Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency non-Markovian noise) and show theoretically that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.One well-established possibility to realize a qubit with electron spins in a semiconductor is to use the m s = 0 spin singlet and triplet states of two electrons as computational basis states [1]. In contrast to single electron spins this encoding allows for all-electrical qubit control. Very long coherence times of up to 200 µs [2], all aspects of single-qubit operation (e.g. initialization [3] and single-shot readout [4]) and a first two-qubit gate [5] have been demonstrated experimentally for such singlettriplet (ST) qubits in GaAs quantum dots. Universal single-qubit control was also shown [6] but subject to large uncharacterized errors. Limiting control error rates to ∼ 10 −3 is a crucial requirement for fault tolerant quantum computing with quantum error correction (QEC) [7][8][9]. Estimates based on coherence time measurements [2,10] indicate that very high gate fidelities should be possible for GaAs-based two-electron spin qubits. However, nonlinearities in the electric control and experimental constraints make the direct application of control methods such as Rabi driving difficult.Previous theoretical work has shown how universal control on the single-and two-qubit level can be achieved in the face of limited dynamic control range [11]. Additionally, gating sequences which are insensitive to slow (quasistatic) control fluctuations have been proposed for this qubit system [12][13][14][15]. While these proposals provide very useful conceptual guidance, a direct implementation will be impeded by experimental constraints such as finite pulse rise times and sampling rate of voltage pulses. Likewise, decoherence effects caused by charge noise [10] and nuclear spin fluctuations [16] have a significant effect.In this letter we use numerical pulse optimization to address the problems posed by systematic inaccuracies and decoherence. Pulse optimization is common in NMR [17] and is also receiving increasing attention in quantum information [12,[18][19][20][21][22][23][24]. In contrast to these previous approaches, our optimization is specifically tailored to the ST-qubit system and includes not only the relevant physical effects but also the most important hardware constraints and the effect of high-frequency nonMarkovian noise. We use experimentally determined parameters and noise spectra [10,16,25] to compute expected gate fidelities and find implementations with no systematic errors and optimized robustness to both slow and fas...

Semiconductor spin qubits have recently seen major advances in coherence time and control fidelities, leading to a single-qubit performance that is on par with other leading qubit platforms. Most of this progress is based on microwave control of single spins in devices made of isotopically purified silicon. For controlling spins, the exchange interaction is an additional key ingredient which poses new challenges for high-fidelity control. Here, we demonstrate exchange-based single-qubit gates of two-electron spin qubits in GaAs double quantum dots. Using careful pulse optimization and closed-loop tuning, we achieve a randomized benchmarking fidelity of (99.50±0.04)% and a leakage rate of 0.13% out of the computational subspace. These results open new perspectives for microwave-free control of singlet-triplet qubits in GaAs and other materials.

Understanding the decoherence of electron spins in semiconductors due to their interaction with nuclear spins is of fundamental interest as they realize the central spin model and of practical importance for using them as qubits. Interesting effects arise from the quadrupolar interaction of nuclear spins with electric field gradients, which have been shown to suppress diffusive nuclear spin dynamics and might thus enhance electron spin coherence. Here we show experimentally that for gate-defined GaAs quantum dots, quadrupolar broadening of the nuclear Larmor precession reduces electron spin coherence by causing faster decorrelation of transverse nuclear fields. However, this effect disappears for appropriate field directions. Furthermore, we observe an additional modulation of coherence attributed to an anisotropic electronic g-tensor. These results complete our understanding of dephasing in gated quantum dots and point to mitigation strategies. They may also help to unravel unexplained behaviour in self-assembled quantum dots and III–V nanowires.