Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

Zhu, Zhennan; Chen, Tao; Yang, Xiaodong; Bian, Ji; Xue, Zheng‐Yuan; Peng, Xinhua

doi:10.1103/physrevapplied.12.024024

Cited by 94 publications

(34 citation statements)

References 53 publications

(76 reference statements)

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“…In contrast to the earlier adiabatic-process-based geometric quantum computation [35][36][37][38], nonadiabatic geometric quantum computation (NGQC) and nonadiabatic holonomic quantum computation (NHQC) based on Abelian [39][40][41][42][43][44][45][46] and non-Abelian geometirc phases [47][48][49][50][51][52][53][54][55][56] in two-and threelevel system, respectively, can intrinsically protect against environment-induced decoherence, since the the construction times of geometric quantum gates is reduced. The nonadiabatic geometric gates of NGQC and NHQC have been experimentally demonstrated in many systems including superconducting qubit [57][58][59][60][61], NMR [62][63][64][65], NV center in diamond [66][67][68][69]. However, there are many theoretical proposals to apply geometric quantum computation [70][71][72][73] and NGQC [42,[74][75][76][77] in Rydberg atom platform.…”

Section: Introductionmentioning

confidence: 99%

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Liu

Yung

2020

Phys. Rev. Research

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Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the conventional NGQC is that all of the gates are performed with exactly the same amount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation (NNGQC), that arbitrary single-and two-qubit geometric gate can be constructed via noncyclic non-Abelian geometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gates against the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied in various quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate, we make simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can be realized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, our scheme provides a promising way for fast and robust neutral-atom-based quantum computation.

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Section: Introductionmentioning

confidence: 99%

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Liu

Yung

2020

Phys. Rev. Research

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“…Recently, GQC [11][12][13][14][15][16][17] based on the nonadiabatic geometric phases [4,5] have been proposed to implement robust and high-fidelity quantum gates, which eliminate the restriction of slow evolution. Remarkably, experimental demonstrations for elementary geometric quantum gates have also been achieved on various systems, such as trapped ions [18,19], NMR [20][21][22][23], superconducting quantum circuits [24][25][26][27][28][29][30], and nitrogen vacancy centers [31][32][33][34][35][36], etc. Meanwhile, to further consolidate the geometric robustness, many efforts have been made to make GQC being compatible with various optimal-control techniques, including the composite pulse [37,38], dynamical decoupling [39,40], time-optimal control [41], path optimization [42], etc.…”

Section: Introductionmentioning

confidence: 99%

Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource

Chen,

Xue,

Wang

2021

Preprint

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Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls, especially for logical qubits that involve more physical qubits, whose error tolerance is effective in principle though, their experimental demonstration is still demanding. Thus, how to best simplify the needed control and manifest its full advantage has become the key to widespread applications of geometric quantum computation. Here we propose a new fast and robust geometric scheme, with the decoherence-freesubspace encoding, and present its physical implementation on superconducting quantum circuits, where we only utilize the experimentally demonstrated parametrically tunable coupling to achieve high-fidelity geometric control over logical qubits. Numerical simulation verifies that it can efficiently combine the error tolerance from both the geometric phase and logical-qubit encoding, displaying our gate-performance superiority over the conventional dynamical one without encoding, in terms of both gate fidelity and robustness. Therefore, our scheme can consolidate both error suppression methods for logical-qubit control, which sheds light on the future large-scale quantum computation.

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“…But for the realization of an arbitrary single-qubit gate, it needs to concatenate two separate cycles, which will increase the decoherence induced error. To remove this obstacle, researchers have come up with an improved approach enables to realize arbitrary single-qubit gate through a single-loop evolution [19][20][21], which has also been experimentally verified [22][23][24][25][26][27].…”

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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Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace

Cited by 94 publications

References 53 publications

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Error-Tolerant Geometric Quantum Control for Logical Qubits with Minimal Resource

Composite Short-path Nonadiabatic Holonomic Quantum Gates

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