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Physical Chemistry Chemical Physics

Quantum error correction with molecular spin qudits

Mario Chizzini, Luca Crippa, Luca Zaccardi, Emilio Macaluso, Stefano Carretta, Alessandro Chiesa, Paolo Maria Santini

Published Jan 1, 2022• 43 citations
Publisher

Abstract

> 1), coupled to a spin-1/2 electronic ancilla for error detection. By thorough numerical simulations we show that a significant gain in the effective phase memory time can be achieved. This is further enhanced by exploiting pulse-shaping techniques to reduce the leakage and/or the impact of decoherence during correction. Moreover, we simulate the implementation of single-qubit operations on the encoded states.

DOI
10.1039/d2cp01228f

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1), coupled to a spin-1/2 electronic ancilla for error detection. By thorough numerical simulations we show that a significant gain in the effective phase memory time can be achieved. This is further enhanced by exploiting pulse-shaping techniques to reduce the leakage and/or the impact of decoherence during correction. Moreover, we simulate the implementation of single-qubit operations on the encoded states.
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.
The authors propose a quantum memory, implemented on a spin-7/2 nucleus coupled to an electron spin-1/2 qubit, which provides XXX, YYY, and ZZZ error correction using fewer quantum resources than the equivalently effective qubit-based protocols.
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.
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.
Ni} provides the processor and the naturally isolated nuclear spin 3/2 of the Cu ion is used to encode a logical unit with embedded quantum error-correction. We demonstrate by realistic simulations that microwave pulses allow us to rapidly implement gates on the processor and to swap information between the processor and the quantum memory. By combining the storage into the Cu nuclear spin with quantum error correction, information can be protected for times much longer than the processor coherence.
We demonstrate, numerically, the possibility of manipulating the spin states of molecular nanomagnets with shaped microwave pulses designed with quantum optimal control theory techniques. The state-to-state or full gate transformations can be performed in this way in shorter times than using simple monochromatic resonant pulses. This enhancement in the operation rates can therefore mitigate the effect of decoherence. The optimization protocols and their potential for practical implementations are illustrated by simulations performed for a simple molecular cluster hosting a single Gd3+^{3+}3+ ion. Its eight accessible levels (corresponding to a total spin S=7/2S=7/2S=7/2) allow encoding an 888-level qudit or a system of three coupled qubits. All necessary gates required for universal operation can be obtained with optimal pulses using the intrinsic couplings present in this system. The application of optimal control techniques can facilitate the implementation of quantum technologies based on molecular spin qudits.