Max Rossmannek

Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the global SU(2) spin symmetry, remains a major challenge. In fact, expressing total-spin eigenstates in terms of the computational basis can require an exponentially large number of coefficients. In this work, we introduce a novel formalism for designing quantum algorithms directly in an eigenbasis of the total-spin operator. Our strategy relies on the symmetric group approach in conjunction with a truncation scheme for the internal degrees of freedom of total-spin eigenstates. For the case of the antiferromagnetic Heisenberg model, we show that this formalism yields a hierarchy of spin-adapted Hamiltonians, for each truncation threshold, whose ground-state energy and wave function quickly converge to their exact counterparts, calculated on the full model. These truncated Hamiltonians can be encoded with sparse and local qubit Hamiltonians that are suitable for quantum simulations. We demonstrate this by developing a state-preparation schedule to construct shallow quantum-circuit approximations, expressed in a total-spin eigenbasis, for the ground states of the Heisenberg Hamiltonian in different symmetry sectors.

We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by presenting a specific implementation of periodic range-separated DFT coupled to a quantum circuit ansatz, whereby the variational quantum eigensolver and the quantum equation-of-motion algorithm are used to obtain the low-lying spectrum of the embedded fragment Hamiltonian. The application of this scheme to study localized electronic states in materials is showcased through the accurate prediction of the optical properties of the neutral oxygen vacancy in magnesium oxide (MgO). Despite some discrepancies in the position of the main absorption band, the method demonstrates competitive performance compared to state-of-the-art ab initio approaches, particularly evidenced by the excellent agreement with the experimental photoluminescence emission peak.

We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by presenting a specific implementation of periodic range-separated DFT coupled to a quantum circuit ansatz, whereby the variational quantum eigensolver and the quantum equation-of-motion algorithm are used to obtain the low-lying spectrum of the embedded fragment Hamiltonian. Application of this scheme to study localized electronic states in materials is showcased through the accurate prediction of the optical properties of the neutral oxygen vacancy in magnesium oxide (MgO). Despite some discrepancies in the position of the main absorption band, the method demonstrates competitive performance compared to state-of-the-art ab initio approaches, particularly evidenced by the excellent agreement with the experimental photoluminescence emission peak.

Aromaticity is typically regarded as an intrinsic property of a molecule, correlated with electron delocalization, stability, and other properties. Small variations in the molecular geometry usually result in small changes in aromaticity, in line with Hammond's postulate. For example, introducing bond-length alternation in benzene and square cyclobutadiene by modulating the geometry along the Kekulé vibration gradually decreases the magnitude of their ring currents, making them less aromatic and less antiaromatic, respectively. A sign change in the ring current, corresponding to a reversal of aromaticity, typically requires a gross perturbation such as electronic excitation, addition or removal of two electrons, or a dramatic change in the molecular geometry. Here, we use multireference calculations to show how movement along the Kekulé vibration, which controls bond-length alternation, induces a sudden reversal in the ring current of cyclo[16]carbon, C₁₆. This reversal occurs when the two orthogonal π systems of C₁₆ sustain opposing currents. These results are rationalized by a Hückel model which includes bond-length alternation, and which is combined with a minimal model accounting for orbital contributions to the ring current. Finally, we successfully describe the electronic structure of C₁₆ with a "divide-and-conquer" approach suitable for execution on a quantum computer.

Synthetic carbon allotropes such as graphene¹, carbon nanotubes² and fullerenes³ have revolutionized materials science and led to new technologies. Many hypothetical carbon allotropes have been discussed⁴, but few have been studied experimentally. Recently, unconventional synthetic strategies such as dynamic covalent chemistry⁵ and on-surface synthesis⁶ have been used to create new forms of carbon, including γ-graphyne⁷, fullerene polymers⁸, biphenylene networks⁹ and cyclocarbons^10,11. Cyclo[N]carbons are molecular rings consisting of N carbon atoms^12,13; the three that have been reported to date (N = 10, 14 and 18)^10,11 are doubly aromatic, which prompts the question: is it possible to prepare doubly anti-aromatic versions? Here we report the synthesis and characterization of an anti-aromatic carbon allotrope, cyclo[16]carbon, by using tip-induced on-surface chemistry⁶. In addition to structural information from atomic force microscopy, we probed its electronic structure by recording orbital density maps¹⁴ with scanning tunnelling microscopy. The observation of bond-length alternation in cyclo[16]carbon confirms its double anti-aromaticity, in concordance with theory. The simple structure of C₁₆ renders it an interesting model system for studying the limits of aromaticity, and its high reactivity makes it a promising precursor to novel carbon allotropes¹⁵.

Aromaticity is typically regarded as an in-trinsic property of a molecule. It is often correlated with electron delocalization, stability, and other properties. Small variations in the molecular geometry usually result in small changes in aromaticity, in line with Hammond’s postu-late: for example, introducing bond-length alternation in benzene and square cyclobutadiene gradually decreases the magnitude of their ring currents, making them less aromatic and less antiaromatic, respectively. A sign change in the ring current, corresponding to a reversal of aromaticity, typically requires a gross perturbation such as electronic excitation, addition or removal of two electrons, or a dramatic change in the molecular geometry. Here, we use multireference calculations to show how small changes in bond-length alternation induce a sudden reversal in the ring current of cyclo[16]carbon, C16. This reversal occurs when the two orthogonal π systems of C16 sustain opposing currents. These results are rationalized by a Hückel model which includes bond-length alternation combined with a minimal model accounting for orbital contributions to the ring current. Finally, we successfully describe the electron-ic structure of C16 with a divide-and-conquer approach suitable for execution on a quantum computer.

The synthetic carbon allotropes graphene, carbon nanotubes and fullerenes have revolutionised materials science and led to new technologies. Recently, unconventional synthetic strategies such as dynamic covalent chemistry and on-surface synthesis have been used to create new forms of carbon, including γ-graphyne, covalent fullerene polymers, and biphenylene networks, as well as cyclo[10]carbon, cyclo[14]carbon and cyclo[18]carbon. Here, by using tip-induced on-surface chemistry, we report the synthesis and characterisation of an anti-aromatic carbon allotrope, cyclo[16]carbon. In addition to structural information from atomic force microscopy (AFM), we probed its electronic structure by recording orbital density maps with scanning tunnelling microscopy (STM), which have not been reported previously for any cyclocarbon. The observation of bond-length alternation in cyclo[16]carbon confirms its double anti-aromaticity, in concordance with theory. The simple structure of C16 renders it an interesting model system for studying the limits of aromaticity, and its high reactivity makes it a promising precursor to novel carbon allotropes.

Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer.

Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the hardware limitations of the available noisy near-term quantum devices, their application is currently limited only to small chemical systems. One way for extending the range of applicability can be achieved within the quantum embedding approach. Herein, we employ the projection-based embedding method for combining the variational quantum eigensolver (VQE) algorithm, although not limited to, with density functional theory (DFT). The developed VQE-in-DFT method is then implemented efficiently on a real quantum device and employed for simulating the triple bond breaking process in butyronitrile. The results presented herein show that the developed method is a promising approach for simulating systems with a strongly correlated fragment on a quantum computer. The developments as well as the accompanying implementation will benefit many different chemical areas including the computer aided drug design as well as the study of metalloenzymes with a strongly correlated fragment.