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arXiv:2103.09290 · npj Quantum Information

Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings

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

Published Aug 26, 2021• 38 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41534-021-00466-3

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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.
Molecular nanomagnets are quantum spin systems potentially serving as qudits for future quantum technologies thanks to their many accessible low-energy states. At low temperatures, the primary source of error in these systems is pure dephasing, caused by their interactions with the bath of surrounding nuclear spins degrees of freedom. Most importantly, as the system’s dimensionality grows going from qubits to qudits, the control and mitigation of decoherence become more challenging. Here, we analyze the characteristics of pure dephasing in molecular qudits under spin-echo sequences. We use a realistic description of their interaction with the bath, whose non-Markovian dynamics is accurately computed by the cluster correlation expansion technique. First, we show that the differences in the expectation values of the local spin operators on the eigenstates of the qudit are the source of decoherence in these systems. Indeed, we demonstrate that this is a necessary and sufficient condition to prevent the decay of coherence with time, also introducing a parameter to quantify the deviation from such ideal condition. We illustrate this with two paradigmatic systems: a single giant spin and a composite antiferromagnetic spin system. We then advance a proposal for optimized nanomagnets, identifying key ingredients for engineering robust qudits for quantum technologies.
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.
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.
We propose multi-spin molecules as a viable architecture for fault-tolerant quantum computing. To this aim, we introduce a correction protocol handling both diagonal and off-diagonal errors, typically associated with dephasing and relaxation. The scheme is based on a hybrid encoding which combines dephasing-tolerant units suppressing the leading pure dephasing error into a multi-spin molecule implementing a multi-qubit code for residual off-diagonal errors. Our proposal leverages peculiar properties of molecular spins, i.e. the strong hierarchy between different errors and the possibility to engineer multi-spin molecules at the synthetic level. Moreover, it addresses the important issue of the loss of coherences in anharmonic systems subject to off-diagonal errors, which hampers their correction at the single spin level. Thanks to the huge suppression of dephasing by the first-level code, we numerically demonstrate the potential performance of this strategy even with a limited number of spins per logical unit.
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.
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.