Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum algorithm for finding the roots of n^th degree polynomials where n is any positive integer. In classical algorithm, the resources required for solving this problem increase drastically when n increases and it would be impossible to practically solve the problem when n is large. It was found that any polynomial can be rearranged into a corresponding companion matrix, whose eigenvalues are roots of the polynomial. This leads to a possibility to perform a quantum algorithm where the number of computational resources increase as a polynomial of n. In this study, we construct a quantum circuit representing the companion matrix and use eigenvalue estimation technique to find roots of polynomial.

Exploiting the atomistic tight-binding theory with the sp-d exchange term, the electronic and magnetic characteristics of CdSe nanoparticles embedded with Mn, Fe and Co are determined as a function of external magnetic fields to realize the sp-d exchange interactions. The transition metal species and applied magnetic fields are powerful factors to manipulate the electronic and magnetic characteristics of doped CdSe nanoparticles. With growing applied fields, the energies of spin splitting, Zeeman splitting and magnetic polaron improve and are assumed to reach saturation at high fields. All g-factor values are boosted in the presence of the external field and then fade with increasing applied fields. The electron spin-splitting energies and electron g values are ordered as Fe:CdSe > Mn:CdSe > Co:CdSe. The single-particle gaps, hole spin-splitting energies, Zeeman splitting energies and hole g values follow the order Co:CdSe > Fe:CdSe > Mn:CdSe.

The generation of pure spin current through thermal gradients, known as the spin Seebeck effect (SSE), has garnered significant interest in spintronics. In this study, we design and construct a permanent magnetic instrument (PMI) setup to generate a variable external magnetic field using NdFeB permanent magnets to observe the SSE. The experimental setup is composed of three crucial components: the magnetic field, the temperature gradient, and electronic control systems. Si/YIG/Pt and Si/Ni samples, prepared via sputtering techniques, were utilized for standard calibration purposes. The results show that the external magnetic field produced by NdFeB varies with the gap distance between the two magnetic poles, following an exponential decrease in field strength with increasing gap distance. The magnetic field at the center can be adjusted from ±20 Oe to ±5,000 Oe. The temperature gradient stabilizes after approximately 10 minutes, with a temperature difference (ΔT) between the heated and cooled sides ranging from 0K to 30K. For instrument testing, we performed magnetic field and angle-dependent measurements on Si/YIG/Pt and Si/Ni samples. The results indicate that the magnetic field dependence of the PMI does not exhibit the voltage loop switching seen with an alternative magnetic coil (AMC) but shows analogous behavior at high magnetic fields. Moreover, the angle dependence of both PMI and AMC yielded comparable results. In conclusion, our PMI setup procedures effectively facilitates the observation of the spin Seebeck effect.

We present an integrated photonic quantum random number generator combining photon-path selection and time-delay encoding methods to efficiently produce high-quality random bits. True random number generators, particularly quantum-based random number generators, play a critical role in secure communications, cryptographic protocols, and simulations, as they provide genuine unpredictability derived from fundamental quantum processes. This study presents the development of an optical random number generator utilizing a photonic chip, resulting in a very stable, compact, and high key-to-signal ratio device. Our setup employs an attenuated pulsed laser source combined with a photonic circuit featuring a multi-mode interference, whose outputs are monitored by single-photon avalanche diodes. For photon-path encoding, a von Neumann extractor effectively reduces output bias by discarding correlated detection events. In addition, we measure photon arrival times (time-delay encoding) using a novel bin-merging and modulo-based encoding strategy to counteract hardware-induced biases, achieving near-ideal bit uniformity. Experimental results show that combining both encoding techniques doubles the bit-generation rate compared to path-encoding only, achieving 0.49 bits per signal while simultaneously meeting stringent randomness criteria validated by passing all tests in the NIST statistical test suite.