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Chinese Physics B

An SOT-switchable micromagnet scheme of adiabatic geometric gates for silicon spin qubits

Fang-Ge 方阁 Li 李, Ran-Ran 冉冉 Cai 蔡, Bao‐Chuan Wang, Hai-Ou Li, Gang Cao, Guo‐Ping Guo

Published May 26, 2025• 0 citations
Publisher

Abstract

Abstract Geometric phase gates have attracted considerable attention due to their intrinsic robustness against certain types of noise. Significant progress has been achieved in implementing geometric phase gates using microwave control in silicon-based electron spin systems. In this work, we propose an alternative geometric phase gate protocol that differs fundamentally from microwave driving approaches by leveraging square-wave control of rapidly switchable micromagnets driven by spin–orbit torque (SOT) to achieve fast and precise magnetic field modulation. By employing square-wave currents to control magnetization switching, our approach relaxes the requirements on waveform precision while significantly suppressing crosstalk. Moreover, our scheme inherently preserves trajectory closure at the end of each operation, effectively mitigating noise-induced path deviation and enhancing gate robustness even under strong noise conditions, thereby offering a promising pathway toward efficient and reliable quantum operations in large-scale qubit arrays.

DOI
10.1088/1674-1056/addcd3

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Abstract Geometric phase gates have attracted considerable attention due to their intrinsic robustness against certain types of noise. Significant progress has been achieved in implementing geometric phase gates using microwave control in silicon-based electron spin systems. In this work, we propose an alternative geometric phase gate protocol that differs fundamentally from microwave driving approaches by leveraging square-wave control of rapidly switchable micromagnets driven by spin–orbit torque (SOT) to achieve fast and precise magnetic field modulation. By employing square-wave currents to control magnetization switching, our approach relaxes the requirements on waveform precision while significantly suppressing crosstalk. Moreover, our scheme inherently preserves trajectory closure at the end of each operation, effectively mitigating noise-induced path deviation and enhancing gate robustness even under strong noise conditions, thereby offering a promising pathway toward efficient and reliable quantum operations in large-scale qubit arrays.
High-fidelity quantum operations are a key requirement for fault-tolerant quantum information processing. Manipulation of electron spins is usually achieved with time-dependent microwave fields. In contrast to the conventional dynamic approach, adiabatic geometric phase operations are expected to be less sensitive to certain kinds of noise and field inhomogeneities. Here, we introduce an adiabatic geometric phase gate for the electron spin. Benchmarking it against existing dynamic and nonadiabatic geometric gates through simulations and experiments, we show that it is indeed inherently robust against inhomogeneity in the applied microwave field strength. While only little advantage is offered over error-correcting composite pulses for modest inhomogeneities $\ensuremath{\lesssim}10%$, the adiabatic approach reveals its potential for situations where field inhomogeneities are unavoidably large.
Abstract In this study we propose and numerically validate a protocol for high-fidelity non-Abelian holonomic gates in Si/SiGe spin-valley qubits, leveraging geometric phases for inherent fault tolerance. By combining electrical control of valley state energy splitting with cyclic in-plane magnetic fields, we engineer a protected subspace where quantum information evolves via geometric phases. Our simulations show these gates achieve 99.4% fidelity and maintain robustness against charge noise, outperforming conventional dynamic gates by 15% under realistic conditions. The gate exploits cyclic modulation of in-plane magnetic fields while dynamically tuning valley splitting to maintain Valley-Zeeman matching, yielding a Berry connection that enables non-commutative holonomies. Numerical analysis reveals distinct operational regimes, from hybridized states for phase accumulation to isolated states for initialization, within experimentally accessible parameter ranges. This work establishes spin-valley qubits as a promising platform for geometric quantum computation, combining holonomic operations' noise resilience with silicon's scalability. The demonstrated performance and compatibility with existing architectures suggest a viable path toward large-scale, fault-tolerant quantum processors.
Hole spins in silicon quantum dots are a promising platform for quantum computing due to their strong intrinsic spin-orbit coupling (SOC), which enables fast, all-electrical control. However, this coupling also increases their susceptibility to charge noise, thereby limiting coherence times. Moreover, holes in silicon are also affected by hyperfine interactions with residual nuclear spins in the silicon substrate, introducing a non-negligible source of low-frequency noise. Here, we implement a phase-modulated concatenated continuous driving (CCD) technique for hole spin qubits to suppress low-frequency noise through microwave phase modulation. This approach stabilizes Rabi oscillations and extends the oscillation decay time compared to the conventional method. Furthermore, by defining a qubit in the CCD frame, we achieve coherent control while simultaneously protecting the qubit from noise, confirming coherence protection during gate operations. These results demonstrate a viable route toward noise-robust hole spin qubits.
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.
The Rydberg blockade effect plays an important role in realizing two-qubit gates in atomic arrays. Meanwhile, such mechanics will increase the crosstalk between atoms and enhance the decoherence. In this paper, we propose a new scheme to realize the controlled-phase gate without Rydberg blockade. The scheme works effectively with large atomic spacings and is insensitive to the thermal motions of atoms. The proposal is robust against random noises due to the geometric characteristic and operates fast based on the non-adiabatic evolution. The proposed gate is actually a new-type geometric gate that consolidates the non-adiabatic holonomic control and the unconventional geometric control simultaneously. The interference between two different types of geometric phases can be investigated. Furthermore, we show that the scheme with weak Rydberg interaction requires much less physical resources than the present Rydberg blockade scheme. Therefore, our proposal provides a fast and robust way to realize geometric quantum control, and it may trigger the discoveries of new geometric gates in high-dimensional Hilbert space.
While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (∼10) operations. This occurs inspite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. We have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.