Molecular Optimization for Nuclear Spin State Control via a Single Electron Spin Qubit by Optimal Microwave Pulses: Quantum Control of Molecular Spin Qubits

Quantum state control is one of the most important concepts in advanced quantum technology, emerging quantum cybernetics and related fields. Molecular open shell entities can be a testing ground for implementing quantum control technology enabling us to manipulate molecular spin quantum bits (molecular spin qubits). In well-designed molecular spins consisting of unpaired electron and nuclear spins, the electrons and nuclear spins can be bus and client qubits, respectively. Full control of molecular spin qubits, in which client spins interact via hyperfine coupling, is a key issue for implementing quantum computers (QCs). In solid-state QCs, there are two approaches to the control of nuclear client qubits, namely, direct control of nuclear spins by radio-wave (RF) pulses and indirect control via hyperfine interactions by microwave pulses applied to electron spin qubits. Although the latter is less popular in the literature, the indirectness has advantage of greatly reducing unnecessary interactions between a qubit system and its environment. In this work, we investigate molecular spin optimization to find optimal experimental conditions which can afford to achieve the high fidelity of quantum gates by the indirect control scheme. In the present quantum systems, one electron is directly controlled by pulsed ESR techniques without manipulating individual hyperfine resonance, but the states of two nuclear client spins are indirectly steered via hyperfine interactions. Single crystals of potassium hydrogen maleate (KHM) radical and ¹³C-labeled malonyl radical are chosen as typical molecular spin qubits which exemplify the importance of the symmetry of hyperfine tensors and their collinear properties. We have found that both the non-collinearity of the principal axes of hyperfine coupling tensors and the non-distinguishability/non-equivalency between nuclear spins are key issues which extremely reduce the gate fidelity.