Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of Quantum State Transfer

TL;DR

This paper introduces an iterative algorithm for simulating n-qubit Hamiltonian dynamics by decomposing the unitary evolution into manageable unitaries, demonstrated through NMR experiments on quantum state transfer.

Contribution

The paper presents a novel iterative decomposition algorithm for simulating Hamiltonian dynamics and experimentally validates it using NMR for quantum state transfer.

Findings

Algorithm effectively decomposes complex unitaries into simpler gates.

Experimental NMR implementation confirms the viability of the decomposition.

Resilience of quantum state transfer to static errors demonstrated.

Abstract

We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The algorithm product-decomposes $U$ in a chosen operator basis by identifying a certain symmetry of $U$ that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the $n$-qubit Quantum State Transfer unitary by Di Franco et. al. (Phys. Rev. Lett. 101, 230502 (2008)) that transports quantum information from one end of a spin chain to the other; and then implement it in Nuclear Magnetic Resonance to demonstrate that the decomposition is experimentally viable and well-scaled. We furthur experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.