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 dynamical Casimir effect and its detection with Rydberg atoms. The photons are created in a resonant cavity with a plasma mirror of a semiconductor slab which is irradiated by periodic laser pulses. The canonical Hamiltonian is derived for the creation and annihilation operators, showing the explicit time variation in the couplings, which originates from the external configuration such as a nonstationary plasma mirror. The number of created photons is evaluated as squeezing from the Heisenberg equations with the Hamiltonian. Then the detection of the photons as the atomic excitations is examined through the atom-field interaction. Some consideration is made for a feasible experimental realization with a semiconductor plasma mirror.

Optical homodyne detection is examined in view of the joint probability distribution. The usual view is that the relative phase between independent laser fields is localized by photon-number measurements in interference experiments such as homodyne detection. This is why operationally coherent states for laser fields are used in the description of homodyne detection and optical quantum-state tomography. Here, we elucidate these situations by considering the joint probability distribution and the invariance of homodyne detection under the phase transformation of optical fields.

The diffusive propagation of electromagnetic waves in an absorbing random medium is studied and the localization corrections to the diffusion coefficient are calculated. The differences between absorption and inelastic scattering are discussed. Unlike inelastic scattering which introduces a cut-off length into the diffusion coefficient without affecting the total intensity, absorption reduces the intensity but cancels out of the diffusion coefficient. It is predicted that a sharp mobility edge can exist in a sufficiently strongly disordered medium even in the presence of a significant degree of absorption. Novel scaling properties of the transmitted waves at the mobility edge are predicted.

We investigate interference of optical fields by examining the probability distribution of photon detection. The usual description of interference patterns in terms of superposition of classical mean fields with definite phases is elucidated in quantum fashion. Especially, for interference of two independent mixtures of number states with Poissonian or sub-Poissonian statistics, despite lack of intrinsic phases, it is found that the joint probability has a distinct peak manifold in the multidimensional space of the detector outcomes, which is along the trajectory of the mean-field values as the relative phase varies on the unit circle. Then, an interference pattern should mostly appear in each shot of measurement as a point in the peak manifold with a randomly chosen relative phase. On the other hand, for super-Poissonian sources the mean-field description is likely invalidated with rather broad probability distributions.