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arXiv:2602.08157

Spinor Double-Quantum Excitation in the Solution NMR of Near-Equivalent Spin-1/2 Pairs

Urvashi D. Heramun, Mohamed Sabba, Dolnapa Yamano, Christian Bengs, Bonifac Legrady, Giuseppe Pileio, Sam Thompson, Malcolm H. Levitt

quant-phphysics.chem-phSubmitted Feb 8, 2026• Announced Feb 10, 2026
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Abstract

A family of double-quantum excitation schemes is described for the solution nuclear magnetic resonance (NMR) of near-equivalent spin-1/2 pairs. These new methods exploit the spinor behaviour of 2-level systems, whose signature is the change of sign of a quantum state upon a $2π$ rotation. The spinor behaviour is used to manipulate the phases of single-quantum coherences, in order to prepare a double-quantum precursor state which is rapidly converted into double-quantum coherence by a straightforward $π/2$ rotation. One set of spinor-based methods exploits symmetry-based pulse sequences, while the other set exploits SLIC (spin-lock-induced crossing), in which the nutation frequency under a resonant radiofrequency field is matched to the spin-spin coupling. A variant of SLIC is introduced which is well-compensated for deviations in the radiofrequency field amplitude. The methods are demonstrated by performing double-quantum-filtered $^{19}$F NMR on a molecular system containing a pair of diastereotopic $^{19}$F nuclei. The new methods are compared with existing techniques.

Comments
accepted for publication in JCP

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A family of double-quantum excitation schemes is described for the solution nuclear magnetic resonance (NMR) of near-equivalent spin-1/2 pairs. These new methods exploit the spinor behaviour of 2-level systems, whose signature is the change of sign of a quantum state upon a 2π2π2π rotation. The spinor behaviour is used to manipulate the phases of single-quantum coherences, in order to prepare a double-quantum precursor state which is rapidly converted into double-quantum coherence by a straightforward π/2π/2π/2 rotation. One set of spinor-based methods exploits symmetry-based pulse sequences, while the other set exploits SLIC (spin-lock-induced crossing), in which the nutation frequency under a resonant radiofrequency field is matched to the spin-spin coupling. A variant of SLIC is introduced which is well-compensated for deviations in the radiofrequency field amplitude. The methods are demonstrated by performing double-quantum-filtered 19^{19}19F NMR on a molecular system containing a pair of diastereotopic 19^{19}19F nuclei. The new methods are compared with existing techniques.
Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1/2 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1/2, are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover's algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3/2 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1/2 and quadrupolar spin 3/2 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.
Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover’s algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 and quadrupolar spin 3 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.
A modification of the widely-used spin-lock-induced crossing (SLIC) procedure is proposed for the solution nuclear magnetic resonance (NMR) of strongly coupled nuclear spin systems, including singlet NMR and parahydrogen-enhanced hyperpolarised NMR experiments. The compensated-SLIC (cSLIC) scheme uses a repetitive sequence where the repeated element employs two different radiofrequency field amplitudes. Effective compensation for deviations in the radiofrequency field amplitude is achieved without increasing the overall duration of the SLIC sequence. The advantageous properties of cSLIC are demonstrated by numerical simulations and by representative experiments.
The premise of nuclear magnetic resonance (NMR) quantum computing is that pseudopure quantum states, for which the populations of all energy levels but one are equal, can be used instead of pure quantum states. However, for systems with a large number of quantum bits (qubits), it would require elaborate pulse sequences with many steps to prepare these pseudopure states. To overcome this problem, a method using pairs of pseudopure states (POPS) instead of individual pseudopure states as the basis for NMR quantum computing is introduced here. The POPS approach has a significant advantage over the existing methods that, regardless of the number of qubits, only a single step is needed to prepare each pair of pseudopure states. A detailed analysis of a 16-level spin system is given, and the results of applying a c2{c}^{2}c2-NOT quantum logic gate (a controlled-NOT gate conditional upon the state of two other qubits) to all the POPS in the system are presented.
The Aharonov-Anandan phase is a contribution to the phase acquired by the cyclic evolution of a quantum state, which depends only on the geometric properties of its trajectory. We report the study and the exploitation of the Aharonov-Anandan phase by nuclear magnetic resonance interferometry techniques in homonuclear spin-1/2 pairs in the near-equivalence limit. We introduce a new method for engineering effective zero-quantum Hamiltonians with an arbitrary phase in the transverse plane. We use this method to generate a variety of cyclic zero-quantum paths, enabling direct study of the geometric Aharonov-Anandan phase to probe the rotational characteristics of the zero-quantum subspace. We show that the geometric Aharonov-Anandan phase may be used for efficient double-quantum excitation in strongly coupled spin pairs. We find that geometric double-quantum excitation outperforms the standard method by a factor of 2 in experiments performed on a typical case involving near-equivalent spin pairs.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.