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arXiv:1806.01262 · Physical review. B./Physical review. B

Pulse sequence designed for robust C -phase gates in SiMOS and Si/SiGe double quantum dots

Utkan Güngördü, J. P. Kestner

Published Oct 1, 2018• 20 citations
arXivHTMLPDF

Abstract

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 $\ensuremath{\approx}2.5\ifmmode\times\else\texttimes\fi{}$ 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 $\ensuremath{\sim}1$ MHz with experimentally achievable 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.

DOI
10.1103/physrevb.98.165301

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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 CCC-phase infidelity comes out to be \ensuremath≈2.5\ifmmode×\else\texttimes\fi\ensuremath{\approx}2.5\ifmmode\times\else\texttimes\fi{}\ensuremath≈2.5\ifmmode×\else\texttimes\fi the infidelity of the single-qubit operations. Based on experimental data, we model the errors and show that CCC-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/f1/f1/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 \ensuremath∼1\ensuremath{\sim}1\ensuremath∼1 MHz with experimentally achievable 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.
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We present composite pulse sequences that perform fault-tolerant two-qubit gate operations on exchange-only quantum-dot spin qubits in various experimentally relevant geometries. We show how to perform dynamically corrected two-qubit gates in exchange-only systems with the leading hyperfine error term canceled. These pulse sequences are constructed to conform to the realistic experimental constraint of strictly non-negative couplings. We establish that our proposed pulse sequences lead to several orders of magnitude improvement in the gate fidelity compared with their uncorrected counterparts. Together with single-qubit dynamically corrected gates, our results enable noise-resistant universal quantum operations with exchange-only qubits.
We present a scheme for correcting for crosstalk- and noise-induced errors in exchange-coupled singlet-triplet semiconductor double quantum dot qubits. While exchange coupling allows the coupling strength to be controlled independently of the intraqubit exchange couplings, there is also the problem of leakage, which must be addressed. We show that, if a large magnetic field difference is present between the two qubits, leakage is suppressed. We then develop pulse sequences that correct for crosstalk- and noise-induced errors and present parameters describing them for the 24 Clifford gates. We determine the infidelity for both the uncorrected and corrected gates as a function of the error-inducing terms and show that our corrected pulse sequences reduce the error by several orders of magnitude.
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Motivated by recent experiments of Zajac et al. [Science 359, 439 (2018)], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, nonadiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.
Abstract Robust two-qubit gates are essential for scalable silicon spin qubits, but their fidelities are limited by microwave-control imperfections and charge-noise-induced exchange fluctuations. We propose a practical scheme for robust controlled-Z (CZ) and controlled-NOT (CNOT) gates in a silicon double quantum dot. By applying a transverse microwave drive, the effective Hamiltonian can be decomposed into two driven subspaces. In the subspace mainly controlled by the microwave field, a Broadband 1 (BB1) composite pulse is used to suppress errors in the microwave amplitude. In the exchange-assisted subspace, the microwave phases and durations are kept fixed, while a few piecewise-constant exchange amplitudes are optimized by a GRAPE-like procedure. This design reduces the sensitivity to both microwave-amplitude and exchange-amplitude errors while keeping the control waveform simple and experimentally friendly. Numerical simulations show that the optimized CNOT gate reaches a fidelity above 99.99% under experimentally relevant noise strengths, and the CZ gate also maintains a fidelity above 99.9%. These results indicate that combining composite pulses with optimized exchange control provides an experimentally feasible route to robust two-qubit gates in silicon spin qubits.