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Reports on Progress in Physics

Molecular nanomagnets: a viable path toward quantum information processing?

Alessandro Chiesa, Paolo Maria Santini, Elena Garlatti, Fernando M. Luis, Stefano Carretta

Published Feb 5, 2024• 87 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6633/ad1f81

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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.
Abstract Molecular Nanomagnets may enable the implementation of qudit-based quantum error-correction codes which exploit the many spin levels naturally embedded in a single molecule, a promising step towards scalable quantum processors. To fully realize the potential of this approach, a microscopic understanding of the errors corrupting the quantum information encoded in a molecular qudit is essential, together with the development of tailor-made quantum error correction strategies. We address these central points by first studying dephasing effects on the molecular spin qudit produced by the interaction with surrounding nuclear spins, which are the dominant source of errors at low temperatures. Numerical quantum error correction codes are then constructed, by means of a systematic optimization procedure based on simulations of the coupled system-bath dynamics, that provide a striking enhancement of the coherence time of the molecular computational unit. The sequence of pulses needed for the experimental implementation of the codes is finally proposed.
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.
We review the progress made in integrating magnetic molecules containing transition metal ions into nanoelectronic solid-state devices and using them as molecular spin qubits. Molecular spin qubits offer numerous advantages over other material platforms, such as being inherently quantum systems with discrete energy levels, having a rich variety of possible chemical designs, and being synthesizable in large quantities with atomic precision. However, the integration of magnetic molecules into practical and scalable molecular spin qubit devices (MSQDs) that offer initialization, coherent control, and readout of quantum spin states remains one of the major bottlenecks on the way toward applications of these systems in quantum computing technologies. We discuss the evolution of the field of MSQDs and review the first successful implementation of essential qubit operations in a single-molecule transistor based on a TbPc 2 molecule. Further development has been achieved through the merging of molecular electronics with the circuit quantum electrodynamics (cQED) approach where molecular spin states can be manipulated by the microwave frequency photons confined in a superconducting waveguide resonator. We discuss examples of such hybrid devices operating via coupling of a superconducting resonator to large spin ensembles, such as bulk samples and thin films. We also review a possible architecture for single-molecule cQED devices and the potential advantages that it offers. Then, we highlight the possibility and benefits of the optical initialization and readout of molecular spin states. This approach has been realized by using an optical pumping technique for the initialization and changes in photoluminescence for the readout of large molecular spin ensembles coupled to a superconducting resonator. The field of MSQDs is highly interdisciplinary, bringing together progress in synthetic chemistry, molecular electronics, cQED, and optical measurements. While it is still in its infancy, there are promising theoretical designs and encouraging proof-of-concept experiments, and we discuss several proposed device architectures that are eagerly awaiting experimental realization. Advances in hybrid MSQDs will open horizons for quantum technologies.
The implementation of a universal quantum processor still poses fundamental issues related to error mitigation and correction, which demand to investigate also platforms and computing schemes alternative to the main stream. A possibility is offered by employing multi-level logical units (qudits), naturally provided by molecular spins. Here we present the blueprint of a Molecular Spin Quantum Processor consisting of single Molecular Nanomagnets, acting as qudits, placed within superconducting resonators adapted to the size and interactions of these molecules to achieve a strong single spin to photon coupling. We show how to implement a universal set of gates in such a platform and to readout the final qudit state. Single-qudit unitaries (potentially embedding multiple qubits) are implemented by fast classical drives, while a novel scheme is introduced to obtain two-qubit gates via resonant photon exchange. The latter is compared to the dispersive approach, finding in general a significant improvement. The performance of the platform is assessed by realistic numerical simulations of gate sequences, such as Deutsch-Josza and quantum simulation algorithms. The very good results demonstrate the feasibility of the molecular route towards a universal quantum processor.
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.
Molecular nanomagnets can be considered as serious candidates for the definition of a scalable and reliable quantum computing technology: information is encoded on their spins and they ensure relaxation and decoherence times sufficiently long for the execution of tens of quantum operations. Among these devices, Cr7Ni supramolecular complexes are extremely of interest since they implement a universal set of quantum gates, made of single-qubit gates and the two-qubit Controlled-phase gate. A model for analyzing Cr7Ni molecules and a potential quantum computer architecture are proposed: starting from the energy parameters required for spin manipulations, these systems have been proved to implement elementary quantum algorithms. Within this paper, two, three and four-qubit systems have been analyzed: the simulation of quantum operations and the analysis of dynamical non-idealities have been done in parallel. Our approach enables the definition of an operating point - in terms of magnetic driving fields and latency - in which the execution of elementary quantum algorithms is characterized by negligible errors. The proposed model has been entirely implemented in MATLAB, thus obtaining a software infrastructure for the analysis of Cr7Ni molecules that can be extended to quantum systems with analogous Hamiltonian and behavior.