Exploring the level sets of quantum control landscapes

Rothman, Adam E.; Ho, Tak‐San; Rabitz, Herschel

doi:10.1103/physreva.73.053401

Cited by 68 publications

(62 citation statements)

References 24 publications

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“…Two terminal times, T = π and T = 10, are studied, with t = π/499, and the length of the space domain is L = 20, with x = L/299. Optimization is performed with the D-MORPH algorithm [30][31][32] using the gradient forms in Eqs. (11) and (12).…”

Section: Cos(α(x)) − Cos(ω V T)sin(α(x))mentioning

confidence: 99%

Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls

2016

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Bose-Einstein condensates (BECs) offer the potential to examine quantum behavior at large length and time scales, as well as forming promising candidates for quantum technology applications. Thus, the manipulation of BECs using control fields is a topic of prime interest. We consider BECs in the mean-field model of the Gross-Pitaevskii equation (GPE), which contains linear and nonlinear features, both of which are subject to control. In this work we report successful optimal control simulations of a one-dimensional GPE by modulation of the linear and nonlinear terms to stimulate transitions into excited coherent modes. The linear and nonlinear controls are allowed to freely vary over space and time to seek their optimal forms. The determination of the excited coherent modes targeted for optimization is numerically performed through an adaptive imaginary time propagation method. Numerical simulations are performed for optimal control of mode-to-mode transitions between the ground coherent mode and the excited modes of a BEC trapped in a harmonic well. The results show greater than 99% success for nearly all trials utilizing reasonable initial guesses for the controls, and analysis of the optimal controls reveals primarily direct transitions between initial and target modes. The success of using solely the nonlinearity term as a control opens up further research toward exploring novel control mechanisms inaccessible to linear Schrödinger-type systems.

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Section: Cos(α(x)) − Cos(ω V T)sin(α(x))mentioning

confidence: 99%

Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls

2016

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“…Using the D-MORPH algorithm [35][36][37], J is minimized below some target tolerance δ tol given the default tol=1e-7 property, and will proceed through a number of optimization steps dictated by slen property. The slen property is related to the number of optimization steps, but does not necessarily equal the maximum number of iterations.…”

Section: The Optimalcontrol Subclassmentioning

confidence: 99%

PEET: a Matlab tool for estimating physical gate errors in quantum information processing systems

Hocker

Kosut

Rabitz

2016

Quantum Inf Process

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A Physical Error Estimation Tool (PEET) is introduced in Matlab for predicting physical gate errors of quantum information processing (QIP) operations by constructing and then simulating gate sequences for a wide variety of user-defined, Hamiltonian-based physical systems. PEET is designed to accommodate the interdisciplinary needs of quantum computing design by assessing gate performance for users familiar with the underlying physics of QIP, as well as those interested in higherlevel computing operations. The structure of PEET separates the bulk of the physical details of a system into Gate objects, while the construction of quantum computing gate operations are contained in GateSequence objects. Gate errors are estimated by Monte Carlo sampling of noisy gate operations. The main utility of PEET, though, is the implementation of QuantumControl methods that act to generate and then test gate sequence and pulse-shaping techniques for QIP performance. This work details the structure of PEET and gives instructive examples for its operation.

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“…Applications of DMORPH include the continuous variation of a Hamiltonian while preserving or optimizing the value of a quantum-mechanical observable [67,72] and exploring the level sets of state and unitary control [58,69,73]. DMORPH can also be used as direct optimization technique [74].…”

Section: Hybrid Quantum Control: Decoupling-pulse Criteria + Optimentioning

confidence: 99%

Optimized pulses for the control of uncertain qubits

et al. 2012

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Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2-and π-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian.Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2-and π-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

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Exploring the level sets of quantum control landscapes

Cited by 68 publications

References 24 publications

Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls

Optimal nonlinear coherent mode transitions in Bose-Einstein condensates utilizing spatiotemporal controls

PEET: a Matlab tool for estimating physical gate errors in quantum information processing systems

Optimized pulses for the control of uncertain qubits

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