Inverse Design of Molecular Qudits for Quantum Circuitry

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.