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Physical Review A

Universal nonadiabatic geometric gates protected by dynamical decoupling

X. Wu, P. Z. Zhao

Published Sep 29, 2020• 23 citations
Publisher

Abstract

Dynamical decoupling provides an effective method to protect nonadiabatic geometric quantum computation against environment-induced decoherence. Although some dynamical-decoupling-protected nonadiabatic geometric gates were proposed, they need to combine some other dynamical gates to perform universal quantum computation. In this paper we propose a scheme to realize a universal set of dynamical-decoupling-protected nonadiabatic geometric gates, which not only possesses the resilience to environment-induced decoherence but also allows us to perform universal quantum computation all by geometric operations.

DOI
10.1103/physreva.102.032627

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Dynamical decoupling provides an effective method to protect nonadiabatic geometric quantum computation against environment-induced decoherence. Although some dynamical-decoupling-protected nonadiabatic geometric gates were proposed, they need to combine some other dynamical gates to perform universal quantum computation. In this paper we propose a scheme to realize a universal set of dynamical-decoupling-protected nonadiabatic geometric gates, which not only possesses the resilience to environment-induced decoherence but also allows us to perform universal quantum computation all by geometric operations.
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.
Nonadiabatic geometric quantum computation protected by dynamical decoupling combines the robustness of nonadiabatic geometric gates and the decoherence-resilience feature of dynamical decoupling. Solid-state systems provide an appealing candidate for the realization of nonadiabatic geometric quantum computation protected dynamical decoupling since the solid-state qubits are easily embedded in electronic circuits and scaled up to large registers. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian, which not only combines the merits of nonadiabatic geometric gates and dynamical decoupling but also can be realized in a number of solid-state systems, such as superconducting circuits and quantum dots.
The main obstacles to the realization of high-fidelity quantum gates are the control errors arising from inaccurate manipulation of a quantum system and the decoherence caused by the interaction between the quantum system and its environment. Nonadiabatic holonomic quantum computation allows for high-speed implementation of whole-geometric quantum gates, making quantum computation robust against control errors. Dynamical decoupling provides an effective method to protect quantum gates against environment-induced decoherence, regardless of collective decoherence or independent decoherence. In this paper, we put forward a protocol of nonadiabatic holonomic quantum computation protected by dynamical decoupling. Due to the combination of nonadiabatic holonomic quantum computation and dynamical decoupling, our protocol not only possesses the intrinsic robustness against control errors but also protects quantum gates against environment-induced decoherence.
Dynamical decoupling is a promising approach to protect quantum information from decoherence. It averages out the noise by flipping the qubits. In this paper, we demonstrate the protection of geometric gates by using dynamical decoupling with trapped ions. Specifically, a universal set of geometric gates is proposed with trapped ions and these gates are commutative with the decoupling group of the system. Our scheme combines the robust advantages of quantum holonomies and dynamical decoupling and hence can combat both control errors and decoherence. We also investigate the effects of dynamical decoupling pulse errors on the proposed geometric 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.
Geometric phases depend only on the evolution path determined by the closed circuit in the projective Hilbert space but not on evolution details of the quantum system, leading to geometric quantum computation possessing some intrinsic robustness against control errors. Coordinated with dynamical decoupling, geometric quantum computation admits additional resilience to the environment-induced decoherence. However, the previous schemes of geometric quantum computation protected by dynamical decoupling require multiple physical qubits to encode a logical qubit, which undoubtedly increases the consumption of physical-qubit resources and the difficulty in the implementation of the logical-qubit manipulation based on physical-qubit driving. In this work, we put forward a scheme of decoherence-mitigated geometric quantum computation based only on physical qubits rather than logical qubits, hence avoiding the additional overhead of physical-qubit resources for logical-qubit encoding as well as the difficulty in the manipulation of logical qubits. Moreover, our scheme focuses on the most general interaction between an individual qubit and its environment so that it mitigates not just dephasing noise but rather regular decoherence. Our proposal thus represents a more realistic and effective approach towards the realization of geometric control with decoherence mitigation.