Universal robust quantum control is essential for large-scale quantum computation. The geometric phase, as a key element with intrinsic error-resilient features, can be well integrated into a quantum control process to enhance control robustness. However, due to the inability to optionally avoid some trajectory segments seriously affected by systematic errors, the robust universality of current geometric quantum control based on some special geometric evolution trajectories is still lacking, resulting in unsatisfactory performance of arbitrary geometric gate. Here, we propose another scheme for universal robust geometric control based on geometric trajectory correction, where enough available evolution parameters are introduced, without more experimental demands, to ensure the effective reduction of sensitivity to systematic errors. Numerical simulation shows that our implemented arbitrary geometric gates have error-resilient features better than conventional ones. In addition, we also verify the feasibility of the high-fidelity physical implementation of our scheme on superconducting quantum circuits. Therefore, our theoretical work is expected to offer an attractive avenue for realizing practical quantum computation in existing experimental platforms.
Universal robust quantum control is essential for large-scale quantum computation. The geometric phase, as a key element with intrinsic error-resilient features, can be well integrated into a quantum control process to enhance control robustness. However, due to the inability to optionally avoid some trajectory segments seriously affected by systematic errors, the robust universality of current geometric quantum control based on some special geometric evolution trajectories is still lacking, resulting in unsatisfactory performance of arbitrary geometric gate. Here, we propose another scheme for universal robust geometric control based on geometric trajectory correction, where enough available evolution parameters are introduced, without more experimental demands, to ensure the effective reduction of sensitivity to systematic errors. Numerical simulation shows that our implemented arbitrary geometric gates have error-resilient features better than conventional ones. In addition, we also verify the feasibility of the high-fidelity physical implementation of our scheme on superconducting quantum circuits. Therefore, our theoretical work is expected to offer an attractive avenue for realizing practical quantum computation in existing experimental platforms.
A nonadiabatic geometric quantum gate is realized by integrating nonadiabatic geometric phases with global geometric features into the unitary quantum control, thereby removing the limitation of a long evolution time in the adiabatic case. However, systematic errors are inevitable in practical quantum control; these lead to the deviation of the evolution from target conditions to inducing geometric phases, smearing the robustness of the induced geometric quantum gates. Here, we present a general theoretical framework with enhanced robustness for geometric quantum gates by preserving fundamental geometric conditions. We first analytically evaluate the influence of systematic errors on geometric gates and then propose an optimized approach to mitigate this influence. Numerical simulations indicate that, as the geometric conditions are still maintained in the presence of systematic errors in our scheme, the constructed geometric quantum gates exhibit strong robustness, far superior to that of conventional schemes. Furthermore, we propose implementing the scheme in superconducting quantum circuits, where geometric quantum gates can achieve high fidelity with current experimental parameters. Therefore, the enhanced gate performance highlights the promise of our scheme for large-scale quantum computations.
Recently, nonadiabatic geometric quantum computation has received much attention due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and special evolution paths have been proposed, which usually require longer gate-time and more operational steps, and thus lead to lower quality of the implemented quantum gates. Here, we present an effective scheme to find the shortest geometric path under conventional conditions of geometric quantum computation, where high-fidelity and robust geometric gates can be realized by only single-loop evolution, and the gate performances are better than the corresponding dynamical ones. Furthermore, we can optimize the pulse shapes in our scheme to further shorten the gate-time, which is determined by how fast the path is traveled. In addition, we also present its physical implementation on superconducting circuits, consisting of capacitively coupled transmon qubits, where fidelities of geometric single- and two-qubit gates can be higher than 99.95% and 99.80% within the current state-of-the-art experimental technologies, respectively. These results indicate that our scheme is promising for large-scale fault-tolerant quantum computation.
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherent error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls, especially for logical qubits that involve more physical qubits, whose error tolerance is effective in principle, but their experimental demonstration is still demanding. Thus, how to best simplify the needed control and manifest its full advantage has become the key to widespread applications of geometric quantum computation. Here we propose a fast and robust geometric scheme, with decoherence-free subspace encoding, and present its physical implementation on superconducting quantum circuits, where we only utilize the experimentally demonstrated parametrically tunable coupling to achieve high-fidelity geometric control over logical qubits. Numerical simulation verifies that it can efficiently combine the error tolerance from both the geometric phase and logical-qubit encoding, displaying our gate-performance superiority over the conventional dynamical one without encoding, in terms of both gate fidelity and robustness. Therefore, our scheme can consolidate both error suppression methods for logical-qubit control, which sheds light on the future large-scale quantum computation.
Quantum manipulation based on geometric phases provides a promising way towards robust quantum gates. However, in the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions that induce geometric phases, thereby smearing their noise-resilient feature. In a recent experiment [Y. Xu et al., Phys. Rev. Lett. 124, 230503 (2020)], high-fidelity universal geometric quantum gates have been implemented in a superconducting circuit, which are robust to different types of errors under different configurations of the geometric evolution paths. Here, we apply the path-design strategy to explain in detail why both configurations can realize universal quantum gates in a single-loop way. Meanwhile, we purposefully induce our geometric manipulation by selecting the path configuration that is robust against the qubit-frequency-drift-induced error, which is the dominant error source on realistic superconducting circuits and has not been deliberately addressed. Moreover, our proposal can further integrate with the composite scheme to enhance the gate robustness, which is verified by numerical simulations. Therefore, our scheme provides a promising way towards practical realization of high-fidelity and robust nonadiabatic geometric quantum gates.
High-fidelity quantum gates are an essential prerequisite for large-scale quantum computation. When manipulating practical quantum systems, environmentally and operationally induced errors are inevitable, and thus, in addition to being fast, it is preferable that operations should be intrinsically robust against different errors. Here, we propose a general protocol for constructing geometric quantum gates with on-demand trajectories by modulating the applied pulse shapes that define the system's evolution trajectory. Our scheme adopts reverse engineering of the target Hamiltonian using smooth pulses, which also eliminates the difficulty of calculating geometric phases for an arbitrary trajectory. Furthermore, because a particular geometric gate can be induced by various different trajectories, we can further optimize the gate performance under different scenarios; the results of numerical simulations indicate that this optimization can greatly enhance the quality of the gate. In addition, we present an implementation of our proposal using superconducting circuits, showcasing substantial enhancements in gate performance compared with conventional schemes. Our protocol thus presents a promising approach for high-fidelity and strong-robust geometric quantum gates for large-scale quantum computation.
Nonadiabatic holonomic quantum computation (NHQC) based on non-Abelian geometric phases can possess potential robustness advantages due to its intrinsic error-resilient features. However, rigorous geometric conditions, including cyclic evolution and parallel transport conditions, typically demand complex and error-prone control and also involve additional auxiliary resources. Moreover, the limitations of optional evolution paths in previous NHQC schemes make it difficult to avoid path segments that are heavily affected by systematic errors, thereby weakening the error resilience of holonomic gates. To address this problem, we propose a multipath NHQC scheme, which can sufficiently improve the robustness of quantum gates by flexibly correcting geometric evolution paths. Numerical simulation results show that our scheme surpasses previous NHQC schemes in suppressing systematic errors for arbitrary gate types. In addition, we provide a physical implementation based on superconducting quantum circuits, with the decoherence-free-subspace encoding and an experiment-friendly two-body exchange interaction, demonstrating the excellent compatibility of our scheme. Therefore, our scheme offers a promising alternative for future fault-tolerant quantum computation.