Felix Motzoi

Optimal control methods for rapidly time-varying Hamiltonians

In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.

Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator

In qubits made from a weakly anharmonic oscillator the leading source of error at short gate times is leakage of population out of the two dimensional Hilbert space that forms the qubit. In this paper we develop a general scheme based on an adiabatic expansion to find pulse shapes that correct this type of error. We find a family of solutions that allows tailoring to what is practical to implement for a specific application. Our result contains and improves the previously developed DRAG technique [F. Motzoi, et. al., Phys. Rev. Lett. 103, 110501 (2009)] and allows a generalization to other non-linear oscillators with more than one leakage transition.

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:

Improving frequency selection of driven pulses using derivative-based transition suppression

Many techniques in quantum control rely on frequency separation as a means for suppressing unwanted couplings. In its simplest form, the mechanism relies on the low bandwidth of control pulses of long duration. Here we perform a higher-order quantum-mechanical treatment that allows for higher precision and shorter times. In particular, we identify three kinds of off-resonant effects: i) simultaneous unwanted driven couplings (e.g. due to drive crosstalk), ii) additional (initially undriven) transitions such as those in an infinite ladder system, and iii) sideband frequencies of the driving waveform such as we find in corrections to the rotating wave approximation. With a framework that is applicable to all three cases, in addition to the known adiabatic error responsible for a shift of the energy levels we typically see in the spectroscopy of such systems, we derive error terms in a controlled expansion corresponding to higher order adiabatic effects and diabatic excitations. We show, by also expanding the driving waveform in a basis of different order derivatives of a trial function (typically a Gaussian) these different error terms can be corrected for in a systematic way hence strongly improving quantum control of systems with dense spectra.

High-fidelity Rydberg quantum gate via a two-atom dark state

A modified Rydberg blockade gate that employs adiabatic following of a two-atom dark state is proposed. The scheme is resilient to the uncertainty in the interaction strength and can be employed to achieve fault-tolerant quantum computation with neutral atoms.

Simultaneous gates in frequency-crowded multilevel systems using fast, robust, analytic control shapes

We present a few-parameter ansatz for pulses to implement a broad set of simultaneous single-qubit rotations in frequency-crowded multilevel systems. Specifically, we consider a system of two qutrits whose working and leakage transitions suffer from spectral crowding (detuned by

Continuous joint measurement and entanglement of qubits in remote cavities

\delta

Charting the circuit QED design landscape using optimal control theory

). In order to achieve precise controllability, we make use of two driving fields (each having two quadratures) at two different tones to implement arbitrary simultaneous rotations. Expanding the waveforms in terms of Hanning windows, we show how analytic pulses containing smooth and composite-pulse features can easily achieve gate errors less than

Deterministic generation of remote entanglement with active quantum feedback

10^{-4}

High-fidelity quantum gates in the presence of dispersion

and considerably outperform known adiabatic techniques. Moreover, we find a generalization of the WahWah method by Schutjens et al. [Phys. Rev. A 88, 052330 (2013)] that allows precise separate single-qubit rotations for all gate times beyond a quantum speed limit. We find in all cases a quantum speed limit slightly below