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Annalen der Physik

One‐Step Implementation of N‐Qubit Nonadiabatic Holonomic Quantum Gates with Superconducting Qubits via Inverse Hamiltonian Engineering

Yi‐Hao Kang, Ye‐Hong Chen, Zhi‐Cheng Shi, Bi‐Hua Huang, Jie Song, Yan Xia

Published Mar 25, 2019• 10 citations
Publisher

Abstract

Abstract A protocol is proposed to realize one‐step implementation of the N‐qubit nonadiabatic holonomic quantum gates with superconducting qubits. The inverse Hamiltonian engineering is applied in designing microwave pulses to drive superconducting qubits. By combining curve fitting, the wave shapes of the designed pulses can be described by simple functions, which are not hard to realize in experiments. To demonstrate the effectiveness of the protocol, a three‐qubit holonomic controlled π‐phase gate is taken as an example in numerical simulations. The results show that the protocol holds robustness against noise and decoherence. Therefore, the protocol may provide an alternative approach for implementing N‐qubit nonadiabatic holonomic quantum gates.

DOI
10.1002/andp.201800427

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Abstract A protocol is proposed to realize one‐step implementation of the N‐qubit nonadiabatic holonomic quantum gates with superconducting qubits. The inverse Hamiltonian engineering is applied in designing microwave pulses to drive superconducting qubits. By combining curve fitting, the wave shapes of the designed pulses can be described by simple functions, which are not hard to realize in experiments. To demonstrate the effectiveness of the protocol, a three‐qubit holonomic controlled π‐phase gate is taken as an example in numerical simulations. The results show that the protocol holds robustness against noise and decoherence. Therefore, the protocol may provide an alternative approach for implementing N‐qubit nonadiabatic holonomic quantum gates.
Abstract Nonadiabatic holonomic quantum computation has attracted increasing interest because of its robustness. Here, based on the shortcuts to adiabaticity, a scheme to construct a three‐qubit nonadiabatic holonomic gate in a cavity quantum electrodynamics system is proposed. In the scheme, the three‐qubit holonomic gate is implemented in a single step. In addition, by numerical simulations, it is shown that the constructed holonomic quantum gate holds characteristics such as high fidelity, decoherence‐resistance, and error‐immunity.
Geometric phases are noise resilient, and thus provide a robust way towards high-fidelity quantum manipulation. Here we experimentally demonstrate arbitrary nonadiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical nonadiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.
Abstract In this study, a one‐step scheme is proposed to implement time‐optimal three‐qubit nonadiabatic holonomic gates using unconventional Rydberg pumping mechanism. The system dynamics of three Rydberg atoms are investigated in the regime of dipole–dipole interaction, which may provide relatively strong interaction strengths. By analyzing the system dynamics of three atoms, an effective three‐level interaction Hamiltonian is derived. Based on this, a three‐qubit nonadiabatic holonomic gate can be implemented in one step by modulating Rabi frequencies of control pulses on the target atom. The scheme is further optimized using time‐optimal control technology based on quantum‐brachistochrone formalism, which minimizes the evolution time of the system and mitigates the influence from the environmental decoherence. Numerical simulations results show that the scheme is robust against the Doppler dephasing error, system parameter variations, and atomic spontaneous emissions. Therefore, it is hoped that the scheme may facilitate the realization of fault‐tolerant quantum computation in Rydberg atoms.
We proposed a theoretical protocol to generate robust pulses for executing an arbitrary nonadiabatic holonomic quantum gate operations via reverse engineering. Compared with the traditional scheme that the pulse area needs to satisfy the condition 0 Ω dt = π, the reverse engineering scheme no longer requires this constraint, which greatly improves the flexibility of pulse designing. By optimizing the envelope of the pulses, we show that the gate operations are more robust against the frequency detuning than the traditional scheme. In the meanwhile, we also improve the robustness of the pulse against Rabi frequency fluctuations by utilizing the perturbation theory. The robust pulses can be applied to other ensemble qubit systems to realize quantum error correction, qubit initialization, and quantum gate operations, such as ensemble nitrogen-vacancy center systems, superconducting qubit systems, and other systems where qubits are addressed in frequency.
ABSTRACT Nonadiabatic holonomic quantum computation (NHQC) leverages non‐Abelian geometric phases within a nonadiabatic framework to achieve fast and robust quantum gate operations. However, the practical implementation of NHQC is challenged by the imperfect control inherent in experimental environments. Ensuring deep suppression of control error is critical. In this work, we propose a dynamically optimized NHQC scheme to construct universal super‐robust holonomic quantum gates. The proposed scheme is implemented by strategically designing a set of dynamically correcting pulses to achieve cyclic evolution, while ensuring that unwanted and disruptive dynamical phase elements, including previously neglected cross‐coupling terms, are not accumulated. This constructed super‐robust NHQC scheme efficiently safeguards the cyclic evolution process and makes the holonomic gate immune to control error by effectively correcting the error up to the fourth order. Furthermore, when integrated with decoherence‐free subspace (DFS) encoding in superconducting quantum circuits, our scheme can achieve high‐fidelity holonomic gates, and demonstrate robust resilience against both control errors and collective dephasing errors. Consequently, our work offers a promising pathway toward the realization of scalable and fault‐tolerant holonomic quantum computation.
In this paper, we propose a one-step scheme for implementing the nonadiabatic holonomic swap gate with Rydberg atoms. By applying invariant-based reverse engineering to design the effective Hamiltonian of the system, a suitable evolution path for implementing nonadiabatic holonomic quantum computation is found. In addition, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, so that the scheme is insensitive to the systematic error of pulses. We also estimate the effects of random noise, the random initial phase of the pulses, the Doppler shift, and decoherence on the scheme. The numerical results show that the scheme exhibits fairly good performance against these negative factors. Finally, we generalize the scheme to realize the non-Clifford swap gates. Therefore, this scheme can provide a feasible framework for implementing high-fidelity and robust swap gates and non-Clifford swap gates with Rydberg atoms.