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The Journal of Physical Chemistry Letters

Molecular Nanomagnets as Qubits with Embedded Quantum-Error Correction

Alessandro Chiesa, Emilio Macaluso, Francesco Petiziol, Sandro Wimberger, Paolo Maria Santini, Stefano Carretta

Published Sep 16, 2020• 90 citations
Publisher

Abstract

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.

DOI
10.1021/acs.jpclett.0c02213

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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 (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.
A scalable architecture for quantum computing requires logical units supporting quantum-error correction. In this respect, magnetic molecules are particularly promising, since they allow one to define logical qubits with embedded quantum-error correction by exploiting multiple energy levels of a single molecule. The single-object nature of this encoding is expected to facilitate the implementation of error correction procedures and logical operations. In this work, we make progress in this direction by showing how two-qubit gates between error-protected units can be realised, by means of easily implementable sequences of electro-magnetic pulses.
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.
We pinpoint the key ingredients ruling decoherence in multispin clusters, and we engineer the system Hamiltonian to design optimal molecules embedding quantum error correction. These are antiferromagnetically coupled systems with competing exchange interactions, characterized by many low-energy states in which decoherence is dramatically suppressed and does not increase with the system size. This feature allows us to derive optimized code words, enhancing the power of the quantum error correction code by orders of magnitude. We demonstrate this by a complete simulation of the system dynamics, including the effect of decoherence driven by a nuclear spin bath and the full sequence of pulses to implement error correction and logical gates between protected states.
Quantum systems displaying many accessible levels could be very powerful units of forthcoming quantum computing architectures. Indeed, the large number of available states could significantly simplify the actual implementation of several algorithms. Here we show that artificial molecular spins are particularly suitable to realize such a platform. In particular, multispin molecules with competing interactions provide a large number of low-energy multiplets in which decoherence is strongly suppressed compared to a single spin SSS and does not increase with the system size. This feature, combined with the proper connectivity between the multiplets, enables the implementation of complex operations with remarkable fidelity, thus fully unleashing the potential of the molecular approach. We demonstrate the power of this approach by numerically simulating the implementation of one- and two-qudit gates on realistic molecular systems.
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.