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arXiv:2603.04773 · Physical Review Applied

Robust composite two-qubit gates for silicon-based spin qubits

Yang-Yang Yu, Guang-Hui Zhang, Yan-Jie He, Jun Wu, Xue-Ke Song, Dong Wang

quant-phSubmitted Mar 5, 2026• Announced Mar 6, 2026• 0 citations
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Abstract

We propose a universal approach based on Hamiltonian inverse engineering to realize a set of parameterized two-qubit gates. This method possesses unique advantages to simultaneous control of transitions among four energy levels, providing a simpler and effective way to construct composite two-qubit gates with fewer operations than traditional methods. Applied to silicon double quantum dots (DQDs), one can realize a one-step fSim gate and a B gate with only one pulse switch. Of note, the method can be further integrated with various optimization theories to enhance gate performance. Based on quantum optimal control theory, we develop a high-fidelity fSim gate scheme with experimentally feasible pulse shapes, featuring an average gate time of 50 ns and a theoretical fidelity of 99.95% in the presence of decoherence and approximation error. By incorporating geometric quantum gate principles, we propose a combined geometric and dynamic fSim gate scheme. Numerical simulations demonstrate that this hybrid scheme exhibits stronger robustness against systematic errors compared to the purely dynamic approach. Our method is generalizable to arbitrary two-qubit physical systems, offering a feasible pathway for rapidly and robustly constructing composite two-qubit gates.

Journal reference
Physical Review Applied 25, 024076 (2026)
DOI
10.1103/t8xj-6c5m
Comments
17 pages, 9 figures

