Hamiltonian Tomography by Dynamical Decoupling

Alexandre M. Souza

Vladimir I. Man’ko, Liubov A. Markovich

Jared H. Cole

Abstract To harness the power of controllable quantum systems for information processing or quantum simulation, it is essential to be able to accurately characterise the system's Hamiltonian. Although in principle this requires determining less parameters than full quantum process tomography, a general and extendable method for reconstructing a general Hamiltonian has been elusive. In their recent paper, Wang et al (2015 New J. Phys. 17 093017 ) apply dynamical decoupling to the problem of Hamiltonian tomography and show how to reconstruct a general many-body Hamiltonian comprised of arbitrary interactions between qubits.

Sheng-Tao Wang, Dong-Ling Deng, L-M Duan

Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body Hamiltonian with arbitrary long-range interactions, provided the energy density of the Hamiltonian remains finite. Different from quantum process tomography, our scheme is fully scalable with the number of qubits as the required rounds of measurements increase only linearly with the number of coupling terms in the Hamiltonian. The scheme makes use of synchronized dynamical decoupling pulses to simplify the many-body dynamics so that the unknown parameters in the Hamiltonian can be retrieved one by one. We simulate the performance of the scheme under the influence of various pulse errors and show that it is robust to typical noise and experimental imperfections.

Vladimir I. Man’ko

Mark Byrd, Daniel A. Lidar

Strong and fast ``bang-bang'' (BB) pulses have been recently proposed as a means for reducing decoherence in a quantum system. So far theoretical analysis of the BB technique relied on model Hamiltonians. Here we introduce a method for empirically determining the set of required BB pulses, that relies on quantum process tomography. In this manner an experimenter may tailor his or her BB pulses to the quantum system at hand, without having to assume a model Hamiltonian. In addition, the previous work has been extended to a general noiseless evolution via the stabilizer formalism.