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Inorganic Chemistry

Inverse Design of Molecular Qudits for Quantum Circuitry

Edward Latham, Alice M. Bowen, Nicholas J. Cox, Nicholas F. Chilton

Published Apr 4, 2025• 2 citations
Publisher

Abstract

High Resolution Image Download MS PowerPoint Slide The development of molecular quantum bits (qubits) for quantum information processing is a lofty goal. While many contemporary works investigate their potential for error correction, fault-tolerance, memories, etc., there is still a lack of experimental examples of molecular multiqubit sequences. Herein, we perform a theoretical investigation of spin Hamiltonian parameter space to identify molecules that could be used to implement a 4-level superdense coding algorithm that has the least stringent requirements for experimental implementation. To do so, we analyze the zero-field splitting (ZFS) Hamiltonian of an S = 3/2 spin system to determine its effectiveness as a molecular qudit capable of performing the superdense coding circuit with X-band pulsed electron paramagnetic resonance (EPR), accounting for realistic constraints imposed by EPR spectrometers. For an S = 3/2 system, the optimal ZFS parameters are | D | ≈ 0.115 cm –1 and | E | ≈ −0.0383 cm –1 (| E / D | ≈ 0.33 approaching the rhombic limit of 1/3), with a field around 160 mT. Our findings highlight the need to maximize the rhombicity of the spin Hamiltonian for four-level molecular qudits.

DOI
10.1021/acs.inorgchem.5c00298

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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.
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.
The implementation of quantum computation (QC) would revolutionize scientific fields ranging from encryption to quantum simulation. One intuitive candidate for the smallest unit of a quantum computer, a qubit, is electronic spin. A prominent proposal for QC relies on high-spin magnetic molecules, where multiple transitions between the many MS levels are employed as qubits. Yet, over a decade after the original notion, the exploitation of multiple transitions within a single manifold for QC remains unrealized in these high-spin species due to the challenge of accessing forbidden transitions. To create a proof-of-concept system, we synthesized the novel nuclear spin-free complex [Cr(C3S5)3](3-) with precisely tuned zero-field splitting parameters that create two spectroscopically addressable transitions, with one being a forbidden transition. Pulsed electron paramagnetic resonance (EPR) measurements enabled the investigation of the coherent lifetimes (T2) and quantum control (Rabi oscillations) for two transitions, one allowed and one forbidden, within the S = (3)/2 spin manifold. This investigation represents a step forward in the development of high-spin species as a pathway to scalable QC systems within magnetic molecules.
The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multilevel quantum resources, have attracted interest in this context because they offer additional Hilbert space dimensions in a spatially compact and theoretically efficient structure. We present a quantitative analysis of the performance of a spin-qudit-based error-correctable quantum memory, with reference to the actual Hamiltonians of several potential candidate systems. First, the ideal code-word implemented on a spin-7/2 nucleus, which provides first-order Pauli- X , Y and Z error correction, has intrinsic infidelity due to mixed eigenstates under realistic conditions. We confirm that expansion to a spin-9/2 system with tailored code words can compensate for this infidelity. Second, we claim that electric field fluctuations, which are inevitable in real systems, should also be considered as a noise source, and we illustrate an encoding and decoding scheme for a multi-spin-qudit-based error correction code that can simultaneously compensate for both electric- and magnetic-field perturbations. Such strategies are important as we move beyond the current noisy-intermediate quantum era, and fidelities above two or three nines become crucial for the implementation of quantum technologies.
Interacting spin systems in solids underpin a wide range of quantum technologies, from quantum sensors and single-photon sources to spin-defect-based quantum registers and processors. We develop a quantum-computer-aided framework for simulating such devices using a general many-body electron-spin-resonance Hamiltonian that incorporates zero-field splitting, the Zeeman effect, hyperfine interactions, dipole-dipole spin-spin interactions, and electron-phonon decoherence. Within this framework, we combine Gray-encoded qudit-to-qubit mappings, qubit-wise commuting aggregation, and a multi-reference selected quantum Krylov fast-forwarding hybrid algorithm, aiming to access extended-time dynamics within the constraints of NISQ and early fault-tolerant hardware. Numerical simulations demonstrate the computation of operationally useful quantities including autocorrelation functions up to ∼100\sim100∼100 ns, together with microwave absorption spectra and the ℓ1\ell_1ℓ1​-norm of coherence, achieving 18-30%\%% reductions in gate counts and circuit depth for Trotterized time-evolution circuits compared to unoptimized implementations. Using the nitrogen vacancy center in diamond as a testbed, we benchmark the framework against classical simulations and identify the reference-state selection in sQKFF as the primary factor governing accuracy at fixed hardware cost. This methodology provides a flexible blueprint for using quantum computers to design, compare, and optimize solid-state spin-qubit technologies under experimentally realistic conditions.
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.