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Chemical Science

Targeting molecular quantum memory with embedded error correction

Selena J. Lockyer, Alessandro Chiesa, Grigore A. Timco, Eric J. L. McInnes, Tom S. Bennett, Íñigo J. Vitórica‐Yrezábal, Stefano Carretta, Richard E. P. Winpenny

Published Jan 1, 2021• 39 citations
Publisher

Abstract

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.

DOI
10.1039/d1sc01506k

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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.
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.
The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Employing high-dimensional quantum systems (qudits) can offer more hardware-efficient protocols than qubit-based approaches. Using electron-nuclear double resonance, we implement a logical qubit encoded on the four states of a I=3/2 nuclear spin hyperfine-coupled to an S=1/2 electron spin qubit; the encoding protects against the dominant decoherence mechanism in such systems, i.e., fluctuations of the quantizing magnetic field. We explore the dynamics of the encoded state both under a controlled application of the fluctuation and under natural decoherence processes. Our results confirm the potential of these proposals for practical, implementable, fault-tolerant quantum memories.
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 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.