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arXiv:1804.10983 · npj Quantum Information

Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature

Felix Kleißler, Andrii Lazariev, Silvia Arroyo-Camejo

Published Sep 25, 2018• 51 citations
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Abstract

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.

DOI
10.1038/s41534-018-0098-7

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Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature.

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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.

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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.
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.
At its most fundamental level, circuit-based quantum computation relies on the application of controlled phase shift operations on quantum registers. While these operations are generally compromised by noise and imperfections, quantum gates based on geometric phase shifts can provide intrinsically fault-tolerant quantum computing. Here we demonstrate the high-fidelity realization of a recently proposed fast (non-adiabatic) and universal (non-Abelian) holonomic single-qubit gate, using an individual solid-state spin qubit under ambient conditions. This fault-tolerant quantum gate provides an elegant means for achieving the fidelity threshold indispensable for implementing quantum error correction protocols. Since we employ a spin qubit associated with a nitrogen-vacancy colour centre in diamond, this system is based on integrable and scalable hardware exhibiting strong analogy to current silicon technology. This quantum gate realization is a promising step towards viable, fault-tolerant quantum computing under ambient conditions. Quantum gates based on geometric phase shifts offer a promising approach for the realization of fault-tolerant quantum computing. Using nitrogen-vacancy centre qubits in diamond, this study experimentally realises a high-fidelty, non-adiabatic, non-Abelian holonomic single-qubit gate at room temperature.
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
Abstract Geometric quantum computation relies on the geometric phase that arises in adiabatic cyclic evolutions of non-degenerate quantum systems, enabling the design of robust quantum gates. However, the adiabatic condition requires long evolution times, making the system vulnerable to decoherence. In this work, we propose a scheme to realize fast and high-fidelity geometric quantum gates by applying the superadiabatic transitionless driving protocol within the dressed-state framework. We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field, focusing in particular on the nitrogen-vacancy center in diamond. We show how the dynamical phase can be canceled to obtain purely geometric operations. The robustness of the gates is assessed under systematic errors and environmental decoherence, demonstrating high fidelity even in regimes with strong fluctuations. Finally, we extend the protocol to construct nontrivial two-qubit gates, highlighting its feasibility for scalable quantum information processing.
We propose a feasible scheme to implement a universal set of quantum gates based on geometric phases and superadiabatic quantum control. Consolidating the advantages of both strategies, the proposed quantum gates are robust and fast. The diamond nitrogen-vacancy center system is adopted as a typical example to illustrate the scheme. We show that these gates can be realized in a simple two-level configuration by appropriately controlling the amplitude, phase, and frequency of just one microwave field. The gate's robust and fast features are confirmed by comparing the fidelity of the proposed superadiabatic geometric phase (controlled-phase) gate with those of two other kinds of phase (controlled-phase) gates.
We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over 99.299.2%99.2 on the spin state of the nitrogen-vacancy center are realized with average durations shortened by 21.521.5%21.5 compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds 96.596.5%96.5 on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.