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Physical Review A

Quantum computation based on capture-and-release dynamics

S.-Y. Zhang, J.-F. Wei, Pengtao Song, L.-L. Yan, Adam Kinos, Shi‐Lei Su, Gang Chen

Published Jan 2, 2025• 3 citations
Publisher

Abstract

High-fidelity and decoherence-insensitive quantum gates are essential for achieving universal quantum computing. In quantum information processing, decoherence arising from excited states significantly contributes to the scheme's infidelity. Therefore, minimizing the average population of the excited state is crucial when designing quantum protocols. A promising approach involves utilizing capture-and-release dynamics to induce a complex phase on the ground state in a two-level system, effectively suppressing the integrated excited-state population. By applying this dynamics protocol to a $\mathrm{\ensuremath{\Lambda}}$ three-level system, we propose a scheme to construct arbitrary decoherence suppressed single-qubit and nontrivial two-qubit gates; meanwhile, by incorporating the Zeno dynamics process in the construction of two-qubit logic gates, the large detuning and excitation of virtual photons render the scheme insensitive to qubit decoherence and cavity dissipation. Applying our scheme to the nitrogen-vacancy (NV) center as an example, we prove our scheme with higher fidelity than conventional nonadiabatic non-Abelian geometric gates while significantly enhancing the robustness against decoherence and frequency shift errors. These studies provide alternative approaches for constructing robust quantum gate operations. We also emphasize that the scheme is feasible for three-level quantum systems, not limited to NV center systems.

DOI
10.1103/physreva.111.012604

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High-fidelity and decoherence-insensitive quantum gates are essential for achieving universal quantum computing. In quantum information processing, decoherence arising from excited states significantly contributes to the scheme's infidelity. Therefore, minimizing the average population of the excited state is crucial when designing quantum protocols. A promising approach involves utilizing capture-and-release dynamics to induce a complex phase on the ground state in a two-level system, effectively suppressing the integrated excited-state population. By applying this dynamics protocol to a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ three-level system, we propose a scheme to construct arbitrary decoherence suppressed single-qubit and nontrivial two-qubit gates; meanwhile, by incorporating the Zeno dynamics process in the construction of two-qubit logic gates, the large detuning and excitation of virtual photons render the scheme insensitive to qubit decoherence and cavity dissipation. Applying our scheme to the nitrogen-vacancy (NV) center as an example, we prove our scheme with higher fidelity than conventional nonadiabatic non-Abelian geometric gates while significantly enhancing the robustness against decoherence and frequency shift errors. These studies provide alternative approaches for constructing robust quantum gate operations. We also emphasize that the scheme is feasible for three-level quantum systems, not limited to NV center systems.
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.
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.
Robust universal quantum gates with an extremely high fidelity hold an important position in large-scale quantum computing. Here, we propose a scheme for several robust universal photonic quantum gates on a two-or three-photon system, including the controlled-NOT gate, the Toffoli gate, and the Fredkin gate, assisted by low-Q single-sided cavities. In our scheme, the quantum gates are robust against imperfect process occurring with the photons and the electron spins in diamond nitrogen-vacancy (NV) centers inside low-Q cavities. Errors due to the imperfect process are transferred to some heralding responses, which may lead to a direct recycling procedure to remedy the success probability of the quantum gates. As a result, the adverse impact of the imperfect process on fidelity is eliminated, greatly relaxing the restrictions on implementation of various quantum gates in experiments. Furthermore, the scheme is designed in a compact and heralded style, which can increase the robustness against environmental noise and local fluctuation, thus decreasing the operation time, the error probability, and the quantum resource consumption in a large-scale integrated quantum circuit. The near-unity fidelity and not-too-low efficiency with current achievable experimental techniques guarantees the feasibility of the scheme.
Quantum gates are crucial for quantum computation and quantum information processing. However, their effectiveness is often hindered by systematic errors and decoherence. Therefore, achieving resilient quantum gates to these factors is of great significance. We present a method to construct nonadiabatic holonomic single- and two-qubit gates in a Rydberg ground-state-blockade regime. Our approach utilizes a far-off-resonant technique for the single-qubit gate and a modified Rydberg antiblockade for the two-qubit gate. The reduction of the population of single- and two-excitation Rydberg states and the nonadiabatic holonomic process during the construction of the gates ensure robustness to decoherence and systematic errors, respectively. Numerical results demonstrate the fidelity and robustness of our scheme. The proposed scheme holds promise for future applications in quantum computation and quantum information processing tasks.
We propose a scheme to implement a quantum controllable-phase gate via quantum Zeno dynamics. The two qubits are asymmetrically encoded by two four-level atoms coupled via a quantized cavity mode. Under proper conditions, the desirable logic operation can be implemented in one step. Since the qubit is encoded by the ground and the metastable states of the atom and the cavity mode is not really excited, our protocol is robust against the spontaneous decays of the atoms and cavity. Specifically, the feasibility of our generic proposal is demonstrated with two nitrogen-vacancy centers coupled to whispering-gallery microresonator.
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus faster gate operations are highly desired. Here, we propose a nonadiabatic holonomic quantum-computation (NHQC) scheme with detuned interactions on a $\mathrm{\ensuremath{\Delta}}$-type three-level system, which combines the time-optimal control technique with the time-independent detuning adjustment to further accelerate universal gate operations, so that the gate time can be greatly shortened within the hardware limitation, and thus high-fidelity gates can be obtained. Meanwhile, our numerical simulations show that the gate robustness is also stronger than previous schemes. Finally, we present an implementation of our proposal on superconducting quantum circuits, with a decoherence-free subspace encoding, based on the experimentally demonstrated parametrically tunable coupling technique, which simplifies previous investigations. Therefore, our protocol provides a more promising alternative for future fault-tolerant quantum computation.