Quadratic dynamical decoupling: Universality proof and error analysis

Kuo, Wen Jui; Lidar, Daniel A.

doi:10.1103/physreva.84.042329

Cited by 42 publications

(56 citation statements)

References 53 publications

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“…The pioneering strategies for decoupling were introduced in the context of NMR spectroscopy [31]. Since then, many different decoupling sequences have been developed in the context of NMR [32,33,35,36] or QIP [44,46,47,50,53,54,81,97,98].…”

Section: Discussionmentioning

confidence: 99%

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Robust dynamical decoupling

Souza

Álvarez

Suter

2012

Phil. Trans. R. Soc. A.

177

194

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Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.

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Section: Discussionmentioning

confidence: 99%

“…This reduction comes at the expense of an extension of the cycle time by a factor of four. If the delays between the pulses are allowed to be non-equidistant like in UDD, it becomes possible to create hybrid sequences, such as CUDD [50] and QDD [53,97,98].…”

Section: (C) Dynamical Decoupling Sequences With Multiple Rotation Axesmentioning

confidence: 99%

Robust dynamical decoupling

Souza

Álvarez

Suter

2012

Phil. Trans. R. Soc. A.

177

194

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“…We found that the system-bath interaction term proportional to σ x is suppressed with UDD efficiency for all values of N 1 and N 2 [Eq. (35)]. The interactions proportional to σ z and σ y both exhibit parity effects [Eqs.…”

Section: Discussionmentioning

confidence: 99%

Quadratic dynamical decoupling with nonuniform error suppression

Quiroz

Lidar

2011

Phys. Rev. A

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We analyze numerically the performance of the near-optimal quadratic dynamical decoupling (QDD) singlequbit decoherence errors suppression method [J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is formed by nesting two optimal Uhrig dynamical decoupling sequences for two orthogonal axes, comprising N1 and N2 pulses, respectively. Varying these numbers, we study the decoherence suppression properties of QDD directly by isolating the errors associated with each system basis operator present in the system-bath interaction Hamiltonian. Each individual error scales with the lowest order of the Dyson series, therefore immediately yielding the order of decoherence suppression. We show that the error suppression properties of QDD are dependent upon the parities of N1 and N2, and near-optimal performance is achieved for general single-qubit interactions when N1 = N2.

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“…Recently, a preprint of closely related work by Kuo and Lidar [23] became available, with a different proof of the universality of QDD.…”

Section: Operationmentioning

confidence: 99%

Universal dynamical decoupling of multiqubit states from environment

Jiang

Imambekov

2011

Phys. Rev. A

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We study the dynamical decoupling of multiqubit states from environment. For a system of m qubits, the nested Uhrig dynamical decoupling (NUDD) sequence can efficiently suppress generic decoherence induced by the system-environment interaction to order N using (N + 1) 2m pulses. We prove that the NUDD sequence is universal, i.e., it can restore the coherence of an m-qubit quantum system independent of the details of the system-environment interaction. We also construct a general mapping between dynamical decoupling problems and discrete quantum walks in certain functional spaces. Dynamical decoupling (DD) is a powerful tool to protect quantum systems from decoherence induced by the inevitable system-environment interaction [1]. The idea of DD is to dynamically control the system (or environment) evolution to suppress the decoherence caused by interaction. For example, a static magnetic field with unknown magnitude B z σ z can induce dephasing of a qubit, but such dephasing can be fully eliminated by a spin flip σ x (i.e., Hahn echo) at half way of the evolution [2]. In practice, however, the Hahn echo only suppresses the dephasing to O(T 2 ) for total evolution time T , because the magnetic field may have complicated time dependence in both magnitude and orientation due to the evolution of the environment. Furthermore, if the environment consists of quantum degrees of freedom, it can become entangled with the system via the interaction. Hence it is a challenging task to design a universal DD scheme that can suppress decoherence to the desired order independent of the details of the system-environment interaction.One particularly interesting DD scheme is the concatenated DD (CDD), which has been shown to be universal for single qubits [3]. The limitation, however, is that the pulse number increases exponentially with the suppression order N [approximately 4 N pulses to suppress both bit-flip and dephasing processes to O(T N+1 )]. It is the discovery of the universality of the Uhrig DD (UDD) sequence [4][5][6][7][8] that makes the universal DD practically feasible. In contrast to the CDD's demand for exponentially many pulses [3], UDD uses only O(N) spin-flip pulses to suppress the dephasing processes to O(T N+1 ) [5,6]. The discovery of the UDD sequence has inspired many experimental efforts to further improve the coherence over a wide range of quantum systems, including trapped ions [9], electron spins [10], defect centers [10,11], quantum dots [12,13], and superconducting qubits [14]. However, UDD is restricted to pure dephasing errors of a single qubit. It is desirable to have an efficient DD scheme [with poly(N) pulses] to suppress both bit-flip and dephasing processes for multiple qubits to O (T N+1 ). Recently, the quadratic DD (QDD) scheme has been proposed [15], which uses (N + 1) 2 pulses to suppress both bitflip and dephasing errors of single qubits. As a generalization of QDD from a 1-qubit system to an m-qubit system, the nested UDD (NUDD) scheme has been proposed [16][17][18], which uses (N + 1) 2m...

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Quadratic dynamical decoupling: Universality proof and error analysis

Cited by 42 publications

References 53 publications

Robust dynamical decoupling

Robust dynamical decoupling

Quadratic dynamical decoupling with nonuniform error suppression

Universal dynamical decoupling of multiqubit states from environment

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