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arXiv:2409.00601 · Physical Review A

Geometric two-qubit gates in silicon-based double quantum dots

Yong-Yang Lu, Kejin Wei, Chengxian Zhang

Published Apr 10, 2025• 7 citations
arXivHTMLPDF

Abstract

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-$Z$ (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.

DOI
10.1103/physreva.111.042609

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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.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate cnot, cphase, and cz gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a cnot gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to CNOT\sqrt{\mathrm{CNOT}}CNOT​ and CZ\sqrt{\mathrm{CZ}}CZ​ that are used to implement simple two-piece pulse sequences that produce high-fidelity cnot and cz gates in the presence of low-frequency noise.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a CNOT gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to CNOT\sqrt{CNOT}CNOT​ and CZ\sqrt{CZ}CZ​ that are used to implement simple two-piece pulse sequences that produce high-fidelity CNOT and CZ gates in the presence of low-frequency noise.
Motivated by recent experiments of Zajac et al. [Science 359, 439 (2018)], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, nonadiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.
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.
A two-qubit controlled-not (cnot) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity cnot gates robust against electrical noise with the experimentally measured 1/f1.011/{f}^{1.01}1/f1.01 noise spectrum and also against the uncertainty in the interdot tunnel coupling amplitude. Our fine-tuned optimal cnot gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate constructed without considering any noise effect. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.
Electron spins in silicon quantum dots are a promising platform for fault-tolerant quantum computing. Low-frequency noise, including nuclear spin fluctuations and charge noise, is a primary factor limiting gate fidelities. Suppressing this noise is crucial for high-fidelity qubit operations. Here, we report on a two-qubit quantum device in natural silicon with universal qubit control, designed to investigate the upper limits of gate fidelities in a non-purified Si/SiGe quantum dot device. By employing advanced device structures, qubit manipulation techniques, and optimization methods, we have achieved single-qubit gate fidelities exceeding 99% and a two-qubit controlled-Z (CZ) gate fidelity of 91%. Decoupled CZ gates are used to prepare Bell states with an average fidelity of 91%, typically exceeding previously reported values in natural silicon devices. These results underscore that even natural silicon has the potential to achieve high-fidelity gate operations, particularly with further optimization methods to suppress low-frequency noise.