Experimental implementation of an iterative quantum state transfer using NMR

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. We further 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.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. We further 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.

arXiv:0911.5467Physical Review AMar 14, 201216 citations

Quantum Computation with NMR

Jonathan A. Jones

WORLD SCIENTIFIC eBooksJan 1, 20012 citations

Quantum data bus in dipolar coupled nuclear spin qubits

Jingfu Zhang, Michael J. T. Ditty, Daniel Klaus Burgarth +6 more

We implement an iterative quantum state transfer exploiting the natural dipolar couplings in a spin chain of a liquid-crystal NMR system. During each iteration, a finite part of the amplitude of the state is transferred and, by applying an external operation on only the last two spins, the transferred state is made to accumulate on the spin at the end point. The transfer fidelity reaches one asymptotically through increasing the number of iterations. We also implement the inverted version of the scheme which can transfer an arbitrary state from the end point to any other position of the chain and entangle any pair of spins in the chain, acting as a full quantum data bus.We implement an iterative quantum state transfer exploiting the natural dipolar couplings in a spin chain of a liquid-crystal NMR system. During each iteration, a finite part of the amplitude of the state is transferred and, by applying an external operation on only the last two spins, the transferred state is made to accumulate on the spin at the end point. The transfer fidelity reaches one asymptotically through increasing the number of iterations. We also implement the inverted version of the scheme which can transfer an arbitrary state from the end point to any other position of the chain and entangle any pair of spins in the chain, acting as a full quantum data bus.

arXiv:0902.3719Physical Review AJul 16, 200920 citations

NMR Implementation of a Molecular Hydrogen Quantum Simulation with Adiabatic State Preparation

Jiangfeng Du, Nanyang Xu, Xinhua Peng +3 more

It is difficult to simulate quantum systems on classical computers, while quantum computers have been proved to be able to efficiently perform such kinds of simulations. We report an NMR implementation simulating the hydrogen molecule (H2) in a minimal basis to obtain its ground-state energy. Using an iterative NMR interferometer to measure the phase shift, we achieve a 45-bit estimation of the energy value. The efficiency of the adiabatic state preparation is also experimentally tested with various configurations of the same molecule.It is difficult to simulate quantum systems on classical computers, while quantum computers have been proved to be able to efficiently perform such kinds of simulations. We report an NMR implementation simulating the hydrogen molecule (H2) in a minimal basis to obtain its ground-state energy. Using an iterative NMR interferometer to measure the phase shift, we achieve a 45-bit estimation of the energy value. The efficiency of the adiabatic state preparation is also experimentally tested with various configurations of the same molecule.

Physical Review LettersJan 22, 2010274 citations

Principles and Demonstrations of Quantum Information Processing by NMR Spectroscopy

Timothy F. Havel, Shyamal S. Somaroo, Ching-Hsiang Tseng +1 more

arXiv:quant-ph/9812086Applicable Algebra in Engineering Communication and ComputingMay 1, 200025 citations

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. We further 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.