Molar heat capacity at constant pressure, C_p (T), is a central thermodynamic quantity in materials science, but it remains difficult to calculate accurately from first principles when anharmonic vibrational effects become important. In this work, rocksalt ZrC is used as a high-temperature benchmark for the Beyond Quasi-Harmonic (BQH) method, a prepared-supercell first-principles approach that extracts anharmonic vibrational energy directly from density-functional-theory energy evaluations. The calculated BQH molar heat capacity is compared with CALPHAD reference values, a fully anharmonic thermodynamic-integration calculation, a calculated C_v (T) curve from the present work, and a quasi-harmonic calculation. The BQH curve gives a substantial improvement beyond C_v (T) and beyond the quasi-harmonic approximation. Because ZrC is electronically conductive, an electronic heat-capacity correction was also estimated from the density of states at the Fermi level and added to the vibrational BQH result. This correction brings the calculated molar heat capacity into close agreement with the fully anharmonic theoretical benchmark through approximately 1200 K. These results show that the BQH method fully captures important anharmonic phonon contributions missing from ordinary quasi-harmonic calculations.
Molar heat capacity at constant pressure, C_p (T), is a central thermodynamic quantity in materials science, but it remains difficult to calculate accurately from first principles when anharmonic vibrational effects become important. In this work, rocksalt ZrC is used as a high-temperature benchmark for the Beyond Quasi-Harmonic (BQH) method, a prepared-supercell first-principles approach that extracts anharmonic vibrational energy directly from density-functional-theory energy evaluations. The calculated BQH molar heat capacity is compared with CALPHAD reference values, a fully anharmonic thermodynamic-integration calculation, a calculated C_v (T) curve from the present work, and a quasi-harmonic calculation. The BQH curve gives a substantial improvement beyond C_v (T) and beyond the quasi-harmonic approximation. Because ZrC is electronically conductive, an electronic heat-capacity correction was also estimated from the density of states at the Fermi level and added to the vibrational BQH result. This correction brings the calculated molar heat capacity into close agreement with the fully anharmonic theoretical benchmark through approximately 1200 K. These results show that the BQH method fully captures important anharmonic phonon contributions missing from ordinary quasi-harmonic calculations.
Abstract Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we investigate the quantum computing of lattice vibrational and thermodynamical properties by applying the variational quantum eigensolver and variational quantum deflation to phonon Hamiltonians derived from first-principles force constants obtained using density functional theory. The mass-weighted dynamical matrix is mapped onto a qubit-encoded Hermitian operator, enabling computation of the full set of acoustic and optical phonon branches of crystalline silicon and graphene using a reduced qubit register and direct benchmarking against classical diagonalization. The quantum-computed phonon spectrum is further used to evaluate vibrational entropy, constant-volume specific heat, and thermal expansion coefficient, reproducing expected low-temperature quantum behavior and the high-temperature Dulong–Petit limit. We further demonstrate that combined error mitigation strategies help recover phonon dispersions and thermodynamic behavior consistent with expected trends on near-term quantum hardware. Although classical phonon methods remain computationally superior, our results establish phonon-based thermodynamics as a stringent and physically transparent benchmark for assessing variational quantum algorithms on near-term quantum devices.
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we investigate the quantum computing of lattice vibrational and thermodynamical properties by applying the variational quantum eigensolver and variational quantum deflation to phonon Hamiltonians derived from first-principles force constants obtained using density functional theory. The mass-weighted dynamical matrix is mapped onto a qubit-encoded Hermitian operator, enabling computation of the full set of acoustic and optical phonon branches of crystalline silicon and graphene using a reduced qubit register and direct benchmarking against classical diagonalization. The quantum-computed phonon spectrum is further used to evaluate vibrational entropy, constant-volume specific heat, and thermal expansion coefficient, reproducing expected low-temperature quantum behavior and the high-temperature Dulong-Petit limit. We further demonstrate that combined error mitigation strategies help recover phonon dispersions and thermodynamic behavior consistent with expected trends on near-term quantum hardware. Although classical phonon methods remain computationally superior, our results establish phonon-based thermodynamics as a stringent and physically transparent benchmark for assessing variational quantum algorithms on near-term quantum devices.
The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even disordered solids. In general, Path Integral Monte Carlo or Path Integral Molecular Dynamics methods are powerful tools to determine stochastically thermodynamic quantities without systematic bias, not relying on perturbative schemes. Addressing transport properties, for instance calculating thermal conductivity from PIMC, however, is substantially more difficult. Although correlation functions of current operators can be determined by PIMC from analytic continuation on the imaginary time axis, Bayesian methods are usually employed for the numerical inversion back to real time response functions. This task not only strongly relies on the accuracy of the PIMC data but also introduces noticeable dependence on the model used for the inversion. Here, we address both difficulties with care. In particular, we first devise improved estimators for current correlations, which substantially reduce the variance of the PIMC data. Next, we provide a neat statistical approach to the inversion problem, blending into a fresh workflow the classical stochastic maximum entropy method together with recent notions borrowed from statistical learning theory. We test our ideas on a single harmonic oscillator and a collection of oscillators with a continuous distribution of frequencies and provide indications of the performance of our method in the case of a particle in a double well potential. This work establishes solid grounds for an unbiased, fully quantum mechanical calculation of transport properties in solids.
