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 interqubit 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 multiqubit gate operations.
Fast measurement, signal processing, and accurate estimation of Hamiltonian parameters are essential for feedback control in quantum-classical interface circuitry. However, existing frequentist and Bayesian inference methods typically require a large number of measurements to achieve the accuracy needed to mitigate qubit decoherence. Consequently, feedback control of semiconductor qubits has largely been limited to single-qubit frequency stabilization, whereas two-qubit parameter stabilization remains experimentally unexplored. Here, we demonstrate a real-time feedback framework based on sequential Monte Carlo estimation using one bit of data from a single-shot measurement. Using a four-qubit semiconductor quantum dot device, we rapidly estimate individual qubit frequencies, yielding an approximately twofold increase in coherence time compared with a conventional Bayesian strategy. Moreover, sequential two-qubit parameter estimation using two bits of data enables stabilization of qubit-qubit coupling, allowing both quasi-static frequency drift and exchange-interaction noise to be estimated and suppressed. By shortening the time required for precise parameter estimation, these results demonstrate the importance of the synergistic development of classical and quantum electronics for building robust and scalable quantum technologies in fluctuating environments.
The qubit is the fundamental building block of a quantum computer. We fabricate a qubit in a silicon double-quantum dot with an integrated micromagnet in which the qubit basis states are the singlet state and the spin-zero triplet state of two electrons. Because of the micromagnet, the magnetic field difference ΔB between the two sides of the double dot is large enough to enable the achievement of coherent rotation of the qubit's Bloch vector around two different axes of the Bloch sphere. By measuring the decay of the quantum oscillations, the inhomogeneous spin coherence time T2* is determined. By measuring T2* at many different values of the exchange coupling J and at two different values of ΔB, we provide evidence that the micromagnet does not limit decoherence, with the dominant limits on T2* arising from charge noise and from coupling to nuclear spins.
Singlet-triplet qubits offer an attractive encoding for semiconductor quantum computing, combining ancilla-free readout, reduced sensitivity to common-mode noise, and baseband voltage control. However, the Zeeman energy difference
ΔEZ is typically fixed by local magnetic field gradients or
g-factor inhomogeneities, leaving the exchange interaction
J as the only dynamically tunable parameter. This always-on
ΔEZ precludes orthogonal control of the qubit's rotation axes and introduces unwanted state rotations during idling. Here we demonstrate all-electrical orthogonal control of a degenerate singlet-triplet (DST) qubit formed by two hole spins in a germanium double quantum dot. Exploiting the electrically tunable anisotropic
g-factors of the two spins, we identify a regime where both
ΔEZ and
J vanish, making the
S and
T0 states degenerate at the idle point. By applying only baseband voltage pulses, we independently control both
J and
ΔEZ, enabling fully orthogonal
Z- and
X-axis rotations. Randomized benchmarking yields an average physical single-qubit gate fidelity of 99.53\% for a gate duration of approximately 100 ns. Finally, we electrically tune the degenerate point across a wide range of magnetic field orientations, enabling operation in a regime of enhanced coherence time and offering a route towards multi-qubit scaling under a shared global magnetic field.
Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and materials engineering, quantum error correction and dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in a qubit using real-time Hamiltonian parameter estimation. Using a rapidly converging Bayesian approach, we precisely measure the splitting in a singlet-triplet spin qubit faster than the surrounding nuclear bath fluctuates. We continuously adjust qubit control parameters based on this information, thereby improving the inhomogenously broadened coherence time (T2*) from tens of nanoseconds to >2 μs. Because the technique demonstrated here is compatible with arbitrary qubit operations, it is a natural complement to quantum error correction and can be used to improve the performance of a wide variety of qubits in both meteorological and quantum information processing applications.
We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by decoherence. The real-time processing capabilities of a classical controller dynamically generate adaptive probing sequences for qubit-frequency estimation. Each probing evolution time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. The scheme does not require repeated measurements at the same setting, as it accounts for state preparation and measurement errors. Its use of a parametrized probability distribution favors numerical accuracy and computational speed. We show the efficacy of the algorithm by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. As benchmarked by gate-set tomography, the field-programmable gate array (FPGA) powered control electronics partially mitigates non-Markovian noise, which is detrimental to quantum error correction. The mitigation is achieved by dynamically updating and feeding forward the qubit frequency. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms.