Dynamically corrected gates from geometric space curves

Barnes, Edwin; Calderon-Vargas, F. A.; Dong, Wenzheng; Li, Bikun; Zeng, Junkai; Zhuang, Fei

doi:10.1088/2058-9565/ac4421

Cited by 17 publications

(17 citation statements)

References 177 publications

(282 reference statements)

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“…1 If robustness at a certain noise frequency is defined by a vanishing filter function value, robustness against static detuning noise (i.e., at ω = 0) is equivalent to having the position vector trace a closed three-dimensional curve whose curvature κ is given by . Such a geometric interpretation has been noted previously in the literature [52][53][54][55][56][57][58].…”

Section: Dynamical Invariantssupporting

confidence: 80%

Reverse engineering of one-qubit filter functions with dynamical invariants

Colmenar

Kestner

2022

Phys. Rev. A

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We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.

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Section: Dynamical Invariantssupporting

confidence: 80%

Reverse engineering of one-qubit filter functions with dynamical invariants

Colmenar

Kestner

2022

Phys. Rev. A

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“…Thus r(t) can be interpreted as a curve in R 3 for which time is the arc length. This is the starting point of the SCQC formalism [44]. Achieving first-order noise robustness requires A 1 (T ) = 0 ⇒ r(T ) = 0, or equivalently, the curve r must be closed.…”

Section: Landau-zener Transitions and Geometric Formalismmentioning

confidence: 99%

“…In this paper, we present a general method for designing noise-resistant LZ sweeps through avoided crossings. We do this by leveraging a recently developed geometric formalism for designing noise-resistant quantum control called Space Curve Quantum Control (SCQC) [44][45][46][47]. This approach utilizes a surprising connection between the evolution of a qubit and geometric curves in two or three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Noise-resistant Landau-Zener sweeps from geometrical curves

Zhuang

Zeng

Economou

et al. 2022

Quantum

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Landau-Zener physics is often exploited to generate quantum logic gates and to perform state initialization and readout. The quality of these operations can be degraded by noise fluctuations in the energy gap at the avoided crossing. We leverage a recently discovered correspondence between qubit evolution and space curves in three dimensions to design noise-robust Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is purely noise-induced, we prove that operations based on monotonic sweeps cannot be robust to noise. Hence, we design families of phase gates based on non-monotonic drives that are error-robust up to second order. In the general case where there is an avoided crossing even in the absence of noise, we present a general technique for designing robust driving protocols that takes advantage of a relationship between the Landau-Zener problem and space curves of constant torsion.

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“…Because we can perform any logic operations using this, it provides the instruments for geometric quantum computation. This is a promising approach to achieve robust control of a quantum system (Barnes et al, 2022;Tan et al, 2014;Zhuang et al, 2021).…”

Section: B Universal Single-and Two-qubit Controlmentioning

confidence: 99%

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

Ivakhnenko¹,

Shevchenko²,

Nori³

2022

Preprint

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H. Comparison of different methods IV. Interferometry A. Superconducting circuits B. Semiconductor quantum dots C. Donors and impurities (atomic qubits) D. Graphene E. Microscopic systems F. Other systems G. Multilevel systems V. Quantum control A. Coherent control of microscopic and mesoscopic structures B. Universal single-and two-qubit control C. Shortcuts to adiabaticity D. Adiabatic quantum computation VI. Related classical coherent phenomena VII. Conclusion 1. With near-adiabatic limit (Landau) 2. With parabolic cylinder functions (Zener) 3. With contour integrals (Majorana) 4. With WKB approximation and phase integral method (Stückelberg) 5. Duration of the LZSM transition B. Description of a periodically driven two-level system 1. Adiabatic-impulse model a. Adiabatic evolution b. Multiple-passage evolution 2. Rotating-wave approximation (RWA) 3. Floquet theory 4. Rate equation and white noise approach a. Transition rate b. Rate equation c. From Bessel to Airy d. Double-passage regime ReferencesAbbreviations and most-often-used symbols Because this review article is quite long, for the readers' convenience, we present the main abbreviations used. This list also includes some of the topics covered.

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Dynamically corrected gates from geometric space curves

Cited by 17 publications

References 177 publications

Reverse engineering of one-qubit filter functions with dynamical invariants

Reverse engineering of one-qubit filter functions with dynamical invariants

Noise-resistant Landau-Zener sweeps from geometrical curves

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

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