Achieving materials-specific predictions for large, realistic molecules and solids with strong electron correlations remains a long-standing challenge in quantum chemistry. This dissertation develops scalable ab initio quantum many-body methods for crystalline materials, demonstrating that rigorous optimization of theoretical approximations and numerical algorithms enables predictive computation even in strongly correlated systems. The work tackles three interconnected challenges, namely describing material-specific properties of strongly correlated superconductors, achieving linear scaling with k-points for large-scale periodic calculations, and establishing reliable methods for electron-phonon interactions. The following chapters address each challenge in turn. Chapter 2 demonstrates that ab initio density matrix embedding theory, combined with symmetry-breaking strategies for superconducting order parameters, reproduces experimental trends in cuprate superconductivity, including pressure and layer effects on transition temperatures. By directly solving the electronic Schrödinger equation from material structures, these calculations capture multi-orbital covalency effects that simplified model Hamiltonians neglect, revealing their essential role in the spin fluctuations driving pairing. This predictive capability establishes a foundation for efficient computational screening of superconducting materials. Extending these calculations to larger k-point meshes and broader phase diagram explorations, however, demands more efficient computational algorithms. To overcome this computational bottleneck, Chapter 3 introduces interpolative separable density fitting framework. This development enables thermodynamic limit calculations with up to 1000 k-points, as validated on diamond, carbon dioxide, nickel monoxide, and cuprate systems. Integration with density matrix embedding theory and local natural orbital methods further yields converged ground-state energies from accurate correlated wavefunction methods such as CCSD(T) for crystalline materials in the thermodynamic limit. With computational efficiency established, the remaining challenge lies in extending the theoretical framework beyond purely electronic degrees of freedom. Chapter 4 addresses this need by establishing exponential ansatz wavefunctions as competitive approaches for electron-phonon systems. Unlike previous treatments based on perturbation theory, systematic benchmarking of coupled cluster theory and variational Lang-Firsov methods on the Holstein model demonstrates, for the first time, that these approaches accurately describe polaron formation across coupling regimes when combined with appropriate reference state optimization. These results provide a foundation for incorporating phonon effects into ab initio studies of superconducting materials. In addition to these methodological advances, GPU acceleration and MPI parallelization enhance computational throughput, enabling efficient large-scale calculations. Together, these developments constitute a computational framework for predictive ab initio quantum many-body calculations in crystalline materials, opening new avenues for understanding and designing strongly correlated quantum materials.
The quantum harmonic oscillator represents the most common fundamental building block to compute thermal properties of virtually any dielectric crystalline material at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even disordered solids. In general, Path Integral Monte Carlo (PIMC) methods provide a powerful numerical tool to stochastically determine thermodynamic quantities without systematic bias, not relying on perturbative schemes. Addressing transport properties, for instance the calculation of thermal conductivity from PIMC, however, has turned out to be substantially more difficult. Although correlation functions of current operators can be determined by PIMC in the form of analytic continuation on the imaginary time axis, Bayesian methods are usually employed for the numerical inversion back to real-time response functions. This task not only relies strongly on the accuracy of the PIMC data, but also introduces noticeable dependence on the underlying model used for the inversion problem. Here, we address both difficulties with great care. In particular, we first devise improved estimators for current correlations which substantially reduce the variance of the PIMC data. Next, we provide a neat statistical approach to the inversion problem, blending into a fresh workflow the classical stochastic maximum entropy method together with more recent notions borrowed from statistical learning theory. We test our ideas on a single harmonic oscillator and a collection of oscillators with a continuous distribution of frequencies, establishing solid grounds for an unbiased, fully quantum mechanical calculation of transport properties in solids.
During the noisy intermediate-scale quantum (NISQ) era, quantum computational approaches refined to overcome the challenge of limited quantum resources are highly valuable. A comprehensive benchmark for a quantum computational approach in this spirit could provide insights toward further improvements. On the other hand, the accuracy of the molecular properties predicted by most of the quantum computations nowadays is still far off (not within chemical accuracy) compared to their corresponding experimental data. In this work, we propose a promising qubit-efficient quantum computational approach and present a comprehensive investigation by benchmarking quantum computation of the harmonic vibrational frequencies of a large set of neutral closed-shell diatomic molecules with results in great agreement with their experimental data. To this end, we construct the accurate Hamiltonian using molecular orbitals, derived from density functional theory to account for the electron correlation and expanded in the Daubechies wavelet basis set to allow an accurate representation in real space grid points, where an optimized compact active space is further selected so that only a reduced small number of qubits is sufficient to yield an accurate result. Typically, calculations achieved with 2 to 12 qubits using our approach would need 20 to 60 qubits using a traditional cc-pVDZ basis set with frozen core approximation to achieve similar accuracy. To justify the approach, we benchmark the performance of the Hamiltonians spanned by the selected molecular orbitals by first transforming the molecular Hamiltonians into qubit Hamiltonians and then using the exact diagonalization method to calculate the results, regarded as the best results achievable by quantum computation to compare to the experimental data. Furthermore, using the variational quantum eigensolver algorithm with the constructed qubit Hamiltonians, we show that the variational quantum circuit with the chemistry-inspired UCCSD ansatz can achieve the same accuracy as the exact diagonalization method except for systems whose Mayer bond order indices are larger than 2. For those systems, we then demonstrate that the heuristic hardware-efficient RealAmplitudes ansatz, even with a substantially shorter circuit depth, can provide a significant improvement over the UCCSD ansatz, verifying that the harmonic vibrational frequencies could be calculated accurately by quantum computation in the NISQ era.