Path-shortening realizations of nonadiabatic holonomic gates

Xu, Guofu; Tong, D. M.; Sjöqvist, Erik

doi:10.1103/physreva.98.052315

Cited by 43 publications

(18 citation statements)

References 39 publications

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“…Here, we would like to point out that our scheme is based on Abelian geometric phases and thus one only needs to make the diagonal elements vanish for satisfying the parallel transport condition. This is different from the scheme based on non-Abelian geometric phases [69,70], in which one needs to make both diagonal and off-diagonal elements vanish for satisfying the parallel transport condition.…”

Section: The Schemementioning

confidence: 95%

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Zhao

2021

Front. Phys.

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Nonadiabatic geometric quantum computation protected by dynamical decoupling combines the robustness of nonadiabatic geometric gates and the decoherence-resilience feature of dynamical decoupling. Solid-state systems provide an appealing candidate for the realization of nonadiabatic geometric quantum computation protected dynamical decoupling since the solid-state qubits are easily embedded in electronic circuits and scaled up to large registers. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian, which not only combines the merits of nonadiabatic geometric gates and dynamical decoupling but also can be realized in a number of solid-state systems, such as superconducting circuits and quantum dots.

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Section: The Schemementioning

confidence: 95%

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Zhao

2021

Front. Phys.

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“…Geometric quantum computation (GQC) [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] can work for high-fidelity quantum gates by utilizing the geometric characteristics to resist operational imperfection. The early proposals of GQC, based on adiabatic Abelian [33] or adiabatic non-Abelian geometric phases, [34][35][36][37] always suffer from the detrimental influence of decoherence due to slow operations.…”

Section: Introductionmentioning

confidence: 99%

Realization of Deutsch–Jozsa Algorithm in Rydberg Atoms by Composite Nonadiabatic Holonomic Quantum Computation with Strong Robustness Against Systematic Errors

et al. 2021

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Deutsch–Jozsa (DJ) algorithm, as the first example of quantum algorithm, performs better than any classical algorithm for distinguishing balance and constant functions. Here, a scheme to implement the DJ algorithm in Rydberg atoms using the composite nonadiabatic holonomic quantum computation (NHQC) is presented. Taking advantages of composite loops and holonomic features to resist systematic errors, the scheme of composite NHQC works more robustly compared with the standard dynamic counterparts. By exemplifying the DJ algorithm implementation, the performance of single‐loop NHQC‐, composite NHQC‐, and the dynamic counterpart‐based processes are compared both analytically and numerically, indicating the best robustness of composite scheme to systematic errors. In addition, the combination of composite NHQC and quantum algorithm also provides an alternative pathway for the realization of robust quantum algorithm in the future.

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“…However, due to this additional constrain, the geometry phase obtained there is of the unconventional nature [38,39]. Another method of getting faster holonomic quantum gates is achieved via shortening the evolution path [40,41]. Besides the gate-time consideration, the pulse shaping technique is also applied in NHQC schemes [42][43][44][45][46] with experimental demonstrations [47][48][49][50][51][52], mainly to strength the gate-robustness.…”

Section: Introductionmentioning

confidence: 99%

Composite Short-path Nonadiabatic Holonomic Quantum Gates

Liang,

Shen,

Chen

et al. 2021

Preprint

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Nonadiabatic holonomic quantum computation (NHQC) has attracted significant attentions due to its fast evolution and the geometric nature induced resilience to local noises. However, its long operation time and complex physical implementation make it hard to surpass the dynamical scheme, and thus hindering its wide application. Here, we present to implement NHQC with the shortest path under some conditions, through the inverse Hamiltonian engineering technique, which posses higher fidelity and stronger robustness than previous NHQC schemes. Meanwhile, the gate performance in our scheme can be further improved by using the proposed composite dynamical decoupling pulses, which can efficiently improve both the gate fidelity and robustness, making our scheme outperforms the optimal dynamical scheme in certain parameter range. Remarkably, our scheme can be readily implemented with Rydberg atoms, and a simplified implementation of the controlled-not gate in the Rydberg blockade regime can be achieved. Therefore, our scheme represents a promising progress towards future fault-tolerant quantum computation in atomic systems.

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Path-shortening realizations of nonadiabatic holonomic gates

Cited by 43 publications

References 39 publications

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Realization of Deutsch–Jozsa Algorithm in Rydberg Atoms by Composite Nonadiabatic Holonomic Quantum Computation with Strong Robustness Against Systematic Errors

Composite Short-path Nonadiabatic Holonomic Quantum Gates

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