Michael H. Goerz

Optimized production of ultracold ground-state molecules: Stabilization employing potentials with ion-pair character and strong spin-orbit coupling

We discuss the production of ultracold molecules in their electronic ground state by photoassociation employing electronically excited states with ion-pair character and strong spin-orbit interaction. A short photoassociation laser pulse drives a nonresonant three-photon transition for alkali-metal atoms colliding in their lowest triplet state. The excited-state wave packet is transferred to the ground electronic state by a second laser pulse, driving a resonant two-photon transition. After analyzing the transition matrix elements governing the stabilization step, we discuss the efficiency of population transfer using transform-limited and linearly chirped laser pulses. Finally, we employ optimal control theory to determine the most efficient stabilization pathways. We find that the stabilization efficiency can be increased by one and two orders of magnitude when using linearly chirped and optimally shaped laser pulses, respectively.

The quantum speed limit of optimal controlled phasegates for trapped neutral atoms

We study controlled phasegates for ultracold atoms in an optical potential. A shaped laser pulse drives transitions between the ground and electronically excited states where the atoms are subject to a long-range 1/R 3 interaction. We fully account for this interaction and use optimal control theory to calculate the pulse shapes. This allows us to determine the minimum pulse duration, respectively, gate time T that is required to obtain high fidelity. We accurately analyse the speed limiting factors, and we find the gate time to be limited either by the interaction strength in the excited state or by the ground state vibrational motion in the trap. The latter needs to be resolved by the pulses in order to fully restore the motional state of the atoms at the end of the gate. (Some figures in this article are in colour only in the electronic version)

Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: Comparison of gradient-ascent-pulse-engineering and Krotov optimization schemes

We study optimal quantum control of the dynamics of trapped Bose-Einstein condensates: The targets are to split a condensate, residing initially in a single well, into a double well, without inducing excitation, and to excite a condensate from the ground state to the first-excited state of a single well. The condensate is described in the mean-field approximation of the Gross-Pitaevskii equation. We compare two optimization approaches in terms of their performance and ease of use; namely, gradient-ascent pulse engineering (GRAPE) and Krotov’s method. Both approaches are derived from the variational principle but differ in the way the control is updated, additional costs are accounted for, and second-order-derivative information can be included. We find that GRAPE produces smoother control fields and works in a black-box manner, whereas Krotov with a suitably chosen step-size parameter converges faster but can produce sharp features in the control fields.

Robustness of high-fidelity Rydberg gates with single-site addressability

High-fidelity controlled-phase gates based on the Rydberg blockade have been studied and their robustness with respect to noise and experimental inaccuracies in pulse timings and amplitudes using both analytic and numerically optimized pulses have been investigated.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Optimal control theory for a unitary operation under dissipative evolution

We show that optimizing a quantum gate for an open quantum system requires the time evolution of only three states irrespective of the dimension of Hilbert space. This represents a significant reduction in computational resources compared to the complete basis of Liouville space that is commonly believed necessary for this task. The reduction is based on two observations: the target is not a general dynamical map but a unitary operation; and the time evolution of two properly chosen states is sufficient to distinguish any two unitaries. We illustrate gate optimization employing a reduced set of states for a controlled phasegate with trapped atoms as qubit carriers and a iW AP S gate with superconducting qubits.

Optimizing for an arbitrary perfect entangler. I. Functionals

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capableofcreatingamaximallyentangledstateoutofsomeinitialproductstate.Thefunctionaldepends oneasily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.

Optimizing for an arbitrary perfect entangler. II. Application

Author(s): Goerz, MH; Gualdi, G; Reich, DM; Koch, CP; Motzoi, F; Whaley, KB; Vala, J; Muller, MM; Montangero, S; Calarco, T | Abstract:

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a geometric phase gate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov’s method yields considerably better results than either one of the two methods alone.

Charting the circuit QED design landscape using optimal control theory

With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an efficient operating regime. Using state-of-the-art quantum optimal control techniques, we exhaustively explore the landscape for creation and removal of entanglement over a wide range of design parameters. We identify an optimal operating region outside of the usually considered strongly dispersive regime, where multiple sources of entanglement interfere simultaneously, which we name the quasi-dispersive straddling qutrits regime. At a chosen point in this region, a universal gate set is realized by applying microwave fields for gate durations of 50 ns, with errors approaching the limit of intrinsic transmon coherence. Our systematic quantum optimal control approach is easily adapted to explore the parameter landscape of other quantum technology platforms.Quantum computers: global sweet spot for superconducting circuit designThe optimal working regime for so-called transmon qubits exploits a subtle interplay of interaction and quantum interference. Their flexibility in design places superconducting qubits among the hottest contestants in the current race for a quantum computer. Researchers from the University of Kassel, Germany, and the University of California at Berkeley have used optimal control techniques to map out the full range of design parameters with which a superconducting circuit of two transmission-line-coupled qubits can be engineered. Each parameter point was analyzed for its ability to support all the operations required for a universal quantum computer, and the optimum is found in a regime where the qubits straddle each other. These results will guide the design choices for a superconducting quantum computer operating at maximum speed and precision.