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arXiv:1304.7618 · Physical Review B

Size of linear superpositions in molecular nanomagnets

Filippo Troiani, Paolo Zanardi A

Published Sep 10, 2013• 7 citations
arXivHTMLPDF

Abstract

Molecular nanomagnets are zero-dimensional spin systems that exhibit quantum-mechanical behavior at low temperatures. Exploiting quantum-information theoretic measures, we quantify here the size of linear superpositions that can be generated within the ground multiplet of high- and low-spin nanomagnets. Amongst the former class of systems, we mainly focus on Mn${}_{12}$ and Fe${}_{8}$. General criteria for maximizing such measures are also outlined, and illustrated with reference to spin clusters of different geometries. The actual character (micro or macroscopic) of linear superpositions in low-spin systems is inherently ill-defined. Here, this issue is addressed with specific reference to the Cr${}_{7}$Ni and V${}_{15}$ molecules, characterized by an $S=1/2$ ground state. In both cases, the measures we obtain are larger than those of a single $s=1/2$ spin but not proportionate to the number and value of the constituent spins.

DOI
10.1103/physrevb.88.094413

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Molecular nanomagnets are zero-dimensional spin systems that exhibit quantum-mechanical behavior at low temperatures. Exploiting quantum-information theoretic measures, we quantify here the size of linear superpositions that can be generated within the ground multiplet of high- and low-spin nanomagnets. Amongst the former class of systems, we mainly focus on Mn12{}_{12}12​ and Fe8{}_{8}8​. General criteria for maximizing such measures are also outlined, and illustrated with reference to spin clusters of different geometries. The actual character (micro or macroscopic) of linear superpositions in low-spin systems is inherently ill-defined. Here, this issue is addressed with specific reference to the Cr7{}_{7}7​Ni and V15{}_{15}15​ molecules, characterized by an S=1/2S=1/2S=1/2 ground state. In both cases, the measures we obtain are larger than those of a single s=1/2s=1/2s=1/2 spin but not proportionate to the number and value of the constituent spins.
Many problems intractable on classical devices could be solved by algorithms explicitly based on quantum mechanical laws, i.e. exploiting quantum information processing. As a result, increasing efforts from different fields are nowadays directed to the actual realisation of quantum devices. Here we provide an introduction to Quantum Information Processing, focusing on a promising setup for its implementation, represented by molecular spin clusters known as Molecular Nanomagnets. We introduce the basic tools to understand and design quantum algorithms, always referring to their actual realisation on a molecular spin architecture. We then examine the most important sources of noise in this class of systems and one of their most peculiar features, i.e. the possibility to exploit many (more than two) available states to encode information and to self-correct it from errors via proper design of quantum error correction codes. Finally, we present some examples of quantum algorithms proposed and implemented on a molecular spin qudit hardware.
Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.
Molecular nanomagnets are compounds characterized by a high-spin magnetic core that is protected by organic ligands. They have recently gained attention as potential quantum information carriers in solid-state quantum computing platforms, simultaneously exhibiting classical macroscopic properties and quantum features in light of their complex nature and configuration. Addressing the condition when they manifest unquestionable quantum behavior is key to guarantee their effectiveness as resources for quantum information processing. We address the quantumness of molecular nanomagnets using a recently formulated criterion [cf. Krisnanda et al., Phys. Rev. Lett. 119, 120402 (2017)] demonstrating that these systems exhibit an intrinsic quantum nature, as evidenced by their ability to generate and enhance quantum correlations between two non-interacting probes. Our analysis, which is performed addressing various dynamical regimes, paves the way to the design of experimentally viable tests of non-classicality in multipartite registers consisting of ensembles of molecular nanomagnets.
Molecular nanomagnets are compounds characterized by a high-spin magnetic core that is protected by organic ligands. They have recently gained attention as potential quantum information carriers in solid-state quantum computing platforms, simultaneously exhibiting classical macroscopic properties and quantum features in light of their complex nature and configuration. Addressing the condition when they manifest unquestionable quantum behavior is key to guarantee their effectiveness as resources for quantum information processing. We address the quantumness of molecular nanomagnets using a recently formulated criterion [T. Krisnanda , ] demonstrating that these systems exhibit an intrinsic quantum nature, as evidenced by their ability to generate and enhance quantum correlations between two noninteracting probes. Our analysis, which is performed addressing various dynamical regimes, paves the way to the design of experimentally viable tests of nonclassicality in multipartite registers consisting of ensembles of molecular nanomagnets.
We show that molecular nanomagnets have a potential advantage in the crucial rush toward quantum computers.Indeed, the sizable number of accessible low-energy states of these systems can be exploited to define qubits with embedded quantum error correction.We derive the scheme to achieve this crucial objective and the corresponding sequence of microwave/radiofrequency pulses needed for the error correction procedure.The effectiveness of our approach is shown already with a minimal S = 3/2 unit corresponding to an existing molecule, and the scaling to larger spin systems is quantitatively analyzed.