Prof. Fernando G. S. L. Brandao Profile

Prof. Fernando G. S. L. Brandao

at Caltech

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Publications (2)

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Proceedings Article | 2 March 2022 Presentation + Paper

Engineering Kerr-cat qubits for hardware efficient quantum error correction

Qian Xu, Harald Putterman, Joseph Iverson, Kyungjoo Noh, Oskar Painter, Fernando G. S. L. Brandao, Liang Jiang

Proceedings Volume 12015, 120150B (2022) https://doi.org/10.1117/12.2614832

KEYWORDS: Quantum communications, Control systems, Error analysis, Oscillators, Error control coding, Quantum efficiency, Quantum computing

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Stabilized cat qubits that possess biased noise channel with bit-flip errors exponentially smaller than phase-flip errors. Together with a set of bias-preserving (BP) gates, cat qubits are a promising candidate for realizing hardware efficient quantum error correction and fault-tolerant quantum computing. Compared to dissipatively stabilized cat qubits, the Kerr cat qubits can in principle support faster gate operations with higher gate fidelity, benefiting from the large energy gap that protects the code space. However, the leakage of the Kerr cats can increase the minor type of errors and compromise the noise bias. Both the fast implementation of gates and the interaction with environment can lead to such detrimental leakage if no sophisticated controls are applied. In this work, we introduce new fine-control techniques to overcome the above obstacles for Kerr cat qubits. To suppress the gate leakage, we use the derivative-based transition suppression technique to design derivative-based controls for the Kerr BP gates. We show that the fine-controlled gates can simultaneously have high gate fidelity and high noise bias and when applied to concatenated quantum error correction, can not only improve the logical error rate but also reduce resource overhead. To suppress the environment-induced leakage, we introduce colored single-photon dissipation, which can continuously cool the Kerr cats and suppress the minor errors while not enhancing the major errors.

Proceedings Article | 19 October 2017 Presentation

Irreducible private states (Conference Presentation)

Hanna Wojewódka, Fernando G. S. Brandao, Andrzej Grudka, Karol Horodecki, Michal Horodecki, Pawel Horodecki, Ravishankar Ramanathan, Maciej Stankiewicz

Proceedings Volume 10442, 1044202 (2017) https://doi.org/10.1117/12.2279120

KEYWORDS: Chromium, Probability theory, Physics

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The work concerns the problem of finding a protocol for randomness amplification secure against non-signaling adversary with polynomial number of devices, which allows for correlations between the device and the source of weak randomness. We focus on the epsilon-Santha-Vazirani sources, and provide two results in this direction. First we revisit the seminal protocol of R. Colbeck and R. Renner (CR protocol) of randomness amplification using Santha-Vazirani (SV) sources, and prove its security relaxing partially assumptions of independence between the devices and the source at a price of narrowed range of epsilon. The relaxation allows that the SV source can indicate as a final device from which randomness is taken choosen with uniform probability from the insecure devices. The proof of relaxation bases on the assumption which is a generalization of Santha-Vazirani condition - the SV condition for boxes: there does not exist a device such that given its inputs and outputs one can get to know the value of SV source by more than epsilon. Second, we prove security of the CR protocol allowing arbitrary correlations between SV source and device, up to the mentioned SV-box condition, and the assumption that the devices are not correlated with each other. We prove that if the final device chosen in the protocol was not secure, an independent tester could guess the value of SV source bits more than the SV-box condition allows. The strategy of a tester is to choose a random device out of the ones which do not satisfy condition of the Chain Bell inequality. The idea of the proof of the second result indicates that the CR protocol may be secure under attack which arbitrarily correlates SV with devices of arbitrary type, and is promising in studying this problem.

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