To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks.

We investigate the regime of strong coupling of an ensemble of two-dimensional electrons to a single-mode cavity resonator. In particular, we realized such a regime of light-matter interaction by coupling the cyclotron motion of a collection of electrons on the surface of liquid helium to the microwave field in a semi-confocal Fabry-Perot resonator. For the co-rotating component of the microwave field, the strong coupling is pronouncedly manifested by the normal-mode splitting in the spectrum of coupled field-particle motion. We present a complete description of this phenomenon based on classical electrodynamics, as well as show that the full quantum treatment of this problem results in mean-value equations of motion that are equivalent to our classical result. For the counterrotating component of the microwave field, we observe a strong resonance when the microwave frequency is close to both the cyclotron and cavity frequencies. We show that this surprising effect, which is not expected to occur under the rotating-wave approximation, results from the mixing between two polarization components of the microwave field in our cavity. arXiv:1809.06497v2 [cond-mat.mes-hall] 30 Nov 2018

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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 test bed for possible industrial applications. We finally analyze the error scaling of the estimated polarizabilities obtained by the proposed analytical derivative versus the numerical derivative obtained by the finite difference. Numerical calculations suggest that our analytical derivative requires fewer measurements (runs) on quantum computers than the numerical derivative to achieve the same fixed accuracy.