Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0503199 · Physical Review A

Simulation of Heisenberg XY interactions and realization of a perfect state transfer in spin chains using liquid nuclear magnetic resonance

Jingfu Zhang, Gui Lu Long, Wei Zhang, Zhiwei Deng, Wenzhang Liu, Zhiheng Lu

Published Jul 22, 2005• 109 citations
arXivHTMLPDF

Abstract

The three-spin chain with a Heisenberg $XY$ interaction is simulated in a three-qubit nuclear magnetic resonance quantum computer. The evolution caused by the $XY$ interaction is decomposed into a series of single-spin rotations and the $J$-coupling evolutions between the neighboring spins. The perfect state transfer algorithm proposed by Christandl et al.[Phys. Rev. Lett. 92, 187902 (2004)] is realized in the $XY$ chain.

DOI
10.1103/physreva.72.012331

Related papers

Implementation of the perfect state transfer speeded up by three- spin interactions using nuclear magnetic resonance

Jingfu Zhang, Xinhua Peng, Dieter Suter

The speed of perfect state transfer (PST) can be increased by the three- spin interactions in the spin XY chain. By decomposing the evolution of the spin XY chain with three- spin interactions into a series of single- spin rotations and the J- coupling evolutions between the neighboring spins, we simulate such a chain and implement the stepped-up PST using a nuclear magnetic resonance (NMR) quantum computer.

•Dec 25, 2005•0 citations

ENTANGLEMENT IN A 3-SPIN HEISENBERG-XY CHAIN WITH NEAREST-NEIGHBOR INTERACTIONS, SIMULATED IN AN NMR QUANTUM SIMULATOR

‎K‎. ‎R‎. ‎K‎. ‎Rao, Anil Kumar

The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.

arXiv:1109.1954•International Journal of Quantum Information•Jun 1, 2012•9 citations

Speedup of quantum-state transfer by three-qubit interactions: Implementation by nuclear magnetic resonance

Jingfu Zhang, Xinhua Peng, Dieter Suter

Universal quantum information processing requires single-qubit rotations and two-qubit interactions as minimal resources. A possible step beyond this minimal scheme is the use of three-qubit interactions. We consider such three-qubit interactions and show how they can reduce the time required for a quantum state transfer in an $XY$ spin chain. For the experimental implementation, we use liquid-state nuclear magnetic resonance, where three-qubit interactions can be implemented by sequences of radio-frequency pulses.

arXiv:quant-ph/0512229•Physical Review A•Jun 19, 2006•29 citations

Speedup of quantum-state transfer by three-qubit interactions

Dieter Suter, Jingfu Zhang, Xinhua Peng

Universal quantum information processing requires single-qubit rotations and two-qubit interactions as minimal resources. A possible step beyond this minimal scheme is the use of three-qubit interactions. We consider such three-qubit interactions and show how they can reduce the time required for a quantum state transfer in an XY spin chain. For the experimental implementation, we use liquid-state nuclear magnetic resonance, where three-qubit interactions can be implemented by sequences of radio-frequency pulses.

•Jun 19, 2006•14 citations

Quantum Simulations by NMR : Applications to Small Spin Chains and Ising Spin Systems

‎K‎. ‎R‎. ‎K‎. ‎Rao

Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital…

•Jan 1, 2017•0 citations

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

Ashok Ajoy, Rama K. Kamineni, Anil Kumar +1 more

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:0911.5467•Physical Review A•Mar 14, 2012•16 citations
The three-spin chain with a Heisenberg XYXYXY interaction is simulated in a three-qubit nuclear magnetic resonance quantum computer. The evolution caused by the XYXYXY interaction is decomposed into a series of single-spin rotations and the JJJ-coupling evolutions between the neighboring spins. The perfect state transfer algorithm proposed by Christandl et al.[Phys. Rev. Lett. 92, 187902 (2004)] is realized in the XYXYXY chain.
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.
Universal quantum information processing requires single-qubit rotations and two-qubit interactions as minimal resources. A possible step beyond this minimal scheme is the use of three-qubit interactions. We consider such three-qubit interactions and show how they can reduce the time required for a quantum state transfer in an XYXYXY spin chain. For the experimental implementation, we use liquid-state nuclear magnetic resonance, where three-qubit interactions can be implemented by sequences of radio-frequency pulses.
Universal quantum information processing requires single-qubit rotations and two-qubit interactions as minimal resources. A possible step beyond this minimal scheme is the use of three-qubit interactions. We consider such three-qubit interactions and show how they can reduce the time required for a quantum state transfer in an XY spin chain. For the experimental implementation, we use liquid-state nuclear magnetic resonance, where three-qubit interactions can be implemented by sequences of radio-frequency pulses.
Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital…
We propose an iterative algorithm to simulate the dynamics generated by any nnn-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator UUU (unitary) into a product of different time-step unitaries. The algorithm product-decomposes UUU in a chosen operator basis by identifying a certain symmetry of UUU 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 nnn-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.