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New Journal of Physics

Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

Kai Zhang, Naufer Nusran, Bradley R. Slezak, M V Gurudev Dutt

Published May 17, 2016• 8 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/18/5/053029

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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.
We present measurements of the Berry Phase in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. Our results demonstrate the remarkable degree of coherent control achievable in the presence of a highly complex solid-state environment. We manipulate the spin qubit geometrically by careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting phase via spin-echo interferometry. We find good agreement with Berry's predictions within experimental errors. We also investigated the role of the environment on the geometric phase, and observed that unlike other solid-state qubit systems, the dephasing was primarily dominated by fast radial fluctuations in the path.
We experimentally investigate the effects of noise on the adiabatic and cyclic geometric phase, also termed the Berry phase. By introducing artificial fluctuations in the path of the control field, we measure the geometric contribution to dephasing of an effective two-level system for a variety of noise powers and different paths. Our results, measured using a microwave-driven superconducting qubit, clearly show that only fluctuations which distort the path lead to geometric dephasing. In a direct comparison with the dynamic phase, which is path independent, we observe that the Berry phase is less affected by noise-induced dephasing. This observation directly points towards the potential of geometric phases for quantum gates or metrological applications.
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.
Reliable and robust control lies at the core of implementing quantum information processing with nitrogen-vacancy (NV) centers in diamond. However, control pulses inevitably introduce multiple errors, leading to decoherence and hindering scalable applications. Here, we experimentally report an experiment-friendly multiple-noise-resilient nonadiabatic geometric quantum gate (MNR-NGQG) that can significantly improve the conventional dynamical gate in both robustness and coherence. Notably, even when the detuning fluctuation range is comparable to the maximum Rabi frequency, the single-qubit gate performance of the MNR-NGQG remains almost unchanged. Additionally, the coherence decay time of the electron spin under MNR-NGQG driving is significantly extended to 690 $\ifmmode\pm\else\textpm\fi{}$ 30 $\textmu{}\mathrm{s}$, 3.5 times longer than that of the naive dynamical counterpart. As a result, the fidelity of single-qubit gates reaches 0.9992(1), as characterized by quantum process tomography. With its experimentally feasible design and relaxed hardware requirements, our work offers a solid paradigm for achieving high-fidelity quantum control in the NV center system, paving the way for practical applications in quantum information science.
Geometric phases and holonomies are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against parametric noise. However, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. This was partly due to the need for adiabatic time evolution or the requirement of complex, high-dimensional state spaces and a large number of driving field parameters to achieve universal quantum gates employing holonomies. In 2016 Liang et al. proposed universal, superadiabatic, geometric quantum gates exploiting transitionless quantum driving, thereby offering fast and universal quantum gate performance on a simple two-level system. Here, we report on the experimental implementation of a set of non-commuting single-qubit superadiabatic, geometric quantum gates on the electron spin of the nitrogen-vacancy center in diamond under ambient conditions. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.
Abstract Geometric phases and holonomies are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against parametric noise. However, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. This was partly due to the need for adiabatic time evolution or the requirement of complex, high-dimensional state spaces and a large number of driving field parameters to achieve universal quantum gates employing holonomies. In 2016 Liang et al. proposed universal, superadiabatic, geometric quantum gates exploiting transitionless quantum driving, thereby offering fast and universal quantum gate performance on a simple two-level system. Here, we report on the experimental implementation of a set of non-commuting single-qubit superadiabatic, geometric quantum gates on the electron spin of the nitrogen-vacancy center in diamond under ambient conditions. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.