Robustness of composite pulses to time-dependent control noise

Kabytayev, Chingiz; Green, Todd; Khodjasteh, Kaveh; Biercuk, Michael J.; Viola, Lorenza; Brown, Kenneth R.

doi:10.1103/physreva.90.012316

Cited by 91 publications

(110 citation statements)

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“…We prove that cancellation and filtering are inequivalent notions, with highorder cancellation in the Magnus sense not implying highorder filtering in general, and with both notions being a priori equally significant for assessing the control performance. Our results provide a firm foundation for recent analyses where this inequivalence has manifested in the context of compositepulse and Walsh-modulated protocols [13,15], as well as a new perspective on dynamical error control strategies, with potential implications for quantum fault tolerance.Control-theoretic setting.-We consider a general finitedimensional open quantum system S coupled to an uncontrollable environment (bath) B, whose free evolution is described by a joint Hamiltonian of the form H(t) = H S + H SB (t), with respect to the interaction picture associated to the physical bath Hamiltonian H B . Open-loop control is introduced via a time-dependent Hamiltonian H ctrl (t) acting on S alone, with the controlled dynamics being represented in terms of an intended plus error component, namely, H(t) + H ctrl (t) ≡ arXiv:1408.3836v2 [quant-ph]…”

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confidence: 59%

“…the practical implication is that, in general, it is only meaningful to demand a high FO for a subset of the GFFs -e.g., those responsible for filtering the dominant noise contributions over a frequency range, that is, Φ [κ] large for some κ < ∞. Remarkably, within the validity of a first-order fidelity approximation, the distinction between CO and such "truncated" (κ = 2) FO has been already observed for well-known composite-pulse protocols [5]: e.g., so-called Solavay-Kitaev SK1 and Wimperis BB1 sequences for amplitude errors have same FO (= 1) despite being firstand second-order in the Magnus sense, respectively [13,15]. Likewise, Walsh-modulated logic gates with desired noisefiltering features against dephasing noise have been recently implemented in trapped-ion experiments [13].…”

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confidence: 78%

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General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

2014

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We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.PACS numbers: 03.67. Pp, 03.65.Yz, 03.67.Lx, 07.05.Dz Hamiltonian engineering via open-loop quantum control provides a versatile and experimentally validated framework for manipulating the dynamics of a broad class of open quantum systems [1]. Applications range from dynamical decoupling (DD), composite pulse sequences and dynamically corrected quantum gates (DCGs), to noise spectroscopy and quantum simulation -see e.g. [2][3][4][5][6][7][8] for recent contributions. In this context, generalized transfer filter function (FF) techniques motivated by control engineering are providing an increasingly important tool for understanding the dynamical response of the target system in Fourier space and for quantitatively analyzing the control performance [9][10][11][12]. In particular, this formalism has proved remarkably successful in predicting operational fidelities for a variety of control settings in recent trapped-ion experiments [13], as long as noise is sufficiently weak for low-order approximations to be viable.From a control-theory standpoint, a filtering approach to dynamical error suppression is desirable for a variety of reasons. Besides providing an open-loop counterpart to the transfer-function perspective that is central to both classical and quantum feedback networks [14], FF techniques allow, when available, for a substantially more efficient analysis of the underlying noisy dynamics than direct simulation [15,16]. Furthermore, unlike traditional time-dependent perturbative approaches (such as the Magnus expansion [1,17]), a frequency-space picture may open up new possibilities for tailoring control synthesis and optimization to specific spectral features of the noise. The existing FF framework suffers, however, from severe limitations. Even if formal expressions for gate fidelity may be given based on an infinite recursive hierarchy of generalized FFs [12], higher-order FFs become rapidly intractable. Thus, explicit calculations have largely focused thus far on single-qubit controlled dynamics in the presence of classical noise, by truncating this recursion to the lowest order and additionally exploiting Gaussian noise statistics. As...

