Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection

We present a general theory of thermoacoustic phenomena in supercritical fluids near the critical point in a one-dimensional cell. We take into account the effects of the heat conduction in the boundary walls and the bulk viscosity near the critical point. We introduce a coefficient $Z(\omega)$ characterizing reflection of sound with frequency $\omega$ at the boundary. As applications, we examine the acoustic eigenmodes in the cell, the response to time-dependent perturbations, sound emission and reflection at the boundary. Resonance and rapid adiabatic changes are noteworthy. In these processes, the role of the thermal diffusion layers is enhanced near the critical point because of the strong critical divergence of the thermal expansion.Comment: 15 pages, 7 figure

Post-Hartree-Fock method in Quantum Chemistry for Quantum Computer

Quantum computational chemistry is a potential application of quantum computers that is expected to effectively solve several quantum-chemistry problems, particularly the electronic structure problem. Quantum computational chemistry can be compared to the conventional computational devices. This review comprehensively investigates the applications and overview of quantum computational chemistry, including a review of the Hartree-Fock method for quantum information scientists. Quantum algorithms, quantum phase estimation, and variational quantum eigensolver, have been applied to the post-Hartree-Fock method.Comment: 31 pages, 6 figure

Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability

We develop a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE), which is a method to calculate eigenenergies of a given molecular Hamiltonian by utilizing near-term quantum computers and classical computers. We show that all quantities required in the algorithm to calculate the derivative can be evaluated on quantum computers as standard quantum expectation values without using any ancillary qubits. We validate our formula by numerical simulations of quantum circuits for computing the polarizability of the water molecule, which is the second-order derivative of the energy with respect to the electric field. Moreover, the polarizabilities and refractive indices of thiophene and furan molecules are calculated as a testbed for possible industrial applications. We finally analyze the error-scaling of the estimated polarizabilities obtained by the proposed analytical derivative versus the numerical one obtained by the finite difference. Numerical calculations suggest that our analytical derivative may require fewer measurements (runs) on quantum computers than the numerical derivative to achieve the same fixed accuracy.Comment: 34 + 4 page

ADAPT-QSCI: Adaptive Construction of Input State for Quantum-Selected Configuration Interaction

We present a quantum-classical hybrid algorithm for calculating the ground state and its energy of the quantum many-body Hamiltonian by proposing an adaptive construction of a quantum state for the quantum-selected configuration interaction (QSCI) method. QSCI allows us to select important electronic configurations in the system to perform CI calculation (subspace diagonalization of the Hamiltonian) by sampling measurement for a proper input quantum state on a quantum computer, but how we prepare a desirable input state has remained a challenge. We propose an adaptive construction of the input state for QSCI in which we run QSCI repeatedly to grow the input state iteratively. We numerically illustrate that our method, dubbed \textit{ADAPT-QSCI}, can yield accurate ground-state energies for small molecules, including a noisy situation for eight qubits where error rates of two-qubit gates and the measurement are both as large as 1\%. ADAPT-QSCI serves as a promising method to take advantage of current noisy quantum devices and pushes forward its application to quantum chemistry.Comment: 14 page

Variational Quantum Simulation for Periodic Materials

We present a quantum-classical hybrid algorithm that simulates electronic structures of periodic systems such as ground states and quasiparticle band structures. By extending the unitary coupled cluster (UCC) theory to describe crystals in arbitrary dimensions, we numerically demonstrate in hydrogen chain that the UCC ansatz implemented on a quantum circuit can be successfully optimized with a small deviation from the exact diagonalization over the entire range of the potential energy curves. Furthermore, with the aid of the quantum subspace expansion method, in which we truncate the Hilbert space within the linear response regime from the ground state, the quasiparticle band structure is computed as charged excited states. Our work establishes a powerful interface between the rapidly developing quantum technology and modern material science.Comment: 6 + 1 pages, 3 + 1 figure

Orbital optimized unitary coupled cluster theory for quantum computer

We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily available. This feature allows the optimization of molecular structures in VQE without solving any additional equations. Furthermore, the method requires smaller active space and shallower quantum circuit than UCC to achieve the same accuracy. We present numerical examples of OO-UCC using quantum simulators, which include the geometry optimization of the water and ammonia molecules using analytical first derivatives of the VQE

A combined quantum-classical method applied to material design: optimization and discovery of photochromic materials for photopharmacology applications

Integration of quantum chemistry simulations, machine learning techniques, and optimization calculations is expected to accelerate material discovery by making large chemical spaces amenable to computational study; a challenging task for classical computers. In this work, we develop a combined quantum-classical computing scheme involving the computational-basis Variational Quantum Deflation (cVQD) method for calculating excited states of a general classical Hamiltonian, such as Ising Hamiltonian. We apply this scheme to the practical use case of generating photochromic diarylethene (DAE) derivatives for photopharmacology applications. Using a data set of 384 DAE derivatives quantum chemistry calculation results, we show that a factorization-machine-based model can construct an Ising Hamiltonian to accurately predict the wavelength of maximum absorbance of the derivatives, $\lambda_{\rm max}$, for a larger set of 4096 DAE derivatives. A 12-qubit cVQD calculation for the constructed Ising Hamiltonian provides the ground and first four excited states corresponding to five DAE candidates possessing large $\lambda_{\rm max}$. On a quantum simulator, results are found to be in excellent agreement with those obtained by an exact eigensolver. Utilizing error suppression and mitigation techniques, cVQD on a real quantum device produces results with accuracy comparable to the ideal calculations on a simulator. Finally, we show that quantum chemistry calculations for the five DAE candidates provides a path to achieving large $\lambda_{\rm max}$ and oscillator strengths by molecular engineering of DAE derivatives. These findings pave the way for future work on applying hybrid quantum-classical approaches to large system optimization and the discovery of novel materials.Comment: 13pages, 9 figure

Semi-dynamical approach to the shock revival in core-collapse supernovae

We develop a new semi-dynamical method to study shock revival by neutrino heating in core- collapse supernovae. Our new approach is an extension of the previous studies that employ spherically symmetric, steady, shocked accretion flows together with the light bulb approximation. The latter has been widely used in the supernova community for the phenomenological investigation of the criteria for successful supernova explosions. In the present approach, on the other hand, we get rid of the steady-state condition and take into account shock wave motions instead. We have in mind the scenario that not the critical luminosity but the critical fluctuation generated by hydrodynamical instabilities such as SASI and neutrino-driven convection in the post-shock region determines the onset of shock revival. After confirming that the new approach indeed captures the dynamics of revived shock wave qualitatively, we then apply the method to various initial conditions and find that there is a critical fluctuation for shock revival, which can be well fit by the following formula: f_crit ~ 0.8 * (M_in/1.4M_sun) * {1- (rsh/10^8cm)}, in which fcrit denotes the critical pressure fluctuation normalized by the unperturbed post-shock value. Min and rsh stand for the mass of the central compact object and the shock radius, respectively. The critical fluctuation decreases with the shock radius, whereas it increases with the mass of the central object. We discuss the possible implications of our results for 3D effects on shock revival, which is currently controversial in the supernova community.Comment: 15 pages, 10 figures, accepted for publication in Ap