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Communications in Theoretical Physics

Anisotropic Spin Cluster as a Qubit

Xiao-Bo Yan, Mingji Wang

Published Jul 1, 2007• 0 citations
Publisher

Abstract

We study an anisotropic spin cluster of 3 spin S = 1/2 particles with antiferromagnetic exchange interaction with non-uniform coupling constants. A time-dependent magnetic field is applied to control the time evolution of the cluster. It is well known that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magnetic field.

DOI
10.1088/0253-6102/48/1/020

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We study an anisotropic spin cluster of 3 spin S = 1/2 particles with antiferromagnetic exchange interaction with non-uniform coupling constants. A time-dependent magnetic field is applied to control the time evolution of the cluster. It is well known that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magnetic field.
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.
A spin cluster of 3 spin 1/2 particles has been studied as a qubit system. A time dependent magnetic field is applied to control the time evolution of the cluster. The lowest energy level of the cluster has the total spin 1/2 separated far away from the excited states and can be used as a qubit register. The universal 1-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the 6 basic 1-qubit gates can be realized by adjusting the applied time dependent magnetic field. As a many-body system, this qubit system is expected to be robust against the dissipation effect of the thermal radiation fields from the environment.
We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schrödinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.
We study the low energy states of one-dimensional spin chain clusters consisting of three spin-1/2 Heisenberg particles. When applying an external magnetic field on the spin chain cluster, the ground state doublet will generate Zeeman splitting. As a two-level quantum system, the split ground state doublet can be defined as a new 'spin cluster qubit'. The cluster quibit is shown to be more robust with a smaller decoherence rate. We realize universal single-qubit gates with the algebraic dynamical method, by applying a time-dependent magnetic field on the spin cluster. We also investigate a two-qubit system made up of two such Heisenberg spin chain clusters which interact through a tunable Heisenberg coupling. In the two-qubit product basis, the controlled quantum phase gates can be generated by applying a magnetic field along the z-axis on the system of the two clusters. One can realize the controlled-NOT gate through a three-step time evolution by adjusting the corresponding physical parameters. Our scheme involves two kinds of dynamically distinct operations, which is much simpler and more feasible.
We investigate an annular spin cluster made of three particles with anisotropic Heisenberg-chain controlled by a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, we have obtained the exact analytical solution to the time dependent Schrdinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and consequently six special single qubit logic gates can be realized.
We show that a wide range of spin clusters with antiferromagnetic intracluster exchange interaction allows one to define a qubit. For these spin cluster qubits, initialization, quantum gate operation, and readout are possible using the same techniques as for single spins. Quantum gate operation for the spin cluster qubit does not require control over the intracluster exchange interaction. Electric and magnetic fields necessary to effect quantum gates need only be controlled on the length scale of the spin cluster rather than the scale for a single spin. Here, we calculate the energy gap separating the logical qubit states from the next excited state and the matrix elements which determine quantum gate operation times. We discuss spin cluster qubits formed by one- and two-dimensional arrays of s=1/2s=1/2s=1/2 spins as well as clusters formed by spins s>1/2.s>1/2.s>1/2. We illustrate the advantages of spin cluster qubits for various suggested implementations of spin qubits and analyze the scaling of decoherence time with spin cluster size.