Quantum chemistry on quantum computers: quantum simulations of the time evolution of wave functions under the S2 operator and determination of the spin quantum number S

Quintet Dinitrenes with Negative Zero-Field Splitting: Effect of Spin-Orbit Coupling on the Sign of Magnetic Anisotropy

We report on W-band EPR and quantum chemical investigation of novel organic tetraradicals with negative axial zero-field splitting (ZFS) parameter D. These belong to the class of quintet 1,3,5-tribromophenylene-2,4-dinitrenes bearing different substituents in position 6 of the benzene ring (1b, N₃; 1c, F; 1d, CN; 1e; Cl; 1f, Br). Analysis of the W-band EPR spectrum of dinitrene 1c reveals its large negative ZFS parameter D = -0.27 cm^-1. Quantum chemical calculations show that negative D gradually grows in the row of 1c(F) < 1b(N₃) < 1d(CN) < 1e(Cl) < 1f(Br) dinitrenes due to decreasing of the through-space distance between the nitrene units and neighboring bromine atoms. Shorter steric N···Br distance results in the stronger contribution of the spin-orbit coupling (SOC) to the total ZFS. The sign of D depends on the interplay of three factors: (i) the angle θ between the "easy" z-axes of the dipolar spin-spin (D_SS) and spin-orbit (D_SOC) interaction tensors, (ii) the ratio of D_SOC/D_SS values, and (iii) the rhombicity parameters E_SS/D_SS and E_SOC/D_SOC. The study demonstrates in which cases organic quintet tetraradicals may have negative ZFS owing to the presence of heavy atoms at appropriate sites nearby the nitrene units and, thus, possess the bistability property as single-molecule magnets.

Adiabatic state preparation of correlated wave functions with nonlinear scheduling functions and broken-symmetry wave functions

Adiabatic state preparation (ASP) can generate the correlated wave function by simulating the time evolution of wave function under the time-dependent Hamiltonian that interpolates the Fock operator and the full electronic Hamiltonian. However, ASP is inherently unsuitable for studying strongly correlated systems, and furthermore practical computational conditions for ASP are unknown. In quest for the suitable computational conditions for practical applications of ASP, we performed numerical simulations of ASP in the potential energy curves of N₂, BeH₂, and in the C_2v quasi-reaction pathway of the Be atom insertion to the H₂ molecule, examining the effect of nonlinear scheduling functions and the ASP with broken-symmetry wave functions with the S² operator as the penalty term, contributing to practical applications of quantum computing to quantum chemistry. Eventually, computational guidelines to generate the correlated wave functions having the square overlap with the complete-active space self-consistent field wave function close to unity are discussed.

Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps

Quantum computers can perform full configuration interaction (full-CI) calculations by utilising the quantum phase estimation (QPE) algorithms including Bayesian phase estimation (BPE) and iterative quantum phase estimation (IQPE). In these quantum algorithms, the time evolution of wave functions for atoms and molecules is simulated conditionally with an ancillary qubit as the control, which make implementation to real quantum devices difficult. Also, most of the problems in chemistry discuss energy differences between two electronic states rather than total energies themselves, and thus direct calculations of energy gaps are promising for future applications of quantum computers to real chemistry problems. In the race of finding efficient quantum algorithms to solve quantum chemistry problems, we test a Bayesian phase difference estimation (BPDE) algorithm, which is a general algorithm to calculate the difference of two eigenphases of unitary operators in the several cases of the direct calculations of energy gaps between two electronic states on quantum computers, including vertical ionisation energies, singlet-triplet energy gaps, and vertical excitation energies. In the BPDE algorithm, state preparation is carried out conditionally on the ancillary qubit, and the time evolution of the wave functions in superposition of two electronic states are executed unconditionally. Based on our test, we conclude that BPDE is capable of computing the energy gap with an accuracy similar to BPE without controlled-time evolution simulations and with the smaller number of iterations in Bayesian optimisations.

Quantum Algorithm for the Direct Calculations of Vertical Ionization Energies

Recently, a quantum algorithm that is capable of directly calculating the energy gap between two electronic states having different spin quantum numbers without inspecting the total energy of the individual electronic states was proposed. This quantum algorithm guarantees an exponential speedup, like quantum phase estimation (QPE)-based full-CI, with much lower costs. In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates, extending the quantum algorithm to the direct calculation of vertical ionization energies. Numerical quantum circuit simulations for the ionization of light atoms (He, Li, Be, B, C, and N) and small molecules (HF, BF, CF, CO, O₂, NO, CN, F₂, H₂O, and NH₃) revealed that the proposed quantum algorithm affords the vertical ionization energies within 0.1 eV of precision.

Recent advances in chemistry of high-spin nitrenes

Experimental and theoretical studies on aromatic nitrenes bearing from three to six unpaired electrons and having quartet, quintet, sextet or septet ground spin states, published in the last 15 years are analyzed. A comparative analysis of the magnetic properties of high-spin nitrenes and all other known high-spin organic molecules is performed. Promising areas of practical application of high-spin nitrenes as molecular magnets and as qubits and qudits for quantum computations are discussed.

The bibliography includes 214 references.

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

The Heisenberg exchange coupling parameter J (H = -2J S i · S j ) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term j S 2, the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H2 under a covalent bond dissociation, C, O, Si, NH, OH+, CH2, NF, O2, and triple bond dissociated N2 molecule revealed that the BxB can compute the J value within 1 kcal mol-1 of errors with less computational costs than conventional quantum phase estimation-based approaches.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

A probabilistic spin annihilation method for quantum chemical calculations on quantum computers

A probabilistic spin annihilation method based on the quantum phase estimation algorithm is presented for quantum chemical calculations on quantum computers. This approach can eliminate more than one spin component from the spin contaminated wave functions by single operation. Comparison with the spin annihilation operation on classical computers is given.