Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems

Buterakos, Donovan; Sarma, Sankar Das; Barnes, Edwin

doi:10.1103/prxquantum.2.010341

Cited by 37 publications

(32 citation statements)

References 73 publications

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“…[47], it was shown that arbitrary, noise-resistant single-qubit gates can be obtained using this method. The SCQC formalism has been further extended to multi-level systems and to multiple noise sources and time-dependent noise [58][59][60][61][62][63]. We note in passing that other geometric reverse-engineering approaches to error-correcting control have also been devised based on alternative parameterizations of the evolution operator [64,65].…”

Section: Landau-zener Transitions and Geometric Formalismmentioning

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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Section: Landau-zener Transitions and Geometric Formalismmentioning

confidence: 99%

Noise-resistant Landau-Zener sweeps from geometrical curves

Zhuang

Zeng

Economou

et al. 2022

Quantum

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“…In Ref. [96], it was discovered that a geometric structure also underlies the Schrödinger equation for multi-level and multi-qubit systems. These more general cases have a geometric interpretation in terms of curves in higher dimensions.…”

Section: Space Curve Formalism For Multi-level and Multi-qubit System...mentioning

confidence: 99%

“…In Ref. [96], it was shown that the multi-dimensional SCQC formalism described above can be used to design noisecancelling pulses for an important class of two-qubit problems. This class includes systems in which the two qubits 13 are coupled via an Ising-like interaction, as is the case for superconducting transmon qubits in the dispersive regime [97][98][99][100][101][102] and also for capacitively coupled or exchange-coupled singlet-triplet spin qubits in semiconductor quantum dots [103][104][105][106][107][108].…”

Section: B Noise-cancellation In Multi-qubit Quantum Gatesmentioning

confidence: 99%

Dynamically corrected gates from geometric space curves

Barnes¹,

Calderon-Vargas²,

Dong³

et al. 2021

Preprint

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Quantum information technologies demand highly accurate control over quantum systems. Achieving this requires control techniques that perform well despite the presence of decohering noise and other adverse effects. Here, we review a general technique for designing control fields that dynamically correct errors while performing operations using a close relationship between quantum evolution and geometric space curves. This approach provides access to the global solution space of control fields that accomplish a given task, facilitating the design of experimentally feasible gate operations for a wide variety of applications.

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“…A more complex study would be to apply this method to coupled spins system, similarly to Ref. [67] for state to state control problems.…”

Section: Discussionmentioning

confidence: 99%

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

Van Damme,

Sugny,

Glaser

2021

Preprint

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We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.

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Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems

Cited by 37 publications

References 73 publications

Noise-resistant Landau-Zener sweeps from geometrical curves

Noise-resistant Landau-Zener sweeps from geometrical curves

Dynamically corrected gates from geometric space curves

Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

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