Optimizing NMR quantum information processing via generalized transitionless quantum driving

Abstract

High performance quantum information processing requires efficient control of undesired decohering effects, which are present in realistic quantum dynamics. To deal with this issue, a powerful strategy is to employ transitionless quantum driving (TQD), where additional fields are added to speed up the evolution of the quantum system, achieving a desired state in a short time in comparison with the natural decoherence time scales. In this paper, we provide an experimental investigation of the performance of a generalized approach for TQD to implement shortcuts to adiabaticity in nuclear magnetic resonance (NMR). As a first discussion, we consider a single nuclear spin-1 2 system in a time-dependent rotating magnetic field. While the adiabatic dynamics is violated at a resonance situation, the TQD Hamiltonian is shown to be robust against resonance, allowing us to mimic the adiabatic behavior in a fast evolution even under the resonant configurations of the original (adiabatic) Hamiltonian. Moreover, we show that the generalized TQD theory requires less energy resources, with the strength of the magnetic field less than that required by standard TQD. As a second discussion, we analyze the experimental implementation of shortcuts to single-qubit adiabatic gates. By adopting generalized TQD, we can provide feasible time-independent driving Hamiltonians, which are optimized in terms of the number of pulses used to implement the quantum dynamics. The robustness of adiabatic and generalized TQD evolutions against typical decoherence processes in NMR is also analyzed.

Generalized transitionless quantum driving for open quantum systems

“…Generalized TQD can provide feasible time-independent TQD Hamiltonians, which can be applied to implement quantum gates through controlled evolutions and to speed up the dynamics of two-level atomic systems under Landau-Zener transitions [42]. Experimentally, generalized TQD has been used to design energy enhanced TQD microwave fields to implement shortcuts to adiabaticity in trapped ion system [33] and nuclear magnetic resonance [47].…”

Quantum adiabatic brachistochrone for open systems

“…In this regard, the equivalence of Lagrangians establishes conditions on the energy gaps to assert whether the dissipation will play a role on the brachistochrone, or if focusing on the Hamiltonian dynamics (and its relatively smaller dimension) is sufficient. Considering these points, the brachistochrone appears as a promising approach to optimize quantum information schemes, such as those found in trapped ions [16,38], and superconducting systems [39], for example.…”

Charging power and stability of always-on transitionless driven quantum batteries

“…where ||A|| HS = (Tr AA † ) 1/2 is the Hilbert-Schmidt norm of the operator A. We observe that Σ(τ ) has been used in experimental implementations of TQD in order to quantify the energy cost of simulating adiabatic and TQD evolutions [39,40]. Moreover, it has recently been shown in ref.…”