New method of quantum dynamics simulation based on the quantum tomography

Bohdan Yavorskyy

Thiago O. Maciel, Reinaldo O. Vianna

We develop a quantum process tomography method, which variationally reconstruct the map of a process, using noisy and incomplete information about the dynamics. The new method encompasses the most common quantum process tomography schemes. It is based on the variational quantum tomography method (VQT) proposed by Maciel \emph{et al.} in arXiv:1001.1793[quant-ph] \cite{VQT}.

Dafa Zhao, Chao Wei, Shunzhong Xue +7 more

Developments of quantum techniques have drastically improved the control ability of current quantum processors. Characterizing quantum simulations performed on these processors has become a vital topic in quantum information processing. Traditional characterizing techniques such as quantum process and state tomography fully characterize quantum simulations, but always with the exponentially increased resource cost, unfortunately. It may place their applications only in small-scale quantum systems. Meanwhile, many potential characterizing methods have been put forward in the past decades. In this work we experimentally test and compare different methods for characterizing quantum simulations of Ising Hamiltonians on the nuclear magnetic resonance (NMR) platform, including the recent quantum Hamiltonian tomography with polynomial complexity to estimate the generator of quantum simulations and nonrepetitive direct fidelity estimation with the Monte Carlo method to estimate the fidelity of dynamical states. We also experimentally estimate the parameters of Hamiltonian via full quantum process tomography and quantum state tomography for the comparison. These methods have merits and demerits in accuracy, the required resource, and prior knowledge. Our experiments test the performance of different methods while providing a beneficial reference for characterizing quantum simulations in the future.

Giacomo Mauro D’Ariano, Lorenzo Maccone

Giacomo Mauro D’Ariano, Matteo G. A. Paris, Massimiliano Federico Sacchi

Jincheng Zhang

Quantum simulation of dynamical systems offers a promising approach to tackling complex problems in various fields, including physics, chemistry, and biology. However, simulating these systems often faces significant computational challenges due to the exponential scaling of traditional methods. This paper introduces a novel technique, quantum state tomography, for efficiently simulating dynamical systems with reduced dimensionality, addressing the computational bottleneck and enhancing feasibility. We demonstrate the technique's effectiveness through the simulation of a simplified, yet illustrative, example, showcasing improved accuracy and reduced computational cost compared to existing methods. This advancement holds the potential to unlock new possibilities in simulating complex systems and provides a foundation for future research in quantum simulation.