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Engineering Higher-order Effective Hamiltonians

Jiahui Chen, David Cory

Abstract

Advancing quantum technologies requires precise and robust coherent control of quantum systems. Robust higher-order Hamiltonian engineering is essential for high-precision control and for accessing effective dynamics absent at zeroth order. Here, we introduce a systematic methodology for achieving the precision, robustness, and complexity required for quantum control through the engineering of higher-order processes and effective Hamiltonians. We identify the minimal subspace of achievable effective Hamiltonian at each order and provide universal cost functions for achieving desired targets. Examples include robust sequences for decoupling, three-body interactions and detuning/interaction correlations.

Engineering Higher-order Effective Hamiltonians

Abstract

Advancing quantum technologies requires precise and robust coherent control of quantum systems. Robust higher-order Hamiltonian engineering is essential for high-precision control and for accessing effective dynamics absent at zeroth order. Here, we introduce a systematic methodology for achieving the precision, robustness, and complexity required for quantum control through the engineering of higher-order processes and effective Hamiltonians. We identify the minimal subspace of achievable effective Hamiltonian at each order and provide universal cost functions for achieving desired targets. Examples include robust sequences for decoupling, three-body interactions and detuning/interaction correlations.
Paper Structure (13 sections, 55 equations, 10 figures, 1 algorithm)

This paper contains 13 sections, 55 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Engineering zeroth-order average Hamiltonians
  3. General method for Engineering $\bar{H}^{(r-1)}$
  4. Total cost function
  5. Engineering $\bar{H}^{(r-1)}$ on qubit networks
  6. Examples
  7. Decoupling
  8. Engineering 3-body Hamiltonian
  9. Correlation spectroscopy through first-order effective Hamiltonians
  10. Discussion and outlook
  11. Conclusion
  12. Correlated $\mathscr C$-integrals
  13. Performance comparison of decoupling sequences

Figures (10)

  • Figure 1: Nonisomorphic parameter graphs associated with Magnus terms.
  • Figure 2: Networks with different topology and the parameter graphs that need to be considered for $\bar{H}^{(2)}$. From left to right: qubit pairs, nearest-neighbor chain, square lattice, and all-to-all ensemble. Only the parameter graphs with no loops are shown here.
  • Figure 3: Control parameters of the sequences (a) $P_\rho$ and (b) $P_\text{uni}$.
  • Figure 4: Autocorrelation of $\rho_0=\sum_{i=1}^N\sigma_x^i$ under different sequences. The results are obtained from simulations with a 6-qubit ensemble, averaged over 100 realizations.
  • Figure 5: Control parameters of the sequences (a) $P_{xyz}$ and (b) $P_\text{cross}$.
  • ...and 5 more figures