Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
High-fidelity quantum gates are crucial for achieving fault-tolerant quantum computing; however, decoherence significantly reduces gate fidelities during long operation times. Although optimal control techniques can theoretically minimize these operation times, they often neglect realistic uncertainties in system parameters. In this work, we demonstrate that by using robust optimal control strategies, the cross-resonance gate in superconducting systems can be operated within 64 ns, achieving fidelities of [Formula: see text] while maintaining robustness against up to 10% uncertainty in a single parameter. Alternatively, by extending the control time to 71 ns, we achieve fidelities of [Formula: see text] with robustness against up to 3% uncertainty. Our results identify the minimal control times attainable with experimentally feasible pulses and system parameters, as well as the maximum allowable static parameter error for high-fidelity operations. Furthermore, we demonstrate simultaneous robustness against both static and time-dependent errors by generating 100 ns control pulses ([Formula: see text]) that maintain robustness against 10% static parameter error and time-dependent parameter fluctuations two orders of magnitude stronger than typical experimental noise. These findings demonstrate a viable open-loop strategy for implementing fast, high-fidelity quantum gates in the presence of realistic system uncertainties that would otherwise degrade conventional control pulses.
Fault-tolerant quantum computing requires quantum gates that combine short duration, high fidelity, and robustness to noise. As quantum processors scale, robustness becomes increasingly important because exhaustive characterization and frequent recalibration of individual gates become impractical. We present a comprehensive optimal-control framework for controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons that systematically accounts for intrinsic Hamiltonian errors and realistic decoherence mechanisms, including energy relaxation and dephasing. Using smooth, single-shot flux pulses, we obtain 12-ns CZ gates---close to the theoretical speed limit of 11.6 ns---with intrinsic errors suppressed to the 2×10−5 level. We construct dephasing noise models, calibrated against published experimental measurements, that capture fast dephasing from room-temperature control electronics and slow dephasing from 1/f flux noise. Using these models, we identify dephasing sweet spots that suppress sensitivity to dephasing noise. We further exploit transmon asymmetry as a design parameter to access distinct noise-resilient operating regimes. These results establish an experimentally applicable framework for balancing gate speed, fidelity, and noise robustness while reducing characterization and recalibration overhead.
Single-qubit gates on superconducting quantum processors are typically implemented using microwave pulses applied through dedicated control lines. However, these microwave pulses may also drive other qubits due to crosstalk arising from capacitive coupling and wavefunction overlap in systems with closely spaced transition frequencies. Crosstalk and frequency crowding increase errors during simultaneous single-qubit operations relative to isolated gates, thus forming a major bottleneck for scaling superconducting quantum processors. In this work, we combine model-based qubit frequency optimization with pulse shaping to demonstrate crosstalk error mitigation in single-qubit gates on a 49-qubit superconducting quantum processor. We introduce and experimentally verify an analytical model of simultaneous single-qubit gate error caused by microwave crosstalk that depends on a given pulse shape. By employing a model-based optimization strategy of qubit frequencies, we minimize the crosstalk-induced error across the processor and achieve a mean simultaneous single-qubit gate fidelity of 99.96% for a 16-ns gate duration, approaching the mean individual gate fidelity. To further reduce the simultaneous error and required qubit frequency bandwidth on high-crosstalk qubit pairs, we introduce a crosstalk transition suppression (CTS) pulse shaping technique that minimizes the spectral energy around transitions inducing leakage and crosstalk errors. Finally, we combine CTS with model-based frequency optimization across the device and experimentally show a systematic reduction in the required qubit frequency bandwidth for high-fidelity simultaneous gates, supported by simulations of systems with up to 1000 qubits. By alleviating constraints on qubit frequency bandwidth for parallel single-qubit operations, this work represents an important step for scaling towards larger quantum processors.
State-of-the-art single-qubit gates on superconducting transmon qubits can achieve the fidelities required for error-corrected computations. However, parameter fluctuations due to qubit instabilities, environmental changes, and control inaccuracies make it difficult to maintain this performance. To mitigate the effects of these parameter variations, we numerically derive gates robust to amplitude and frequency errors using gradient ascent pulse engineering (GRAPE). We analyze how fluctuations in qubit frequency, drive amplitude, and coherence affect gate performance over time. The robust pulses suppress coherent errors from drive amplitude drifts over 15 times more than a Gaussian pulse with derivative removal by adiabatic gate (DRAG) corrections. Furthermore, the robust gates, originally designed to compensate for quasi-static errors, also demonstrate resilience to stochastic, time-dependent noise, which is reflected in the dephasing time. They suppress added errors during increases in dephasing by up to 1.7 times more than DRAG.
Quantum computers store and manipulate information in individual quantized energy levels. These devices, not yet realized in their full potential, have the ability to perform certain computational tasks more efficiently than any classical computer. One possible way to implement a quantum computer is to use superconducting circuits controlled by single-mode electromagnetic fields. These circuits constitute the physical quantum bits, or qubits, that are used to store quantum information. A complete, fault-tolerant quantum computer potentially consists of at least millions of physical qubits which are grouped to form fault-tolerant logical qubits. Controlling each physical qubit individually requires a great amount of energy, and hence a future challenge is to reduce the energy consumption in qubit control while maintaining the high precision. In this thesis, we derive a fundamental upper bound for the gate fidelity of a single-qubit not gate implemented with a single resonant driving pulse. It is shown that the upper bound approaches unity inversely proportionally to the increasing mean photon number of the pulse. Furthermore, we find that the upper bound is achieved with an optimal superposition of squeezed states. The typically employed coherent state produces twice as high gate error as the corresponding optimal state. In addition, we present and numerically study a correction protocol that allows using the same drive state for multiple qubit operations. This sustained state is refreshed by sequentially coupling ancillary qubits to it, effectively resetting it and removing entanglement with the previously operated qubits. Thus our protocol allows using the same drive state to implement not gates for different qubits indefinitely, and hence provides a possible route to energy-efficient large-scale quantum computing.
Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate fidelities and renders full Hilbert-space control optimization prohibitively difficult. Here, we overcome this challenge by reducing the full-system optimization to crosstalk-robust control over constant-sized subsystems, which dramatically reduces the computational cost. Our method effectively eliminates the leading-order gate operation deviations induced by crosstalk, thereby suppressing error rates. Within this framework, we construct analytical pulse solutions for parallel single-qubit gates and numerical pulses for parallel multi-qubit operations. We validate the proposed approach numerically across multiple platforms, including coupled nitrogen-vacancy centers, a nuclear-spin processor, and superconducting-qubit arrays with up to 200 qubits. As a result, the noise scaling is reduced from exponential to linear for parallel single-qubit gates, and an order-of-magnitude reduction is achieved for parallel multi-qubit gates. Moreover, our method does not require precise knowledge of crosstalk strengths and makes no assumption about the underlying qubit connectivity or lattice geometry, thereby establishing a scalable framework for parallel quantum control in large-scale quantum architectures.