underlying statistics of the experimental noise. We demonstrate the capability of our approach by finding smooth shapes which suppress the effects of noise within the logical subspace as well as leakage out of that subspace.
When a system is thermally coupled to only a small part of a larger bath, statistical fluctuations of the temperature (more precisely, the internal energy) of this sub-bath around the mean temperature defined by the larger bath can become significant
. We show that these temperature fluctuations generally give rise to 1/f-like noise power spectral density from even a single two-level system. We extend these results to a distribution of fluctuators, finding the corresponding modification to the Dutta-Horn relation. Then we consider the specific situation of charge noise in silicon quantum dot qubits and show that recent experimental data [E. J. Connors, et al., Phys. Rev. B 100, 165305 (2019)] can be modeled as arising from as few as two two-level fluctuators, and accounting for sub-bath size improves the quality of the fit.
We theoretically consider a cross-resonance (CR) gate implemented by pulse sequences proposed by Calderon-Vargas & Kestner, Phys. Rev. Lett. 118, 150502 (2017). These sequences mitigate systematic error to first order, but their effectiveness is limi
ted by one-qubit gate imperfections. Using additional microwave control pulses, it is possible to tune the effective CR Hamiltonian into a regime where these sequences operate optimally. This improves the overall feasibility of these sequences by reducing the one-qubit operations required for error correction. We illustrate this by simulating randomized benchmarking for a system of weakly coupled transmons and show that while this novel pulse sequence does not offer an advantage with the current state of the art in transmons, it does improve the scaling of CR gate infidelity with one-qubit gate infidelity.
Addressability of spin qubits in a silicon double quantum dot setup in the (1,1) charge configuration relies on having a large difference between the Zeeman splittings of the electrons. When the difference is not sufficiently large, the rotating wave
approximation becomes inaccurate. We consider a device working in this regime, with always-on exchange coupling, and describe how a CZ gate and arbitrary one-qubit gates which are robust against charge noise can be implemented by smoothly pulsing the microwave source, while eliminating the crosstalk. We find that the most significant deviations from the rotating wave approximation, which are analogous to the Bloch-Siegert shift in a two-level system, can be compensated using local virtual gates.
Achieving high-fidelity control of quantum systems is essential for realization of a practical quantum computer. Composite pulse sequences which suppress different types of errors can be nested to suppress a wide variety of errors but the result is o
ften not optimal, especially in the presence of constraints such as bandwidth limitations. Robust smooth pulse shaping provides flexibility, but obtaining such analytical pulse shapes is a non-trivial problem, and choosing the appropriate parameters typically requires a numerical search in a high-dimensional space. In this work, we extend a previous analytical treatment of robust smooth pulses to allow the determination of pulse parameters without numerical search. We also show that the problem can be reduced to a set of coupled ordinary differential equations which allows for a more streamlined numerical treatment.
Characterizing charge noise is of prime importance to the semiconductor spin qubit community. We analyze the echo amplitude data from a recent experiment [Yoneda et al., Nat. Nanotechnol. 13, 102 (2018)] and note that the data shows small but consist
ent deviations from a $1/f^alpha$ noise power spectrum at the higher frequencies in the measured range. We report the results of using a physical noise model based on two-level fluctuators to fit the data and find that it can mostly explain the deviations. While our results are suggestive rather than conclusive, they provide what may be an early indication of a high-frequency cutoff in the charge noise. The location of this cutoff, where the power spectral density of the noise gradually rolls off from $1/f$ to $1/f^2$, crucial knowledge for designing precise qubit control pulses, is given by our fit of the data to be around 200 kHz.
Recent work on Ising-coupled double-quantum-dot spin qubits in GaAs with voltage-controlled exchange interaction has shown improved two-qubit gate fidelities from the application of oscillating exchange along with a strong magnetic field gradient bet
ween adjacent dots. By examining how noise propagates in the time-evolution operator of the system, we find an optimal set of parameters that provide passive stroboscopic circumvention of errors in two-qubit gates to first order. We predict over 99% two-qubit gate fidelities in the presence of quasistatic and 1/$textit{f}$ noise, which is an order of magnitude improvement over the typical unoptimized implementation.
We theoretically analyze the errors in one- and two-qubit gates in SiMOS and Si/SiGe spin qubit experiments, and present a pulse sequence which can suppress the errors in exchange coupling due to charge noise using ideal local rotations. In practice,
the overall fidelity of the pulse sequence will be limited only by the quality of the single-qubit gates available: the C-phase infidelity comes out to be $approx 2.5 times$ the infidelity of the single-qubit operations. Based on experimental data, we model the errors and show that C-phase gate infidelities can be suppressed by two orders in magnitude. Our pulse sequence is simple and we expect an experimental implementation would be relatively straightforward. We also evaluate the performance of this gate against $1/f$ noise. Assuming a soft ultraviolet cutoff, we show that the pulse sequence designed for quasistatic noise still performs well when the cutoff occurs below $sim 1$MHz given fast enough one-qubit Rabi frequencies, suppressing the infidelity by an order of magnitude compared to the existing direct adiabatic protocol. We also analyze the effects of nonadiabaticity during finite rise periods, and find that adiabaticity is not a limitation for the current values of exchange coupling.
We develop a systematic method of performing corrected gate operations on an array of exchange-coupled singlet-triplet qubits in the presence of both fluctuating nuclear Overhauser field gradients and charge noise. The single-qubit control sequences
we present have a simple form, are relatively short, and form the building blocks of a corrected CNOT gate when also implemented on the inter-qubit exchange link. This is a key step towards enabling large-scale quantum computation in a semiconductor-based architecture by facilitating error reduction below the quantum error correction threshold for both single-qubit and multi-qubit gate operations.
