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arXiv:2205.02693 · Physical Review Research

Coherence-protected nonadiabatic geometric quantum computation

K. Z. Li, Guofu Xu, D. M. Tong

Published May 10, 2021• 7 citations
arXivHTMLPDF

Abstract

Because of using geometric phases, nonadiabatic geometric gates have robustness against control errors.On the other hand, decoherence still affects nonadiabatic geometric gates, which is a key factor in reducing their fidelities.In this paper, we show that based on the system Hamiltonian that realizes a nonadiabatic geometric gate, one may construct a system Hamiltonian by the use of which not only the geometric feature of the nonadiabatic geometric gate is preserved, but also the system's coherence is protected.As a result, a coherence-protected nonadiabatic geometric gate is realized with this system Hamiltonian, and this gate has robustness against both control errors and decoherence.We further implement our scheme with nitrogen-vacancy centers and show that a universal set of coherence-protected nonadiabatic geometric gates can be realized.Our scheme does not need auxiliary systems or the encoding of logical qubits with physical qubits, which saves resources for the implementation.Due to the robustness against both control errors and decoherence, our scheme provides a promising way to realize high-fidelity quantum gates.

DOI
10.1103/physrevresearch.3.023104

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Because of using geometric phases, nonadiabatic geometric gates have robustness against control errors.On the other hand, decoherence still affects nonadiabatic geometric gates, which is a key factor in reducing their fidelities.In this paper, we show that based on the system Hamiltonian that realizes a nonadiabatic geometric gate, one may construct a system Hamiltonian by the use of which not only the geometric feature of the nonadiabatic geometric gate is preserved, but also the system's coherence is protected.As a result, a coherence-protected nonadiabatic geometric gate is realized with this system Hamiltonian, and this gate has robustness against both control errors and decoherence.We further implement our scheme with nitrogen-vacancy centers and show that a universal set of coherence-protected nonadiabatic geometric gates can be realized.Our scheme does not need auxiliary systems or the encoding of logical qubits with physical qubits, which saves resources for the implementation.Due to the robustness against both control errors and decoherence, our scheme provides a promising way to realize high-fidelity quantum gates.
Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the previous schemes in this direction have been based on the conventional geometric phases, of which the dynamical phases need to be removed. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases, of which the dynamical phases do not need to be removed. Specifically, by using three physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of geometric gates nonadiabatically and unconventionally. Our scheme not only maintains all the merits of nonadiabatic geometric quantum computation in decoherence-free subspaces, but also avoids the additional operations required in the conventional schemes to cancel the dynamical phases.
Abstract Unconventional nonadiabatic geometric quantum computation not only possesses the geometric robustness of conventional ones but also avoids the need to remove the dynamical phase. Dynamical decoupling is a promising method to protect unconventional nonadiabatic geometric gates against decoherence. Here, we propose a protocol to implement unconventional nonadiabatic geometric quantum computation protected by dynamical decoupling. By using three physical qubits to encode a logical qubit and choosing a system Hamiltonian that commutes with the decoupling group, a universal set of dynamical-decoupling-protected unconventional nonadiabatic geometric gates can be realized. Our work maintains the robustness of unconventional nonadiabatic geometric gates while protecting quantum gates against both collective and independent decoherence.
A nonadiabatic geometric quantum gate is realized by integrating nonadiabatic geometric phases with global geometric features into the unitary quantum control, thereby removing the limitation of a long evolution time in the adiabatic case. However, systematic errors are inevitable in practical quantum control; these lead to the deviation of the evolution from target conditions to inducing geometric phases, smearing the robustness of the induced geometric quantum gates. Here, we present a general theoretical framework with enhanced robustness for geometric quantum gates by preserving fundamental geometric conditions. We first analytically evaluate the influence of systematic errors on geometric gates and then propose an optimized approach to mitigate this influence. Numerical simulations indicate that, as the geometric conditions are still maintained in the presence of systematic errors in our scheme, the constructed geometric quantum gates exhibit strong robustness, far superior to that of conventional schemes. Furthermore, we propose implementing the scheme in superconducting quantum circuits, where geometric quantum gates can achieve high fidelity with current experimental parameters. Therefore, the enhanced gate performance highlights the promise of our scheme for large-scale quantum computations.
Nonadiabatic geometric quantum computation is dedicated to the realization of high-fidelity and robust quantum gates, which is the necessity of fault-tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate-time and abrupt pulse control, and thus weaken the gate performance. Here, we propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolutions, which effectively shorten the gate duration, and universal quantum gates can be realized in one step without path mutation. Our numerical simulation shows that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistant not only to noise but also to decoherence effect. In addition, our scheme can also be implemented on a superconducting circuit platform, with the fidelities of single-qubit and two-qubit gates higher than 99.97%\%% and 99.84%\%%, respectively. Therefore, our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.
Nonadiabatic holonomic quantum computation (NHQC) provides an essential way to construct robust and high-fidelity quantum gates due to its geometric features. However, NHQC is more sensitive to decay and dephasing errors than a conventional dynamical gate since it requires an ancillary intermediate state. Here, we utilize the Hamiltonian reverse engineering technique to study the influence of intermediate-state decoherence on NHQC gate fidelity, and propose schemes to construct an arbitrary single-qubit holonomic gate and nontrivial two-qubit holonomic gate with high fidelity and robustness to the decoherence. Although the proposed method is generic and can be applied to many experimental platforms, such as superconducting qubits, trapped ions, and quantum dots, here we take a nitrogen-vacancy center as an example to show that the gate fidelity can be significantly enhanced from 89% to 99.6% in contrast to recent experimental NHQC schemes [Phys. Rev. Lett. 119, 140503 (2017); Nat. Photonics 11, 309 (2017); Opt. Lett. 43, 2380 (2018)], and the robustness against decoherence can also be significantly improved. All in all, our scheme provides a promising way for fault-tolerant geometric quantum computation.
Quantum gates constructed by geometric phase are naturally robust to control errors due to the global nature of the geometric evolution path. Therefore, how to cope with the inevitable decoherence errors is worthy of serious attention for geometric quantum computation. Different from conventional nonadiabatic geometric quantum computation (NGQC), which needs the same evolution time for any geometric rotation angle, we have proposed and experimentally demonstrated nonadiabatic noncyclic geometric quantum computation (NNGQC) without the requirement of the cyclic evolution condition, which thus reduces decoherence errors due to shortened evolution time [J. W. Zhang et al., Phys. Rev. Lett. 127, 030502 (2021)]. In addition, the use of decoherence-free subspaces (DFS) is another effective strategy to protect quantum gates from dephasing error and has been studied in nonadiabatic holonomic quantum computation [G. F. Xu et al., Phys. Rev. Lett. 109, 170501 (2012)]. Motivated by previous studies, we propose a one-step scheme to implement single-qubit NNGQC operation in DFS constructed by two Rydberg atoms, and then generalize the scheme to the two-logical-qubit case in one step. The numerical results show that our scheme is robust against decoherence in contrast to the NGQC counterparts. The present scheme combines the features of NNGQC and DFS and can further reduce the impact of decoherence on gate infidelity, which may provide an option for the realization of Rydberg-atom-based quantum computation in the future.