Time-optimal control of a dissipative qubit

Lin, Chungwei; Sels, Dries; Wang, Yebin

doi:10.1103/physreva.101.022320

Cited by 29 publications

(41 citation statements)

References 53 publications

(68 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10and (13) gives the c-Hamiltonian for systems having both unitary and dissipative dynamics. In principle, optimal control solutions can be found by iteratively solving for the (co)-state, extracting the switching function and updating the controls [40]. The downside is that one has to explicitly propagate the density matrix and its costates.…”

Section: Density Matrix Formulation and Pontryagin's Maximum Prinmentioning

confidence: 99%

“…Using the formalism developed in Ref. [40], the optimal controls, switching functions, and c-Hamiltonians for both problems are given in Fig. 1; these solutions are referred to as the "exact" solutions and will be served as the reference for comparison.…”

Section: A Single Qubit Problemmentioning

confidence: 99%

“…Pontryagin's Maximum Principle (PMP) [36][37][38][39] is a powerful formalism in classical control theory, and it has been applied to quantum state preparation [28,40], non-adiabatic quantum computation [41,42]. Due to the linearity of Schrödinger's equation, PMP implies the time-optimal control typically has the so called bang-bang form (the control takes its extreme values); the bang-bang form puts strong constraints on the structure of optimal solutions and is found to be the case in some problems [28,41,43].…”

Section: Introductionmentioning

confidence: 99%

“…For general quantum problems, however, the optimal control often includes a singular part [40,42,44,45], which makes PMP less informative about the solution. While one can in principle explicitly solve for the behavior one the singular arcs [40], such analysis is restricted to small systems as it quickly becomes intractable. The main usefulness of PMP thus appears to be numerical: first, it provides an efficient way to compute the gradient of the terminal cost function; second, PMP gives the necessary conditions for an optimal solution which can be used to check the quality of any numerical solutions.…”

Section: Introductionmentioning

confidence: 99%

“…A bang control corresponds to non-zero Φ (dotted curves) whereas a singular control to the vanishing Φ. The exact optimal controls (dashed curves) are obtained using the formalism developed in Ref [40]…”

mentioning

confidence: 99%

See 4 more Smart Citations

Stochastic optimal control formalism for an open quantum system

Lin

Sels

et al. 2020

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing the density matrix. Specifically, the proper dynamical update rules are presented for the stochastic costate variables introduced by Pontryagin's maximum principle and restrictions on the form of the terminal cost function are discussed. The proposed procedure is confirmed by comparing the results to those obtained from optimal control on Lindbladian dynamics. Numerically, the proposed formalism becomes time and memory efficient for large systems, and it can be generalized to describe non-Markovian dynamics.

show abstract

Section: Density Matrix Formulation and Pontryagin's Maximum Prinmentioning

confidence: 99%

Section: A Single Qubit Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Stochastic optimal control formalism for an open quantum system

Lin

Sels

et al. 2020

Phys. Rev. A

Self Cite

View full text Add to dashboard Cite

show abstract

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

Stefanatos

Paspalakis

2021

Quantum Inf Process

View full text Add to dashboard Cite

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.

show abstract

Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates

Volkov¹,

Моржин²,

Pechen³

2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Mathematical analysis of quantum control landscapes, which aims to prove either absence or existence of traps for quantum control objective functionals, is an important topic in quantum control. In this work, we provide a rigorous analysis of quantum control landscapes for ultrafast generation of single-qubit quantum gates and show, combining analytical methods based on a sophisticated analysis of spectrum of the Hessian, and numerical optimization methods such as gradient ascent pulse engineering, differential evolution, and dual annealing, that control landscape for ultrafast generation of phase shift gates is free of traps.

show abstract

Time-optimal control of a dissipative qubit

Cited by 29 publications

References 53 publications

Stochastic optimal control formalism for an open quantum system

Stochastic optimal control formalism for an open quantum system

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

Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates

Contact Info

Product

Resources

About