Amplification of quadratic Hamiltonians

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 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.

Quantum amplification of mechanical oscillator motion

“…This amplification technique can enhance measurement sensitivity in protocols that use phase-stable displacements, such as photon-recoil spectroscopy (26,27), where the phase of momentum kicks from photon absorption can be controlled by modulating the photon source. Our method can be extended to amplify displacements of unknown frequency or phase, following the recent proposal in (28). The parametric modulation used for squeezing can also be combined with a spindependent force to enhance phonon-mediated spin-spin interactions (28,29), which are used to create entanglement in quantum simulation and quantum information processing experiments.…”

“…Our method can be extended to amplify displacements of unknown frequency or phase, following the recent proposal in (28). The parametric modulation used for squeezing can also be combined with a spindependent force to enhance phonon-mediated spin-spin interactions (28,29), which are used to create entanglement in quantum simulation and quantum information processing experiments. Our methods are also applicable to the generation of exotic nonclassical motional states and to continuous-variable quantum information processing (30).…”

Translating Uncontrolled Systems in Time

“…That is, in order to effect the transformation |ψ 1 → U (T 1 ) |ψ 1 , with T 1 > 0, then one needs to invest, at least, time T 1 . That fast-forward is impossible for unknown Hamiltonians was already established in [10,11,12] (note that fast-forward is possible, though, for controlled systems under the promise that the Hamiltonian belongs to a family of quadratic polynomials of the canonical operators [13]). In this regard, we show that such nogo results also extend to scenarios where we allow for arbitrarily small probabilities of success.…”

Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency

“…Quantum squeezing has been investigated as a valuable tool in amplifying interaction strength to speed up quantum dynamics for alleviating decoherence [9,29,30]. It has been shown that squeezing operators can amplify a coherent state through parametric modulation on the potential [9,29].…”