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General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

2014

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“…Pulse optimization is common in NMR [17] and is also receiving increasing attention in quantum information [12,[18][19][20][21][22][23][24]. In contrast to these previous approaches, our optimization is specifically tailored to the ST-qubit system and includes not only the relevant physical effects but also the most important hardware constraints and the effect of high-frequency nonMarkovian noise.…”

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confidence: 99%

High-Fidelity Single-Qubit Gates for Two-Electron Spin Qubits in GaAs

et al. 2014

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Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency non-Markovian noise) and show theoretically that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.One well-established possibility to realize a qubit with electron spins in a semiconductor is to use the m s = 0 spin singlet and triplet states of two electrons as computational basis states [1]. In contrast to single electron spins this encoding allows for all-electrical qubit control. Very long coherence times of up to 200 µs [2], all aspects of single-qubit operation (e.g. initialization [3] and single-shot readout [4]) and a first two-qubit gate [5] have been demonstrated experimentally for such singlettriplet (ST) qubits in GaAs quantum dots. Universal single-qubit control was also shown [6] but subject to large uncharacterized errors. Limiting control error rates to ∼ 10 −3 is a crucial requirement for fault tolerant quantum computing with quantum error correction (QEC) [7][8][9]. Estimates based on coherence time measurements [2,10] indicate that very high gate fidelities should be possible for GaAs-based two-electron spin qubits. However, nonlinearities in the electric control and experimental constraints make the direct application of control methods such as Rabi driving difficult.Previous theoretical work has shown how universal control on the single-and two-qubit level can be achieved in the face of limited dynamic control range [11]. Additionally, gating sequences which are insensitive to slow (quasistatic) control fluctuations have been proposed for this qubit system [12][13][14][15]. While these proposals provide very useful conceptual guidance, a direct implementation will be impeded by experimental constraints such as finite pulse rise times and sampling rate of voltage pulses. Likewise, decoherence effects caused by charge noise [10] and nuclear spin fluctuations [16] have a significant effect.In this letter we use numerical pulse optimization to address the problems posed by systematic inaccuracies and decoherence. Pulse optimization is common in NMR [17] and is also receiving increasing attention in quantum information [12,[18][19][20][21][22][23][24]. In contrast to these previous approaches, our optimization is specifically tailored to the ST-qubit system and includes not only the relevant physical effects but also the most important hardware constraints and the effect of high-frequency nonMarkovian noise. We use experimentally determined parameters and noise spectra [10,16,25] to compute expected gate fidelities and find implementations with no systematic errors and optimized robustness to both slow and fas...

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“…Dynamical decoupling (DD) is an active (or error correcting) scheme, based on the repeated application of control pulses designed to coherently average out unwanted interactions with the environment 17,18 . Improvement against 1/f noise in single-qubit gates via DD [19][20][21][22][23][24][25][26] , composite pulses [27][28][29][30] , dynamically corrected gates 30,31 and quantum optimal control 32,33 , has been demonstrated. In superconducting qubits pulsed control has been exploited to reduce dephasing due to charge-and magnetic fluxnoise 8,[34][35][36][37][38][39][40][41] .…”

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confidence: 99%

High-fidelity two-qubit gates via dynamical decoupling of local1/fnoise at the optimal point

D’Arrigo¹,

Falci²,

Paladino³

2016

Phys. Rev. A

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We investigate the possibility to achieve high-fidelity universal two-qubit gates by supplementing optimal tuning of individual qubits with dynamical decoupling (DD) of local 1/f noise. We consider simultaneous local pulse sequences applied during the gate operation and compare the efficiencies of periodic, Carr-Purcell and Uhrig DD with hard π-pulses along two directions (π z/y pulses). We present analytical perturbative results (Magnus expansion) in the quasi-static noise approximation combined with numerical simulations for realistic 1/f noise spectra. The gate efficiency is studied as a function of the gate duration, of the number n of pulses, and of the high-frequency roll-off. We find that the gate error is non-monotonic in n, decreasing as n −α in the asymptotic limit, α ≥ 2 depending on the DD sequence. In this limit πz-Urhig is the most efficient scheme for quasi-static 1/f noise, but it is highly sensitive to the soft UV-cutoff. For small number of pulses, πz control yields anti-Zeno behavior, whereas πy pulses minimize the error for a finite n. For the current noise figures in superconducting qubits, two-qubit gate errors ∼ 10 −6 , meeting the requirements for fault-tolerant quantum computation, can be achieved. The Carr-Purcell-Meiboom-Gill sequence is the most efficient procedure, stable for 1/f noise with UV-cutoff up to gigahertz.

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Robustness of composite pulses to time-dependent control noise

Cited by 91 publications

References 55 publications

General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

High-Fidelity Single-Qubit Gates for Two-Electron Spin Qubits in GaAs

High-fidelity two-qubit gates via dynamical decoupling of local1/fnoise at the optimal point

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