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Machine Learning Science and Technology

Robust high-fidelity three-qubit gates design for superconducting quantum computers via model-free reinforcement learning

Xinxin Zhu, Yangyang Fei, Liu FuDong, Zheng Shan

Published Oct 1, 2026• 0 citations
Publisher

Abstract

Abstract Multi-qubit gates are crucial to realizing quantum algorithms. Direct implementation of these gates will facilitate a reduction in circuit depth. However, existing model-based methods rely on precise characterization of the system Hamiltonian as well as execution of the control fields, which present challenges in obtaining high fidelity multi-qubit gates. In this paper, we exploit the bang–bang control protocol and model-free reinforcement learning to realize several kinds of three-qubit gates for superconducting quantum computers with tunable/fixed frequency qubits, including the iToffoli gate, the parity check gate and the CCZ gate. The simulation results show that the fidelity of each gate can achieve 99.2% with the Adam gradient descent optimizer. Moreover, the proposed method is robust against random noise in the control pulse. Gate fidelity can be maintained over 95% even in the case of Gaussian noise with variance of 0.3. Besides, the impacts of parameter iterative optimization strategies are also analyzed.

DOI
10.1088/2632-2153/aeb481

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Abstract Multi-qubit gates are crucial to realizing quantum algorithms. Direct implementation of these gates will facilitate a reduction in circuit depth. However, existing model-based methods rely on precise characterization of the system Hamiltonian as well as execution of the control fields, which present challenges in obtaining high fidelity multi-qubit gates. In this paper, we exploit the bang–bang control protocol and model-free reinforcement learning to realize several kinds of three-qubit gates for superconducting quantum computers with tunable/fixed frequency qubits, including the iToffoli gate, the parity check gate and the CCZ gate. The simulation results show that the fidelity of each gate can achieve 99.2% with the Adam gradient descent optimizer. Moreover, the proposed method is robust against random noise in the control pulse. Gate fidelity can be maintained over 95% even in the case of Gaussian noise with variance of 0.3. Besides, the impacts of parameter iterative optimization strategies are also analyzed.
Three-qubit gates can be constructed using combinations of single-qubit and two-qubit gates, making their independent realization unnecessary. However, direct implementation of three-qubit gates reduces the depth of quantum circuits, streamlines quantum programming, and facilitates efficient circuit optimization, thereby enhancing overall performance in quantum computation. In this work, we propose and experimentally demonstrate a high-fidelity scheme for implementing a three-qubit controlled-controlled-z (ccz) gate in a flip-chip superconducting quantum processor with tunable couplers. This direct ccz gate is implemented by simultaneously leveraging two tunable couplers interspersed between three qubits to enable three-qubit interactions, achieving an average final state fidelity of 97.94% and a process fidelity of 93.54%. This high fidelity cannot be achieved through a simple combination of single- and two-qubit gate sequences from processors with similar performance levels. Our experiments also verify that multilayer direct implementation of the ccz gate exhibits lower leakage compared to decomposed gate approaches. As a showcase, we utilize the ccz gate as an oracle to implement the Grover search algorithm on three qubits, demonstrating high performance with the target probability amplitude significantly enhanced after two iterations. These results highlight the advantage of our approach, and facilitate the implementation of complex quantum circuits.
The development of noisy intermediate-scale quantum (NISQ) devices has extended the scope of executable quantum circuits with high-fidelity single- and two-qubit gates. Equipping NISQ devices with three-qubit gates will enable the realization of more complex quantum algorithms and efficient quantum error correction protocols with reduced circuit depth. Several three-qubit gates have been implemented for superconducting qubits, but their use in gate synthesis has been limited due to their low fidelity. Here, using fixed-frequency superconducting qubits, we demonstrate a high-fidelity iToffoli gate based on two-qubit interactions, the so-called cross-resonance effect. As with the Toffoli gate, this three-qubit gate can be used to perform universal quantum computation. The iToffoli gate is implemented by simultaneously applying microwave pulses to a linear chain of three qubits, revealing a process fidelity as high as 98.26(2)%. Moreover, we numerically show that our gate scheme can produce additional three-qubit gates which provide more efficient gate synthesis than the Toffoli and Toffoli gates. Our work not only brings a high-fidelity iToffoli gate to current superconducting quantum processors but also opens a pathway for developing multi-qubit gates based on two-qubit interactions.
Abstract The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence begin to dominate, limiting algorithmic complexity. An alternative approach is to explore gates involving more than two qubits. In previous work (X. Wu et al., Physical Review X 14, 041030 (2024)), we demonstrated a new superconducting qubit architecture with user-selectable two-qubit interactions via a reconfigurable router, used to connect pairs of qubits. Here, we leverage this novel architecture to realize programmable and efficient multi-qubit operations involving more than two qubits, resulting in faster preparation of multi-qubit entangled states with good fidelities. We also successfully apply model-free reinforcement learning to perform multi-qubit gates, including training a two-qubit controlled-Z gate as well as three-qubit controlled-SWAP and controlled-controlled-phase (Fredkin and Toffoli) gates. Higher nnnth-order gates may also be feasible, using our high-connectivity router design. This could provide a more efficient and higher-fidelity implementation of complex quantum algorithms and a more practical approach to quantum computation.
Higher-dimensional quantum systems, such as qudits, offer architectural and algorithmic advantages over qubits, but their increased spectral crowding and limited controllability render high-fidelity quantum gates particularly challenging. We propose a hybrid optimization framework that integrates optimal control theory methods with contextual deep reinforcement learning to achieve robust controlled-phase gates on two qutrits. Optimal control is first used to design high-fidelity control pulses for a nominal system model. Reinforcement learning is then employed as a calibration stage that learns small residual corrections to these pulses in the presence of static model mismatch, thereby preserving good gate performance under realistic parameter uncertainties. By learning structured, low-dimensional residual corrections conditioned on device-specific parameter variations, reinforcement learning enhances the transfer robustness of nominally optimal but parameter-sensitive control solutions across ensembles of devices. Crucially, the reinforcement learning step in our framework does not compete with the optimal control step but provides the adaptability required for realistic hardware, systematically reducing the sensitivity to parameter fluctuations. Our results establish reinforcement learning as a practical and scalable ingredient for robust calibration of quantum gates in high-dimensional systems.
Fast quantum gates are crucial not only for the contemporary era of noisy intermediate-scale quantum devices but also for the prospective development of practical fault-tolerant quantum computing. Leakage errors, which arise from data qubits jumping beyond the confines of the computational subspace, are the main challenges in realizing nonadiabatically driven, fast gates. In this work, we propose and illustrate the usefulness of reinforcement learning (RL) to generate fast two-qubit gates in practical multilevel superconducting qubits. In particular, we show that the RL controller offers great effectiveness in finding piecewise constant gate-pulse sequences that act on two transmon data qubits coupled by a tunable coupler to generate a controlled-ZZZ (cz) gate with a gate time of 10 ns and an error rate of approximately $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. Using a gradient-based method to solve the same optimization problem often does not achieve high fidelity for such fast gates. However, we show that using the gate pulses discovered by RL as an ansatz for the gradient-based controller can substantially enhance fidelity compared to using RL alone. While for a 10-ns pulse, this improvement is marginal, the combined RL + gradient approach decreases the gate errors below ${10}^{\ensuremath{-}4}$ for a gate of length 20 ns.