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Journal of Applied Physics

Magnetic materials for finite-temperature quantum computing

Ralph Skomski, Jian Zhou, Andrei Y. Istomin, Anthony F. Starace, D. J. Sellmyer

Published May 15, 2005• 7 citations
Publisher

Abstract

The potential use of interacting magnetic nanodots for quantum computing (qubit) operations is investigated by model calculations. The quantum entanglement of the low-lying ferromagnetic states, as quantified by the concurrence, exhibits a resonant peak whose position and width depend on parameters such as dot anisotropy, interdot exchange, and external field gradient. The maximum operation temperature is proportional to the magnetocrystalline anisotropy of the dot material. A specific condition is that the dots are sufficiently small so that the interatomic exchange ensures a coherent magnetization state and quantum coherence at finite temperatures. From a material point of view, there is a quite rigid upper limit of about 100 K, but to avoid decoherence it will be necessary to sacrifice a substantial fraction of this temperature, probably at least one order of magnitude.

DOI
10.1063/1.1860832

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The potential use of interacting magnetic nanodots for quantum computing (qubit) operations is investigated by model calculations. The quantum entanglement of the low-lying ferromagnetic states, as quantified by the concurrence, exhibits a resonant peak whose position and width depend on parameters such as dot anisotropy, interdot exchange, and external field gradient. The maximum operation temperature is proportional to the magnetocrystalline anisotropy of the dot material. A specific condition is that the dots are sufficiently small so that the interatomic exchange ensures a coherent magnetization state and quantum coherence at finite temperatures. From a material point of view, there is a quite rigid upper limit of about 100 K, but to avoid decoherence it will be necessary to sacrifice a substantial fraction of this temperature, probably at least one order of magnitude.
Anisotropic magnetic nanodots are promising physical realizations of qubits for quantum computing at finite temperature owing to their well-separated low-lying energy levels and scalability. The entanglement of two interacting magnetic nanodots is investigated and shown both analytically and numerically to be resonantly dependent on their interaction strength and on differences in their properties. These results provide criteria for fabricating and coupling magnetic nanodots so that their low-lying eigenstates can be significantly entangled.
Anisotropic magnetic nanodots are promising physical realizations of qubits for quantum computing at finite temperature owing to their well-separated low-lying energy levels and scalability. The entanglement of two interacting magnetic nanodots is investigated and shown both analytically and numerically to be resonantly dependent on their interaction strength and on differences in their properties. These results provide criteria for fabricating and coupling magnetic nanodots so that their low-lying eigenstates can be significantly entangled.
Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.
We propose two potential realizations for quantum bits based on nanometre-scale magnetic particles of large spin S and high-anisotropy molecular clusters. In case (1) the bit-value basis states |0⟩ and |1⟩ are the ground and first excited spin states S z = S and S -1, separated by an energy gap given by the ferromagnetic resonance frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0⟩, and antisymmetric, |1⟩, combinations of the twofold degenerate ground state S z = ± S . In each case the temperature of operation must be low compared to the energy gap, Δ, between the states |0⟩ and |1⟩. The gap Δ in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.
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.
The electron-electron correlations in a many-electron (Ne=1,2,…,5)({N}_{e}=1,2,\dots{},5)(Ne​=1,2,…,5) quantum dot confined by a parabolic potential is investigated in the presence of a single magnetic ion and a perpendicular magnetic field. We obtained the energy spectrum and calculated the addition energy which exhibits cusps as a function of the magnetic field. The vortex properties of the many-particle wave function of the ground state are studied and for large magnetic fields are related to composite fermions. The position of the impurity influences strongly the spin-pair-correlation function when the external field is large. In a small applied magnetic field, the spin-exchange energy together with the Zeeman terms leads to a ferromagnetic-antiferromagnetic (FM-AFM) transition. When the magnetic ion is shifted away from the center of the quantum dot, a remarkable re-entrant AFM-FM-AFM transition is found as a function of the strength of the Coulomb interaction. Thermodynamic quantities such as the heat capacity, the magnetization, and the susceptibility are also studied. The cusps in the energy levels show up as peaks in the heat capacity and the susceptibility.