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arXiv:1812.09513 · Annalen der Physik

Shortcut Scheme for One‐Step Implementation of a Three‐Qubit Nonadiabatic Holonomic Gate

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

Published Sep 21, 2018• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/andp.201800179

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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.
High-fidelity quantum gates are essential for large-scale quantum computation. However, any quantum manipulation will inevitably affected by noises, systematic errors and decoherence effects, which lead to infidelity of a target quantum task. Therefore, implementing high-fidelity, robust and fast quantum gates is highly desired. Here, we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity. In our proposal, the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally, leading to high-fidelity quantum gates in a simple setup. Besides, our scheme is readily realizable in physical system currently pursued for implementation of quantum computation. Therefore, our proposal represents a promising way towards fault-tolerant geometric quantum computation.
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 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.
When a quantum system is driven slowly through a parametric cycle in a degenerate Hilbert space, the state would acquire a non-Abelian geometric phase, which is stable and forms the foundation for holonomic quantum computation (HQC). However, in the adiabatic limit, the environmental decoherence becomes a significant source of errors. Recently, various nonadiabatic holonomic quantum computation (NHQC) schemes have been proposed, but all at the price of increased sensitivity to control errors. Alternatively, there exist theoretical proposals for speeding up HQC by the technique of "shortcut to adiabaticity" (STA), but no experimental demonstration has been reported so far, as these proposals involve a complicated control of four energy levels simultaneously. Here, we propose and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture. With this scheme, all holonomic single-qubit operations can be realized nonadiabatically through a single cycle of state evolution. As a result, we are able to experimentally benchmark the stability of STA+HQC against NHQC in the same platform. The flexibility and simplicity of our scheme makes it also implementable on other systems, such as nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance. Finally, our scheme can be extended to construct two-qubit holonomic entangling gates, leading to a universal set of STAHQC gates.
Nonadiabatic holonomic gates provide a promising way to realize high-fidelity quantum gates because of their robustness and high-speed implementation. Compared with quantum computation that consists of many nonadiabatic holonomic one-qubit and two-qubit gates, the nonadiabatic holonomic multiqubit gate, which can reduce the number of quantum gates, is more efficient to construct simpler and faster complicated quantum computation. We propose the simplest scheme to realize nonadiabatic holonomic three-qubit controlled gates. On the one hand, the parameters we set to realize the three-qubit controlled gates are all time independent, which makes it easy to control and operate the quantum systems. On the other hand, our scheme avoids the combination of the elementary gates and realizes the three-qubit controlled gates only by one-shot implementation.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate. In this paper we put forward a scheme by which one can directly realize an arbitrary holonomic one-qubit gate with a single-shot implementation, avoiding the extra work of combining two gates into one. Based on a three-level model driven by laser pulses, we show that any single-qubit holonomic gate can be realized by varying the detuning, amplitude, and phase of lasers. Our scheme is compatible with previously proposed nonadiabatic holonomic two-qubit gates, combining with which the arbitrary holonomic one-qubit gates can play universal nonadiabatic holonomic quantum computation. We also investigate the effects of some unavoidable realistic errors on our scheme.