Soft-pulse dynamical decoupling with Markovian decoherence

Pryadko, Leonid P.; Quiroz, Gregory

doi:10.1103/physreva.80.042317

Cited by 21 publications

(20 citation statements)

References 62 publications

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“…While hard π pulses commute with the relaxation superoperator, sequences of soft pulses can modify the structure of the relaxation and in particular, redistribute relaxation rates between different channels preserving the combination of 2γ 1 + γ 2 [57].…”

Section: Sequence Design a Dynamical Decoupling Basicsmentioning

confidence: 99%

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

Pryadko

2014

Phys. Rev. A

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We describe how a universal set of dynamically-corrected quantum gates can be implemented using sequences of shaped decoupling pulses on any qubit network forming a sparse bipartite graph with always-on Ising interactions. These interactions are constantly decoupled except when they are needed for two-qubit gates. We analytically study the error operators associated with the constructed gates up to third order in the Magnus expansion, analyze these errors numerically in the unitary time evolution of small qubit clusters, and give a bound on high-order errors for qubits on a large square lattice. We prove that with a large enough toric code the present gate set can be used to implement fault-tolerant quantum memory.

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Section: Sequence Design a Dynamical Decoupling Basicsmentioning

confidence: 99%

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

Pryadko

2014

Phys. Rev. A

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“…Then for an even number of equal-duration QED cycles, the no-relaxation evolution (36) will be compensated exactly (as in the uncollapsing procedure [29,31,32,35]), and the QED infidelity 1 − F qed will be only due to the contribution from P all . (The use of π-pulses resembles dynamical decoupling of the "bang-bang" type [36]; however, the resemblance is accidental, since dynamical decoupling cannot protect against the energy relaxation [37]. )…”

Section: Discussionmentioning

confidence: 99%

Simplified quantum error detection and correction for superconducting qubits

Keane

Korotkov

2012

Phys. Rev. A

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We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive N -qubit codes cannot be used for quantum error correction, but can be used for quantum error detection. In the latter case it is sufficient to use only two qubits for the encoding. In the analysis we demonstrate a useful technique of unraveling the qubit energy relaxation into "relaxation" and "no relaxation" scenarios. Also, we propose and numerically analyze several two-qubit algorithms for quantum error detection/correction, which can be readily realized at the present-day level of the phase qubit technology.

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“…For example, figure 3(b) shows a CAFE (3,5,2) × 2 sequence. The advantages of symmetrizing or antisymmetrizing sequences using similar methods are well established in decoupling; for an early treatment from NMR see [35] and for a more recent discussion, see [21].…”

Section: Piecing Together Sequences: Splice and Invertmentioning

confidence: 99%

“…Early studies of always-on DD arose in the problem of dipolar decoupling in solid-state NMR [20], culminating from substantial work in extending pulsed decoupling techniques to 'soft', or low-power, pulses. A modern consideration of this problem in the quantum information context is found in [21]. More recently, optimal control approaches to customizing continuous, bounded controls to decouple a specific but arbitrary noise bath were considered in [22][23][24].…”

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confidence: 99%

Dynamical decoupling of a qubit with always-on control fields

2012

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We consider dynamical decoupling schemes in which the qubit is continuously manipulated by a control field at all times. Building on the theory of the Uhrig dynamical decoupling (UDD) sequence and its connections to Chebyshev polynomials, we derive a method of always-on control by expressing the UDD control field as a Fourier series. We then truncate this series and numerically optimize the series coefficients for decoupling, constructing the Chebyshev and Fourier expansion sequence. This approach generates a bounded, continuous control field. We simulate the decoupling effectiveness of our sequence versus a continuous version of UDD for a qubit coupled to fullyquantum and semi-classical dephasing baths and find comparable performance. We derive filter functions for continuous-control decoupling sequences, and we assess how robust such sequences are to noise on control fields. The methods we employ provide a variety of tools to analyze continuous-control dynamical decoupling sequences. 4. Decoupling a qubit from a quantum bath 13 5. Filter function analysis 16 6. Decoupling a qubit from Born-Markov classical baths 18 7. Conclusion 20 Acknowledgments 20 Appendix A. Proof that Fourier series components do not affect 'sine'-like DD constraints 20 Appendix B. Derivation of filter function for continuous sequences 22 References 23simple solution to this problem: by applying a determined sequence of control pulses, one can significantly enhance the lifetime of a qubit. Early work in DD sought to suppress decoherence by applying a periodic sequence of instantaneous 'bang-bang' pulses, which periodically flip the state of a qubit and undo the coupling to the bath [12][13][14][15]. This work was extended to Hamiltonian engineering by using decoupling sequences to selectively enable coupling Hamiltonians [16,17]. Subsequently, attention turned to using Eulerian graphs to design sequences using bounded control operations that were robust to many types of systematic control errors [18]. This led to the notion of dynamically-corrected gates [19], which combine techniques from DD and composite pulse sequences from NMR to produce error-suppressing quantum gates.The idealized 'bang-bang' control pulse is instantaneous, like the Dirac delta function. However, real physical pulses can only approximate 'bang-bang' control, because such idealized control would require infinite power. The implications of a real, continuous-time function can be significant. Most DD sequences are designed to correct noise errors between pulses, but offer no intrinsic protection to errors during pulses. Early studies of always-on DD arose in the problem of dipolar decoupling in solid-state NMR [20], culminating from substantial work in extending pulsed decoupling techniques to 'soft', or low-power, pulses. A modern consideration of this problem in the quantum information context is found in [21]. More recently, optimal control approaches to customizing continuous, bounded controls to decouple a specific but arbitrary noise bath were considered in [22][2...

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Soft-pulse dynamical decoupling with Markovian decoherence

Cited by 21 publications

References 62 publications

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault tolerance with the toric code

Simplified quantum error detection and correction for superconducting qubits

Dynamical decoupling of a qubit with always-on control fields

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