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Physical Review A

Protecting geometric gates by dynamical decoupling

Guofu Xu, Guilu Long

Published Aug 22, 2014• 71 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.90.022323

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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.
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.
We present a scheme to implement a universal set of quantum gates based on achievable interactions, and the gates can be protected against decoherences through dynamical-decoupling approach without encoding. By properly designing system evolutions, the desired system interactions commute with the elements forming dynamical decoupling pulses. Thus, the effect of decoherences can be eliminated by repeatedly applying the pulses, without noticeably affecting the system evolutions governed by the desired system interactions given small enough time interval between pulses. Moreover, due to the commutation between the elements forming the pulses and the desired system interactions, our scheme is resistant to different types of decoherences, and so not limited to specific decoherences. Our scheme also works well in the case that the desired system interactions cannot be achieved ideally due to imperfect control of system parameters, through the action of dynamical-decoupling pulses.
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.
We present a scheme to implement a universal set of quantum gates based on achievable interactions, and the gates can be protected against decoherence through a dynamical-decoupling approach without encoding. By properly designing system evolution, the desired system interactions commute with the elements forming dynamical decoupling pulses. Thus, the effect of decoherence can be eliminated by repeatedly applying the pulses, without noticeably affecting the system evolution governed by the desired system interactions given a small enough time interval between pulses. Moreover, due to the commutation between the elements forming the pulses and the desired system interactions, our scheme is resistant to different types of decoherence, and so not limited to specific decoherence. Our scheme also works well in the case that the desired system interactions cannot be achieved ideally due to imperfect control of system parameters, through the action of dynamical-decoupling pulses.