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We develop an energy calculation algorithm leveraging quantum phase difference estimation (QPDE) scheme and a tensor-network-based unitary compression method in the preparation of superposition states and time-evolution gates. Alongside its efficient implementation, this algorithm reduces depolarization noise affections exponentially. We demonstrated energy gap calculations for one-dimensional Hubbard models on IBM superconducting devices using circuits up to 32-system (plus one-ancilla) qubits, a five-fold increase over previous QPE demonstrations, at the 7242 controlled-Z gate level of standard transpilation, keying a Q-CTRL error suppression module. Additionally, we propose a technique towards molecular executions using spatial orbital localization and index sorting, verified by an eight-qubit butadiene simulation. Since QPDE can handle the same objectives as QPE, our algorithm represents a leap forward in quantum computing on real devices., Comment: 24 pages

Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is employed to obtain the ground state with higher accuracy than QMC alone. We propose an algorithm combining QC-QMC with a hybrid tensor network to extend the applicability of QC-QMC beyond a single quantum device size. In a two-layer quantum-quantum tree tensor, our algorithm for the larger trial wave function can be executed than preparable wave function in a device. Our algorithm is evaluated on the Heisenberg chain model, graphite-based Hubbard model, hydrogen plane model, and MonoArylBiImidazole using full configuration interaction QMC. Our algorithm can achieve energy accuracy (specifically, variance) several orders of magnitude higher than QMC, and the hybrid tensor version of QMC gives the same energy accuracy as QC-QMC when the system is appropriately decomposed. Moreover, we develop a pseudo-Hadamard test technique that enables efficient overlap calculations between a trial wave function and an orthonormal basis state. In a real device experiment by using the technique, we obtained almost the same accuracy as the statevector simulator, indicating the noise robustness of our algorithm. These results suggests that the present approach will pave the way to electronic structure calculation for large systems with high accuracy on current quantum devices., Comment: 32 pages, 24 figures, 3 tables

The ground and excited state calculations at key geometries, such as the Frank-Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol$^{-1}$ even on the ibm_kawasaki device.

A quantum chemistry study of the first singlet (S1) and triplet (T1) excited states of phenylsulfonyl-carbazole compounds, proposed as useful thermally activated delayed fluorescence (TADF) emitters for organic light emitting diode (OLED) applications, was performed with the quantum Equation-Of-Motion Variational Quantum Eigensolver (qEOM-VQE) and Variational Quantum Deflation (VQD) algorithms on quantum simulators and devices. These quantum simulations were performed with double zeta quality basis sets on an active space comprising the highest occupied and lowest unoccupied molecular orbitals (HOMO, LUMO) of the TADF molecules. The differences in energy separations between S1 and T1 ($\Delta E_{st}$) predicted by calculations on quantum simulators were found to be in excellent agreement with experimental data. Differences of 16 and 88 mHa with respect to exact energies were found for excited states by using the qEOM-VQE and VQD algorithms, respectively, to perform simulations on quantum devices without error mitigation. By utilizing error mitigation by state tomography to purify the quantum states and correct energy values, the large errors found for unmitigated results could be improved to differences of, at most, 3 mHa with respect to exact values. Consequently, excellent agreement could be found between values of $\Delta E_{st}$ predicted by quantum simulations and those found in experiments., Comment: 18 pages, 14 figures

Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show herein that the number of qubits required for simulations on a quantum computer can be reduced by limiting the number of orbitals in the active space. Thus, we have utilized ans\"atze that approximate exact classical matrix eigenvalue decomposition methods (Full Configuration Interaction). Such methods are appropriate for computations with the Variational Quantum Eigensolver algorithm to perform computational investigations on the rearrangement of the lithium superoxide dimer with both quantum simulators and quantum devices. These results demonstrate that, even with a limited orbital active space, quantum simulators are capable of obtaining energy values that are similar to the exact ones. However, calculations on quantum hardware underestimate energies even after the application of readout error mitigation.