arXiv 0902.12762009-02-19cond-mat.stat-mechcond-mat.str-elmath-phmath.MPquant-ph

Implementing Quantum Gates using the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

Tom Michoel, Jaideep Mulherkar, Bruno Nachtergaele

备注：: Updated Acknowledgements
发表信息：: New J. Phys. 12 (2010) 025003
DOI：: 10.1088/1367-2630/12/2/025003

英文摘要：

We demonstrate an implementation scheme for constructing quantum gates using unitary evolutions of the one-dimensional spin-J ferromagnetic XXZ chain. We present numerical results based on simulations of the chain using the time-dependent DMRG method and techniques from optimal control theory. Using only a few control parameters, we find that it is possible to implement one- and two-qubit gates on a system of spin-3/2 XXZ chains, such as Not, Hadamard, Pi-8, Phase, and C-Not, with fidelity levels exceeding 99%.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Isolated Eigenvalues of the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions

We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Delta and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J>= 3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

2007-12-18cond-mat.stat-mechmath-phmath.MP

Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions

We give a precise definition for excitations consisting of a droplet of size n in the XXZ chain with various choices of boundary conditions, including kink boundary conditions and prove that, for each n, the droplet energies converge to a boundary condition independent value in the thermodynamic limit. We rigorously compute an explicit formula for this limiting value using the Bethe ansatz.

2005-08-25cond-mat.stat-mechmath-phmath.MP

On the density matrix for the kink ground state of higher spin XXZ chain

The exact expression for the density matrix of the kink ground state of higher spin XXZ chain is obtained.

2009-05-11cond-mat.stat-mech

Density matrix for the kink ground state of the ferromagnetic XXZ chain

The exact expression for the density matrix of the kink ground state of the ferromagnetic XXZ chain is obtained. Utilizing this, we exactly calculate various correlation functions such as the longitudinal and transverse spin-spin correlation functions, and the ferromagnetic and antiferromagnetic string formation probabilities. The asymptotic behaviors of these correlation functions are also analyzed. As a consequence, we find that the spin-spin correlation functions decay exponentially for large distances, while the string formation probabilities exhibit Gaussian decay for large strings. We al…

2008-12-29cond-mat.stat-mechmath-phmath.MP

Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field

The Heisenberg XXZ spin-1/2 chain is considered in the massive antiferromagnetic regime in the presence of a staggered longitudinal magnetic field. The Hamiltonian of the model is characterised by the anisotropy parameter $Δ<-1$, and by the magnetic field strength h. At zero magnetic field, the model is exactly solvable. In the thermodynamic limit, it has two degenerate vacua and the kinks (which are also called spinons) interpolating between these vacua, as elementary excitations. Application of the staggered magnetic field breaks integrability of the model and induces the long-range attracti…

2018-04-03cond-mat.stat-mechcond-mat.str-el

Instability of interfaces in the antiferromagnetic XXZ chain at zero temperature

For the antiferromagnetic, highly anisotropic XZ and XXZ quantum spin chains, we impose periodic boundary conditions on chains with an odd number of sites to force an interface (or kink) into the chain. We prove that the energy of the interface depends on the momentum of the state. This shows that at zero temperature the interface in such chains is not stable. This is in contrast to the ferromagnetic XXZ chain for which the existence of localized interface ground states has been proven for any amount of anisotropy in the Ising-like regime.

2003-01-17cond-mat.stat-mechmath-phmath.MP

更多相关论文收起更多论文

The Ferromagnetic Heisenberg XXZ chain in a pinning field

We investigate the effect of a magnetic field supported at a single lattice site on the low-energy spectrum of the ferromagnetic Heisenberg XXZ chain. Such fields, caused by impurities, can modify the low-energy spectrum significantly by pinning certain excitations, such as kink and droplet states. We distinguish between different boundary conditions (or sectors), the direction and also the strength of the magnetic field. E.g., with a magnetic field in the z-direction applied at the origin and ++ boundary conditions, there is a critical field strength B_c (which depends on the anisotropy of th…

2002-10-01cond-mat.stat-mechmath-phmath.MP

Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain

The infinite Heisenberg XXZ spin-(1/2) chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic field h induces a long-range attractive potential between two adjacent spinons leading to their confinement into 'meson' bound states. Exploiting the integrability of the XXZ model in the deconfined phase h = 0, we perform perturbative calculations of the energy spectra of the two-spinon bound state…

2022-10-14cond-mat.stat-mechcond-mat.str-el

The complete set of ground states of the ferromagnetic XXZ chains

We show that the well-known translation invariant ground states and the recently discovered kink and antikink ground states are the complete set of pure infinite-volume ground states (in the sense of local stability) of the spin-S ferromagnetic XXZ chains with Hamiltonian H=-sum_x [ S^1_x S^1_{x+1} + S^2_x S^2_{x+1} + Delta S^3_x S^3_{x+1} ], for all Delta >1, and all S=1/2,1,3/2,.... For the isotropic model (Delta =1) we show that all ground states are translation invariant. For the proof of these statements we propose a strategy for demonstrating completeness of the list of the pure infinite…

1998-04-13cond-mat.stat-mechmath-phmath.MP

带隙 XYZ 自旋 - $\frac{1}{2}$ 链中的纠缠不对称性

Entanglement asymmetry in the gapped XYZ spin-$\frac12$ chain

Center of Mathematics, Computing, and Cognition, Federal University of ABC（计算与认知数学中心，ABC联邦大学）

研究相互作用的 XYZ 链在带隙、破缺 $U(1)$ 相中大区间的 Rényi 纠缠不对称性，结合电荷矩恒等式、非守恒和规则及 Baxter - Johnson - Krinsky - McCoy 解，通过密度矩阵重整化群模拟重现主公式。

2026-07-29cond-mat.stat-mechhep-thquant-ph