Quadratic dynamical decoupling with nonuniform error suppression

Quiroz, Gregory; Lidar, Daniel A.

doi:10.1103/physreva.84.042328

Cited by 20 publications

(47 citation statements)

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“…QDD N,N (where the inner and outer UDD sequences have the same decoupling order) was conjectured to suppress arbitrary qubit-bath coupling to order N by using O(N 2 ) pulses, an exponential improvement over all previously known DD schemes for general qubit decoherence [25]. This conjecture was based on numerical studies for N 6 [25], and these were recently extended to N 24 [40], in support of the conjecture. An early argument for the universality and performance of QDD (which below we refer to as "validity of QDD"), based on an extension of the UDD proof for time-independent Hamiltonian [31] to analytically time-dependent Hamiltonians [41], fell short of a proof since the effective Hamiltonian resulting from the inner UDD sequences in QDD is not analytic.…”

Section: Introductionmentioning

confidence: 88%

Quadratic dynamical decoupling: Universality proof and error analysis

Kuo

Lidar

2011

Phys. Rev. A

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We prove the universality of the generalized QDD N 1 N 2 (quadratic dynamical decoupling) pulse sequence for near-optimal suppression of general single-qubit decoherence. Earlier work showed numerically that this dynamical decoupling sequence, which consists of an inner Uhrig DD (UDD) and outer UDD sequence using N 1 and N 2 pulses, respectively, can eliminate decoherence to O(T N ) using O(N 2 ) unequally spaced "ideal" (zero-width) pulses, where T is the total evolution time and N = N 1 = N 2 . A proof of the universality of QDD has been given for even N 1 . Here we give a general universality proof of QDD for arbitrary N 1 and N 2 . As in earlier proofs, our result holds for arbitrary bounded environments. Furthermore, we explore the single-axis (polarization) error suppression abilities of the inner and outer UDD sequences. We analyze both the single-axis QDD performance and how the overall performance of QDD depends on the single-axis errors. We identify various performance effects related to the parities and relative magnitudes of N 1 and N 2 . We prove that using QDD N 1 N 2 decoherence can always be eliminated to O(T min{N 1 ,N 2 } ).

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Section: Introductionmentioning

confidence: 88%

Quadratic dynamical decoupling: Universality proof and error analysis

Kuo

Lidar

2011

Phys. Rev. A

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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%

“…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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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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“…A number of techniques are currently being developed to make reliable quantum computing possible in the presence of environmental noise. A relatively simple technique is dynamical decoupling (DD) [3][4][5][6][7][8][9][10][11][12][13][14][15], which uses sequences of control pulses applied to the system qubits. This technique does not require any overhead in terms of ancilla qubits and requires no additional types of control over those that are already needed for information processing.…”

Section: Introductionmentioning

confidence: 99%

Iterative rotation scheme for robust dynamical decoupling

2012

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The loss of quantum information due to interactions with external degrees of freedom, which is known as decoherence, remains one of the main obstacles for large-scale implementations of quantum computing. Accordingly, different measures are being explored for reducing its effect. One of them is dynamical decoupling (DD) which offers a practical solution because it only requires the application of control pulses to the system qubits. Starting from basic DD sequences, more sophisticated schemes were developed that eliminate higher-order terms of the system-environment interaction and are also more robust against experimental imperfections. A particularly successful scheme, called concatenated DD (CDD), gives a recipe for generating higher-order sequences by inserting lower-order sequences into the delays of a generating sequence. Here, we show how this scheme can be improved further by converting some of the pulses to virtual (and thus ideal) pulses. The resulting scheme, called (XY 4) n , results in lower power deposition and is more robust against pulse imperfections than the original CDD scheme.

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Quadratic dynamical decoupling with nonuniform error suppression

Cited by 20 publications

References 50 publications

Quadratic dynamical decoupling: Universality proof and error analysis

Quadratic dynamical decoupling: Universality proof and error analysis

Robust dynamical decoupling

Iterative rotation scheme for robust dynamical decoupling

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