Correction of Arbitrary Field Errors in Population Inversion of Quantum Systems by Universal Composite Pulses

Genov, Genko T.; Schraft, Daniel; Halfmann, Thomas; Vitanov, Nikolay V.

doi:10.1103/physrevlett.113.043001

Cited by 129 publications

(155 citation statements)

References 26 publications

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“…Hence, with regard to the diagonal elements U kk , the DR sequence for qutrits (13) is The rephasing error (infidelity) is defined as the distance between the actual propagator and the desired identity matrix,…”

Section: Effects Of Finite Pulse Durationmentioning

confidence: 99%

“…,N) can be rephased in a similar manner as the two-, three-, and four-state systems above with a set of free-evolution intervals sandwiched by π pulses applied on the transition between two of the N states at a time. The DR sequences can be built by starting with the sequence π jk τ π jk and then prepend or append π pulses on new pairs of states until all states (for N even) or all states but one (for N odd) (13) in Fig. 4(c) vs the rephasing pulse width T .…”

Section: Rephasing Sequences For Quditsmentioning

confidence: 99%

“…Another important development is the concept of robust DD sequences [10], which are resilient to pulse errors. In the first type of robust DD sequences, the single π pulses are replaced by composite pulses [11,12] as in a recent experiment in doped solids [13] by adiabatic pulses [14] or by a combination of them-composite adiabatic pulses [15,16]. In the second type of robust DD, the sequences are made inherently robust to pulse errors by using the relative phases between the π pulses [10], the simplest example being the XY -4 sequence, and the best performer is the Knill's DD sequence [10,17].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical rephasing of ensembles of qudits

Vitanov

2015

Phys. Rev. A

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Dynamical decoupling is an established tool for protecting the quantum state of a qubit from decoherence. This paper extends the simplest dynamical decoupling technique for qubits-the Carr-Purcell-Meiboom-Gill's two-pulse rephasing sequence-to qudits with an arbitrary number of states. The pulse sequences introduced here are particularly well suited for dynamical rephasing of the collective coherence of inhomogeneously broadened ensembles of atomic qudits.

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Section: Effects Of Finite Pulse Durationmentioning

confidence: 99%

Section: Rephasing Sequences For Quditsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical rephasing of ensembles of qudits

Vitanov

2015

Phys. Rev. A

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“…We make no assumptions about Ω(t) and ∆ (p) (t), which may vary for the different qubits. The dynamics of a qubit due to a pulse is described by a propagator U pulse , which connects the density matrices of the system at the initial and final times t ı and t f : ρ(t f ) = U pulse ρ(t ı )U † pulse and can be parametrized [15] as…”

mentioning

confidence: 99%

“…A phase shift φ in the Rabi frequency, Ω(t) → Ω(t)e ıφ , is imprinted in U pulse as β → β + φ [15][16][17]. The phase φ is assumed the same for every qubit (unlike β), which is usually experimentally feasible.…”

mentioning

confidence: 99%

Arbitrarily Accurate Pulse Sequences for Robust Dynamical Decoupling

et al. 2017

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We introduce universally robust sequences for dynamical decoupling, which simultaneously compensate pulse imperfections and the detrimental effect of a dephasing environment to an arbitrary order, work with any pulse shape, and improve performance for any initial condition. Moreover, the number of pulses in a sequence grows only linearly with the order of error compensation. Our sequences outperform the state-of-the-art robust sequences for dynamical decoupling. Beyond the theoretical proposal, we also present convincing experimental data for dynamical decoupling of atomic coherences in a solid-state optical memory.Introduction.-Quantum technologies are increasingly important nowadays for a multitude of applications in sensing, processing, and communication of information. Nevertheless, protection of quantum systems from unwanted interactions with the environment remains a major challenge. Dynamical decoupling (DD) is a widely used approach that aims to do this by nullifying the average effect of the unwanted qubit-environment coupling through the application of appropriate sequences of pulses [1][2][3][4].Most DD schemes focus on dephasing processes because they have maximum contribution to information loss in many systems, e.g., in nuclear magnetic resonance and quantum information [5,6]. Then, the major limitation to DD are pulse imperfections whose impact often exceeds the effect of the perturbations from the environment [6][7][8]. Some sequences, e.g., the widely used Carr-Purcell-Meiboom-Gill (CPMG) sequence, work efficiently for specific quantum states only [6,9]. Robust sequences for any state with limited error compensation have been demonstrated experimentally, e.g., XY4 (PDD), Knill DD (KDD) [6]. Composite pulses, designed for static errors, were also recently shown to be robust to time-dependent non-Markovian noise up to a noise frequency threshold [10]. A common feature of most robust DD sequences so far is pulse error compensation in one or two parameters only (flip angle error, detuning). High fidelity error compensation has been proposed, e.g., by nesting of sequences, but only at the price of a very fast growth in the number of pulses [6].In this Letter, we describe a general theoretical procedure to derive universally robust (UR) DD sequences that compensate pulse imperfections in any experimental parameter (e.g., variations of pulse shapes or intensities), and the effect of a slowly changing environment to an arbitrary order in the permitted error. We note that the term universal is applied for pulse errors. The UR sequences work at high efficiency for any initial condition. The number of pulses for higher order error compensation grows only linearly with the order of the residual error. The concept works for arbitrary pulse shapes. Our only assumptions are identical pulses in a sequence and

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Robust Quantum State Manipulation by Composite Pulses in Five‐Level Systems

Wang,

Shi,

Chen

et al. 2024

Adv Quantum Tech

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A scheme is proposed for achieving robust population inversion in five‐level systems by means of composite pulses. An example of such a system consists of the magnetic sublevels with angular momenta and . Through elaborately constructing the relative phases of pulse pairs, the composite sequences perform well in suppressing the uncorrelated pulse area errors. In particular, the five pulse‐pair sequence possesses good robustness and a short evolution time. The composite sequences are further designed to compensate for a single type of pulse area errors to any desired order. This work provides a high‐efficiency way for robust quantum state manipulation in five‐level systems.

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Correction of Arbitrary Field Errors in Population Inversion of Quantum Systems by Universal Composite Pulses

Cited by 129 publications

References 26 publications

Dynamical rephasing of ensembles of qudits

Dynamical rephasing of ensembles of qudits

Arbitrarily Accurate Pulse Sequences for Robust Dynamical Decoupling

Robust Quantum State Manipulation by Composite Pulses in Five‐Level Systems

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