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We propose a universal approach based on Hamiltonian inverse engineering to realize a set of parameterized two-qubit gates. This method possesses unique advantages to simultaneous control of transitions among four energy levels, providing a simpler and effective way to construct composite two-qubit gates with fewer operations than traditional methods. Applied to silicon double quantum dots (DQDs), one can realize a one-step fSim gate and a B gate with only one pulse switch. Of note, the method can be further integrated with various optimization theories to enhance gate performance. Based on quantum optimal control theory, we develop a high-fidelity fSim gate scheme with experimentally feasible pulse shapes, featuring an average gate time of 50 ns and a theoretical fidelity of 99.95% in the presence of decoherence and approximation error. By incorporating geometric quantum gate principles, we propose a combined geometric and dynamic fSim gate scheme. Numerical simulations demonstrate that this hybrid scheme exhibits stronger robustness against systematic errors compared to the purely dynamic approach. Our method is generalizable to arbitrary two-qubit physical systems, offering a feasible pathway for rapidly and robustly constructing composite two-qubit gates.
Achieving high-fidelity two-qubit gates is crucial for spin qubits in silicon-based double quantum dots. However, these gates are sensitive to charge noise in experimental settings, which remains a significant challenge. Geometric gates, which utilize pure geometric phases for gate operations, are a promising approach to achieving robust control. In this work, we theoretically propose a feasible strategy to implement geometric two-qubit gates for silicon-based spin qubits considering experimental control environments. By operating in the suitable region where the local magnetic field gradient is significantly larger than the exchange interaction, we can implement both entangling and nonentangling geometric gates through analytical and numerical methods. It is found that the geometric gates obtained are highly compatible with existing experimental techniques using electric dipole spin resonance in silicon. Moreover, the implemented geometric controlled-ZZZ (CZ) gates can achieve fidelities exceeding 99% under experimental noise levels and the gate times are as short as 20 ns. Our work paves the way for the realization of high-fidelity geometric two-qubit gates for spin qubits in silicon.
Abstract Robust two-qubit gates are essential for scalable silicon spin qubits, but their fidelities are limited by microwave-control imperfections and charge-noise-induced exchange fluctuations. We propose a practical scheme for robust controlled-Z (CZ) and controlled-NOT (CNOT) gates in a silicon double quantum dot. By applying a transverse microwave drive, the effective Hamiltonian can be decomposed into two driven subspaces. In the subspace mainly controlled by the microwave field, a Broadband 1 (BB1) composite pulse is used to suppress errors in the microwave amplitude. In the exchange-assisted subspace, the microwave phases and durations are kept fixed, while a few piecewise-constant exchange amplitudes are optimized by a GRAPE-like procedure. This design reduces the sensitivity to both microwave-amplitude and exchange-amplitude errors while keeping the control waveform simple and experimentally friendly. Numerical simulations show that the optimized CNOT gate reaches a fidelity above 99.99% under experimentally relevant noise strengths, and the CZ gate also maintains a fidelity above 99.9%. These results indicate that combining composite pulses with optimized exchange control provides an experimentally feasible route to robust two-qubit gates in silicon spin qubits.
Due to its fast and robust characteristics, nonadiabatic geometric quantum computation with various optimized techniques has received much attention. However, these strategies either require precise pulse control or can only mitigate partial systematic errors, hindering their experimental development. Here, we propose a scheme for optimized composite nonadiabatic geometric quantum gates (OCNGQGs), which can further enhance the gate performance of the composite nonadiabatic geometric scheme. Specifically, by optimizing the path parameter, our scheme effectively resists systematic errors in both directions, i.e., Rabi frequency and detuning errors, while preserving the flexibility of pulse shapes. Numerical simulations demonstrate that our scheme offers superior gate robustness against these two types of errors compared to conventional schemes. Additionally, we propose to implement our scheme on superconducting transmon qubits, where the numerical results show the robustness of universal gates remaining evident within current technology. Therefore, our proposal provides a promising approach to achieve robust quantum gates for future scalable quantum computation.
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions among multiple levels or qubits and a longer gate time than the corresponding dynamical ones. Here, we propose a general framework of geometric quantum computation with the integration of the time-optimal control technique, where the shortest smooth geometric path is found to realize accelerated geometric quantum gates and thus greatly decreases the gate errors induced by both the decoherence effect and operational imperfections. Meanwhile, we faithfully implement our idea on a scalable platform of a two-dimensional superconducting transmon-qubit lattice, with simple and experimentally accessible interactions. In addition, numerical simulations show that our implemented geometric gates possess higher fidelities and stronger robustness, which outperform the best performance of the corresponding dynamical ones. Therefore, our scheme provides a promising alternative route toward scalable fault-tolerant solid-state quantum computation.
Silicon-based donor flip-flop qubits offer a promising path toward scalable, fault-tolerant quantum computing by combining the long coherence times of nuclear spins with fast, fully electrical control and long-range dipole-dipole coupling between qubits. However, realizing high-fidelity entangling operations in this platform remains challenging. The entangling interaction is intrinsically coupled to electron orbital dynamics, which can lead to leakage into non-computational states and unwanted phase accumulation. Furthermore, in multi-qubit architectures, residual dipolar couplings from spectator qubits distort the effective interaction landscape. In this work, we employ a numerical simulation framework, FlipFlopQSim, that models the spin-orbital dynamics of interacting flip-flop qubits to extract effective logical operations from realistic electrical control pulses. Using Makhlin invariants, we map the entangling landscape generated by electrically controlled dipole-dipole interactions and identify operating regions locally equivalent to canonical two-qubit gates, such as iSWAP\sqrt{iSWAP}iSWAP​ and iSWAPiSWAPiSWAP. We then optimize the control parameters of physically realizable, electrically driven RzR_zRz​ rotations to implement the necessary local corrections and maximize composite gate fidelity. Finally, we scale our analysis to multi-qubit registers with various geometries and connectivity patterns to evaluate spectator-induced distortions. Our results demonstrate that high-fidelity entangling operations cannot be optimized in isolation; rather, they require a co-design approach that simultaneously optimizes pulse control, local phase compensation, and physical device geometry. This work provides a robust numerical framework for assessing the scalability of electrically controlled silicon quantum processors and outlines key design principles for robust multi-qubit gate implementation.
Multiple-qubit quantum logic gates are an important element in the implementation of quantum computers. The direct construction of multiple-qubit quantum logic gates in an efficient way has important values compared to the construction of multiple-qubit gates using a series of two-qubit and single-qubit gates. We propose a scheme to construct a multiple-qubit CkU{\mathrm{C}}_{k}\mathrm{U}Ck​U gate (kkk denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.