Generation of arbitrary qubit states by adiabatic evolution split by a phase jump

Abstract

We propose a technique for accurate, flexible and robust generation of arbitrary coherent superpositions of two quantum states. It uses a sequence of two adiabatic pulses split by a phase jump serving as a control parameter. Each pulse has a chirped detuning, which induces a half crossing, and acts as a $\pi /2$ pulse in the adiabatic regime. The phase jump is imprinted onto the population ratio of the created superposition state. Of the various possible relations between the two pulses, we select the case when the Rabi frequency and the detuning of the second pulse are mirror images of those of the first pulse, and the two detunings have opposite signs. Then the mixing angle of the superposition state depends on the phase jump only. For other arrangements, the superposition mixing angle is shifted by the dynamic phases of the propagators, which makes these cases suitable for state tomography. This twin setup comes along with the advantage that it reduces the error $\epsilon$ of each individual pulse down to $4{\epsilon }^2$ overall. Therefore, the proposed technique combines the benefits of robustness stemming from adiabatic evolution with accuracy generated by the twin-pulse error suppression, and flexibility of the superposition state controlled by the phase jump $\varphi$. In addition, we present a simple exactly soluble trigonometric model in order to illustrate the proposed technique. In this model, when the pulse area $A$ increases the nonadiabatic oscillations are damped as $A^{-1}$ for a single pulse and $A^{-2}$ for the two-pulse sequence. Finally, the proposed technique is extended to sequences of $N=2^n$ pulses by concatenating $\pi /2$ sequences and splitting them by a phase jump, thereby further reducing the nonadiabatic error $\epsilon$ to $(2\epsilon {)}^N$. This makes the proposed technique suitable for generating high-fidelity quantum rotation gates.

arXiv comment10 pages, 4 figures

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• Robust transitionless quantum driving: Concatenated approach
• Extension of the Morris-Shore transformation to arbitrary time-dependent driving fields
• Efficiency of optimal control for noisy spin qubits in diamond