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Physical Review B

Simultaneous SU(2) rotations on multiple quantum dot exciton qubits using a single shaped pulse

Reuble Mathew, Hong Yi Shi Yang, Kimberley C. Hall

Published Oct 8, 2015• 5 citations
Publisher

Abstract

Recent experimental demonstration of a parallel $(\ensuremath{\pi},2\ensuremath{\pi})$ single qubit rotation on excitons in two distant quantum dots [Nano Lett. 13, 4666 (2013)] is extended in numerical simulations to the design of pulses for more general quantum state control, demonstrating the feasibility of full SU(2) rotations of each exciton qubit. Our results show that simultaneous high-fidelity quantum control is achievable within the experimentally accessible parameter space for commercial Fourier-domain pulse shaping systems. The identification of a threshold of distinguishability for the two quantum dots (QDs) for achieving high-fidelity parallel rotations, corresponding to a difference in transition energies of $\ensuremath{\sim}0.25\phantom{\rule{4pt}{0ex}}\mathrm{meV}$, points to the possibility of controlling more than 10 QDs with a single shaped optical pulse.

DOI
10.1103/physrevb.92.155306

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Nano Letters•Sep 3, 2013•24 citations
Recent experimental demonstration of a parallel (\ensuremathπ,2\ensuremathπ)(\ensuremath{\pi},2\ensuremath{\pi})(\ensuremathπ,2\ensuremathπ) single qubit rotation on excitons in two distant quantum dots [Nano Lett. 13, 4666 (2013)] is extended in numerical simulations to the design of pulses for more general quantum state control, demonstrating the feasibility of full SU(2) rotations of each exciton qubit. Our results show that simultaneous high-fidelity quantum control is achievable within the experimentally accessible parameter space for commercial Fourier-domain pulse shaping systems. The identification of a threshold of distinguishability for the two quantum dots (QDs) for achieving high-fidelity parallel rotations, corresponding to a difference in transition energies of \ensuremath∼0.25meV\ensuremath{\sim}0.25\phantom{\rule{4pt}{0ex}}\mathrm{meV}\ensuremath∼0.25meV, points to the possibility of controlling more than 10 QDs with a single shaped optical pulse.
Shaped ultrafast pulses designed for controlled-rotation (C-ROT) operations on exciton qubits in semiconductor quantum dots are demonstrated using a quantum control apparatus operating at ∼1 eV. Optimum pulse shapes employing amplitude and phase shaping protocols are implemented using the output of an optical parametric oscillator and a programmable pulse shaping system, and characterized using autocorrelation and multiphoton intrapulse interference phase scan techniques. We apply our pulse characterization results and density matrix simulations to assess the fundamental limits on the fidelity of the C-ROT operation, providing a benchmark for the evaluation of sources of noise in other quantum control experiments. Our results indicate the effectiveness of pulse shaping techniques for achieving high fidelity quantum operations in quantum dots with a gate time below 1 ps.
Semiconductor quantum dots have been featured in a number of proposals for quantum computing because of the advantages afforded by confinement on the nanoscale, such as well separated, discrete energy levels and ease of optical manipulation. In addition, they can leverage established semiconductor fabrication techniques and, like the quantum dots used in this work, can be designed to match the telecommunication band, improving the scalability and potential integration of the platform into existing technologies. This thesis work applied optical pulse engineering to manipulate exciton qubits in self-assembled InAs quantum dots. Optimal quantum control theory was used to design pulse shapes that implement high fidelity single-qubit and two-qubit operations, with constraints on the numerical optimization that ensure that the pulses can be accurately implemented using a commercial 4f pulse shaper. In the case of single-qubit operations, the results showed that two uncoupled qubits can be manipulated in parallel using a single phase-shaped laser pulse, provided their optoelectronic properties are sufficiently different. It was demonstrated that targeted differences in inversion and phase between the qubits can be achieved on an ultrafast timescale with high fidelity. In the case of two-qubit operations, the controlled-rotation gate was optimized using amplitude-only and phase-only pulse shaping schemes. The shaped pulses for both schemes were shown to produce higher fidelity operations. The ability to implement robust state inversion on short timescales is particularly useful for technologies such as ultrafast optical switches, single-photon sources, and entangled-photon sources. This work has demonstrated state inversion in a single InAs quantum dot via adiabatic rapid passage using linearly chirped laser pulses. The achieved gate times were an order of magnitude shorter than previous demonstrations. Theoretical predictions of the dependence of the inversion efficiency of the exciton on the sign of the pulse chirp were also verified experimentally, allowing for the identification of phonon-mediated dephasing as the dominant source of decoherence.
Abstract Femtosecond pulse shaping provides a means to tailor the interaction of light with matter, enabling the optimization of optical control processes and the achievement of a target final quantum state of the matter system. While this approach has found widespread application in the control of atomic and molecular systems, its use for solid state quantum systems remains in its infancy. This review covers our application of this approach to the manipulation of the quantum states of excitons in semiconductor quantum dots (QDs). The achievement of simultaneous π, 2π rotations on excitons in two different QDs using a single engineered infrared pulse illustrates the flexibility of the pulse shaping approach for solid state quantum systems. This versatility is further explored through simulations that show the feasibility of arbitrary SU(2) control of several quantum dots. Shaping of femtosecond infrared control pulses enables the demonstration of adiabatic rapid passage in a single QD on a subpicosecond time scale, representing a substantial speedup and an important step towards the realization of dynamical decoupling. The dependence of the exciton inversion efficiency on the sign of pulse chirp confirms the role of (and ability to control) phonon‐related dephasing. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Pulse-shaping protocols for subpicosecond optically controlled quantum gates in semiconductor quantum dots are reported. Our emphasis is the development of shaping schemes for either amplitude or phase control of the pulse that are easily implemented using commercial pulse shapers and femtosecond laser systems. We illustrate the efficacy of our approach through simulations of a controlled-rotation gate in a realistic In(Ga)As quantum dot with electronic structure calculated using eight-band, strain-dependent $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ theory. Our results show that amplitude- and phase-shaping protocols both lead to substantial improvements in fidelity when compared with transform-limited pulses with equivalent gate times. Dephasing was found to have a minimal effect on the gate fidelities due to the ultrafast time scale of the quantum operations.
In optimal quantum control (OQC), a target quantum state of matter is achieved by tailoring the phase and amplitude of the control Hamiltonian through femtosecond pulse-shaping techniques and powerful adaptive feedback algorithms. Motivated by recent applications of OQC in quantum information science as an approach to optimizing quantum gates in atomic and molecular systems, here we report the experimental implementation of OQC in a solid-state system consisting of distinguishable semiconductor quantum dots. We demonstrate simultaneous high-fidelity π and 2π single qubit gates in two different quantum dots using a single engineered infrared femtosecond pulse. These experiments enhance the scalability of semiconductor-based quantum hardware and lay the foundation for applications of pulse shaping to optimize quantum gates in other solid-state systems.