Amplification of quadratic Hamiltonians

Christian Arenz1, Denys I. Bondar2, Daniel Burgarth3, Cecilia Cormick4, and Herschel Rabitz1

1Frick Laboratory, Princeton University, Princeton NJ 08544, United States
2Tulane University, New Orleans, LA 70118, United States
3Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia
4Instituto de Física Enrique Gaviola, CONICET and Universidad Nacional de Córdoba, Ciudad Universitaria, X5016LAE, Córdoba, Argentina

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Abstract

Speeding up the dynamics of a quantum system is of paramount importance for quantum technologies. However, in finite dimensions and without full knowledge of the details of the system, it is easily shown to be $impossible$. In contrast we show that continuous variable systems described by a certain class of quadratic Hamiltonians can be sped up without such detailed knowledge. We call the resultant procedure $\textit{Hamiltonian amplification}$ (HA). The HA method relies on the application of local squeezing operations allowing for amplifying even unknown or noisy couplings and frequencies by acting on individual modes. Furthermore, we show how to combine HA with dynamical decoupling to achieve amplified Hamiltonians that are free from environmental noise. Finally, we illustrate a significant reduction in gate times of cavity resonator qubits as one potential use of HA.

Our ability to leverage quantum phenomena in future technologies will rely on approaches for operating on sufficiently fast time scales. However, the dynamics of quantum systems composed of qubits cannot be accelerated beyond an intrinsic limit without full knowledge of and full control over the system parameters. We address this issue by showing that this is no longer true for continuous variable systems such as quantum harmonic oscillators, thereby introducing a new route for the manipulation of quantum system time scales. Consequently, uncertain and noisy couplings in the system, including those between qubits coupled via quantum harmonic oscillators, can be enhanced by locally acting on individual system components.

We show that a large class of Hamiltonians quadratic in the position and momentum operators can generically be amplified by local parametric drives without knowing the parameter details of the Hamiltonian. By combining our findings with dynamical decoupling, we achieve a generic speed up of the evolution a quantum system while decoherence coming from the interaction with the environment is suppressed. Even though such amplification does not work for system only composed of qubits, we demonstrate how the implementation of quantum logical gates in hybrid quantum systems can be sped up through the developed amplification scheme

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Cited by

[1] Wenchao Ge, "Hamiltonian Amplification: Another Application of Parametric Amplification", Quantum Views 4, 41 (2020).

[2] S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, and D. T. C. Allcock, "Quantum amplification of mechanical oscillator motion", Science 364 6446, 1163 (2019).

[3] David Trillo, Benjamin Dive, and Miguel Navascues, "Translating Uncontrolled Systems in Time", arXiv:1903.10568.

[4] Wenchao Ge, Brian Sawyer, Joe Britton, Kurt Jacobs, John Bollinger, and Michael Foss-Feig, "Trapped Ion Quantum Information Processing with Squeezed Phonons", arXiv:1807.00924, Physical Review Letters 122 3, 030501 (2018).

[5] Hoi-Kwan Lau and Aashish A. Clerk, "High-fidelity bosonic quantum state transfer using imperfect transducers and interference", npj Quantum Information 5, 31 (2019).

[6] Wenchao Ge, Brian C. Sawyer, Joseph W. Britton, Kurt Jacobs, Michael Foss-Feig, and John J. Bollinger, "Stroboscopic approach to trapped-ion quantum information processing with squeezed phonons", Physical Review A 100 4, 043417 (2019).

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