Optimal Robust Quantum Control by Inverse Geometric Optimization

Dridi, Ghassen; Liu, Kaipeng; Guérin, S.

doi:10.1103/physrevlett.125.250403

Cited by 61 publications

(37 citation statements)

References 30 publications

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“…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]. In this work, we focus on SCQC because of the simple geometrical interpretation of noise cancellation (closed curve) it affords and because of the direct connection between torsion and the energy gap ∆ (Eq.…”

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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“…The effective Hamiltonian obtained by the Floquet theory [45,46] possesses a RWA-like form. Thus it is compatible with most optimal control methods [28,34,[47][48][49][50][51][52][53][54] which have been applied under the RWA, such as the recently developed methods of super-robust geometric control [53] and doubly geometric quantum control [54]. The proposed protocol can avoid the negative effects caused by the counter-rotating (CR) interactions, including the Bloch-Siegert (BS) shift, which may shift the qubit transition frequency and induce additional systematic noise to the system.…”

mentioning

confidence: 86%

Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives

Chen¹,

Miranowicz²,

Chen³

et al. 2022

Preprint

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We propose a general approach to implement nonadiabatic geometric single-and two-qubit gates beyond the rotating wave approximation (RWA). This protocol is compatible with most optimal control methods used in previous RWA protocols; thus, it is as robust as (or even more robust than) the RWA protocols. Using counter-rotating effects allows us to apply strong drives. Therefore, we can improve the gate speed by 5-10 times compared to the RWA counterpart for implementing highfidelity (≥ 99.99%) gates. Such an ultrafast evolution (nanoseconds, even picoseconds) significantly reduces the influence of decoherence (e.g., the qubit dissipation and dephasing). Moreover, because the counter-rotating effects no longer induce a gate infidelity (in both the weak and strong driving regimes), we can achieve a higher fidelity compared to the RWA protocols. Therefore, in the presence of decoherence, one can implement ultrafast geometric quantum gates with ≥ 99% fidelities.

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“…[24] dissipation is ignored and the minimum transfer time optimal control problem is considered. Besides the above works, which use analytical or numerical optimal control methods to maximize STIRAP efficiency, several other methods, belonging in the family of shortcuts to adiabaticity [25], have been developed [26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Stefanatos

Paspalakis

2021

Quantum Inf Process

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We study the problem of maximizing population transfer efficiency in the STIRAP system for the case where the dissipation rate of the intermediate state is much higher than the maximum amplitude of the control fields. Under this assumption, the original three-level system can be reduced to a couple of equations involving the initial and target states only. We find the control fields which maximize the population transfer to the target state for a given duration T , without using any penalty involving the population of the lossy intermediate state, but under the constraint that the sum of the intensities of the pump and Stokes pulses is constant, so the total field has constant amplitude and the only control parameter is the mixing angle of the two fields. In the optimal solution the mixing angle changes in the bang-singular-bang manner, where the initial and final bangs correspond to equal instantaneous rotations, while the intermediate singular arc to a linear change with time. We show that the optimal angle of the initial and final rotations is the unique solution of a transcendental equation where duration T appears as a parameter, while the optimal slope of the intermediate linear change as well as the optimal transfer efficiency is expressed as functions of this optimal angle. The corresponding optimal solution recovers the counterintuitive pulse-sequence, with nonzero pump and Stokes fields at the boundaries. We also show with numerical simulations that transfer efficiency values close to the optimal derived using the approximate system can also be obtained with the original STIRAP system using dissipation rates comparable to the maximum control amplitude.

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Optimal Robust Quantum Control by Inverse Geometric Optimization

Cited by 61 publications

References 30 publications

Noise-resistant Landau-Zener sweeps from geometrical curves

Noise-resistant Landau-Zener sweeps from geometrical curves

Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives

Optimal shape of STIRAP pulses for large dissipation at the intermediate level

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