Mutually unbiased bases (MUBs) are widely used in quantum information processing and play an important role in quantum cryptography, quantum state tomography and communications. It’s difficult to construct MUBs and remains unknown whether complete MUBs exist for any non prime power. Therefore, researchers have proposed the solution to construct approximately mutually unbiased bases (AMUBs) by weakening the inner product conditions. This paper constructs q AMUBs of ℂq, (q + 1) AMUBs of ℂq-1 and q AMUBs of ℂq-1 by using character sums over Galois rings and finite fields, where q is a power of a prime. The first construction of q AMUBs of ℂq is new which illustrates K AMUBs of ℂK can be achieved. The second and third constructions in this paper include the partial results about AMUBs constructed by W. Wang et al. in [9].

In this paper, we briefly review the concept of superconducting quantum computers and discuss their hardware architecture. We also describe the necessary technologies for the development of a medium-scale quantum computer with more than tens of thousands of quantum bits.

Superconducting nanowire single-photon detector(SNSPD) has been one of the important ingredients for photonic quantum information processing (QIP). In order to see the potential of SNSPDs, I briefly review recent progresses of the photonic QIP with SNSPDs implemented for various purposes and present a possible direction for the development of SNSPDs.

In nanophotonic device operations, characteristic features on a nanometer scale, such as locally excited states, dependence on the excitation number, and spatial symmetry of a system, play an important role. Using these features, selective excitation energy transfer via an optical near field is shown for a quantum-dot system with discrete energy levels. This selectivity strongly depends on a dipole-inactive state of an exciton, which cannot be excited by the far-field light. Operation principles of logic gates, photon storage, and quantum information processing device, which are based on the selectivity, are proposed, and the temporal dynamics are investigated analytically and numerically by using quantum theory. Nanophotonic devices, which are constructed from quantum mechanical and classical dissipative systems, are expected to become one of a key technologies in future device architecture.