Experimental quantum Hamiltonian identification from measurement time traces

Abstract

Identifying Hamiltonian of a quantum system is of vital importance for quantum information processing. In this Letter, we realized and benchmarked a quantum Hamiltonian identification algorithm recently proposed [Phys. Rev. Lett. 113, 080401 (2014)]. we realized the algorithm on liquid nuclear magnetic resonance quantum information processor using two different working media with different forms of Hamiltonian. Our experiment realized the quantum identification algorithm based on free induction decay signals. We also showed how to process data obtained in practical experiment. We studied the influence of decoherence by numerical simulations. Our experiments and simulations demonstrate that the algorithm is effective and robust. Introduction.-One critical task is to characterize a quantum system so that it can be used for quantum information processing tasks, such as quantum teleportation [1], quantum cryptography [2,3], quantum computation [4,5] and quantum metrology [6]. One way of fully characterizing a quantum system is doing quantum processing tomography (QPT). The QPT approach requires an exponential number of experiments, which makes it difficult to be realized for even a small sized quantum system [7][8][9][10].

Several recent developments in estimation and robust control of quantum systems

“…Some approaches have been developed for Hamiltonian identification. For example, a Hamiltonian identification method using measurement time traces has been proposed based on classical system identification theory [32] and it has also been used to experimentally identify the Hamiltonian in spin systems [33]. In [34], dynamical decoupling was employed for identifying parameters in the Hamiltonian.…”

Hamiltonian tomography by the quantum quench protocol with random noise

“…For example, a protocol involving time-dependent measurement records was theoretically proposed for Hamiltonian identification [20]. Later, it was realized experimentally on a liquid nuclear * aczerwin@umk.pl magnetic resonance quantum information processor [21]. Other approaches involve estimation of quantum Hamiltonians via compressive sensing [22] or by local measurements [23].…”

When can a local Hamiltonian be recovered from a steady state?

“…To verify the above devices, it's necessary to recover its Hamiltonian from the measured observables, which makes the Hamiltonian tomography become increasingly important in condensed matter physics and quantum computing. Given the practical value of Hamiltonian tomography and significant development of numerical methods of this task, several Hamiltonian tomography algorithms haven been implemented on real physical systems [33][34][35].…”